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Groups > sci.physics.relativity > #452501 > unrolled thread
| Started by | Thomas Heger <ttt_heg@web.de> |
|---|---|
| First post | 2018-03-13 10:06 +0100 |
| Last post | 2018-04-03 06:45 +0200 |
| Articles | 15 on this page of 95 — 16 participants |
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Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-13 10:06 +0100
Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-13 07:15 -0700
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-13 14:36 +0000
Re: Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-13 07:51 -0700
Re: Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-13 08:34 -0700
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-13 09:20 -0700
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-13 16:27 +0000
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-13 16:28 +0000
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-13 09:45 -0700
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-13 18:39 +0100
Re: Units in spacetime Térov Balónky <iytn@yeicenlw.ik> - 2018-03-13 17:49 +0000
Re: Units in spacetime Térov Balónky <iytn@yeicenlw.ik> - 2018-03-13 17:49 +0000
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-14 13:54 +0100
Re: Units in spacetime Térov Balónky <iytn@yeicenlw.ik> - 2018-03-14 16:02 +0000
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-14 21:47 +0100
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-13 18:02 +0000
Re: Units in spacetime Térov Balónky <iytn@yeicenlw.ik> - 2018-03-13 18:12 +0000
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-13 22:00 +0100
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-13 22:55 +0000
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-14 09:19 -0700
Re: Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-14 09:32 -0700
Re: Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-14 09:52 -0700
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-14 18:07 +0000
Re: Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-14 12:03 -0700
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-14 13:18 -0700
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-14 21:38 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-14 16:27 -0700
Re: Units in spacetime Python <python@python.invalid> - 2018-03-15 01:05 +0100
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-15 03:52 +0000
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-14 23:10 -0700
Re: Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-15 00:16 -0700
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-15 11:55 +0000
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-15 14:40 +0100
Re: Units in spacetime Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-15 16:02 +0100
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-15 15:20 +0000
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-15 09:49 -0700
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-15 19:49 +0000
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-15 11:26 +0100
Re: Units in spacetime mlwozniak@wp.pl - 2018-03-15 04:03 -0700
Re: Units in spacetime Keith Stein <keithstein111@gmail.com> - 2018-03-15 15:50 +0000
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-15 21:15 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-15 10:30 -0700
Re: Units in spacetime Python <python@python.invalid> - 2018-03-15 18:32 +0100
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-15 19:51 +0000
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-15 20:56 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-15 23:20 -0700
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-16 10:11 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-18 22:25 -0700
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-19 09:17 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-19 10:36 -0700
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-19 17:57 +0000
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-19 11:16 -0700
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-19 18:43 +0000
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-19 13:02 -0700
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-19 21:24 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-20 09:32 -0700
Re: Units in spacetime Python <python@python.invalid> - 2018-03-20 17:40 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-20 09:55 -0700
Re: Units in spacetime Dirk Van de moortel <dirkvandemoortel@notmail.com> - 2018-03-20 18:25 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-20 14:21 -0700
Re: Units in spacetime Dirk Van de moortel <dirkvandemoortel@notmail.com> - 2018-03-20 22:57 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-20 16:00 -0700
Re: Units in spacetime Darryl Fletcher <lu@ewiwwe.tt> - 2018-03-20 23:38 +0000
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-22 14:01 +0100
Re: Units in spacetime Koobee Wublee <koobee.wublee@gmail.com> - 2018-03-22 13:45 -0700
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-27 20:18 +0200
Re: Units in spacetime xip1415926@gmail.com - 2018-03-27 14:40 -0700
Re: Units in spacetime xip1415926@gmail.com - 2018-03-26 07:38 -0700
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-27 19:53 +0200
Re: Units in spacetime xip1415926@gmail.com - 2018-03-27 12:21 -0700
Re: Units in spacetime Tom Roberts <tjroberts137@sbcglobal.net> - 2018-03-27 16:47 -0400
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-28 09:34 +0200
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-20 21:12 +0100
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-16 10:32 +0100
Re: Units in spacetime "Paul B. Andersen" <relativity@paulba.no> - 2018-03-16 12:33 +0100
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-17 21:29 +0100
Re: Units in spacetime Odd Bodkin <bodkinodd@gmail.com> - 2018-03-14 20:51 +0000
Re: Units in spacetime "David (Kronos Prime) Fuller" <fuller.david@hotmail.com> - 2018-03-20 15:41 -0700
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-15 14:04 +0100
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-15 20:10 +0100
Re: Units in spacetime Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-22 05:57 +0100
Re: Units in spacetime Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-27 19:57 +0200
Re: Units in spacetime numbernumber1964@gmail.com - 2018-03-20 13:49 -0700
Re: Units in spacetime Keith Stein <keithstein111@gmail.com> - 2018-03-21 07:26 +0000
Re: Units in spacetime numbernumber1964@gmail.com - 2018-03-22 15:28 -0700
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-23 09:57 +0100
Re: Units in spacetime xip1415926@gmail.com - 2018-03-25 18:54 -0700
Re: Units in spacetime numbernumber1964@gmail.com - 2018-03-23 10:48 -0700
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-25 19:03 +0200
Re: Units in spacetime xip1415926@gmail.com - 2018-03-26 06:39 -0700
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-03-26 21:43 +0200
Re: Units in spacetime Keith Stein <keithstein111@gmail.com> - 2018-03-30 11:00 +0100
Re: Units in spacetime Will Bos <sllu@wsws.sb> - 2018-03-30 10:52 +0000
Re: Units in spacetime Will Bos <sllu@wsws.sb> - 2018-03-30 11:02 +0000
Re: Units in spacetime Thomas Heger <ttt_heg@web.de> - 2018-04-03 06:45 +0200
Page 5 of 5 — ← Prev page 1 2 3 4 [5]
| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2018-03-22 05:57 +0100 |
| Message-ID | <760853805.0ifERbkFSE@PointedEars.de> |
| In reply to | #452512 |
Odd Bodkin wrote:
> David (Kronos Prime) Fuller <fuller.david@hotmail.com> wrote:
>> ds²= -(cdt)² + dx² + dy² + dz².
>
> You should be careful here. The formulation of the interval above really
> only applies to spacelike intervals.
Nonsense.
Instead, the value of ds² indicates for a given infinitesimal spacetime
interval (dt, dx, dy, dz) whether the interval (i.e. the corresponding
events’ separation) is either
- spacelike (here: ds² > 0),
- lightlike (ds² = 0), or
- timelike (here: ds² < 0).
The metric signature is (−, +, +, +), and the metric tensor is
(−1 0 0 0)
[η]_µν = diag(−1, 1, 1, 1) = ( 0 1 0 0).
( 0 0 1 0)
( 0 0 0 1)
This is most obvious if you calculate ds² for the extremum cases dt > 0
(i.e., temporal separation), and dx = dy = dz = 0 (i.e., no spatial
separation); and for dt = 0 (no temporal separation), and at least one of
dx ≠ 0, dy ≠ 0, or dz ≠ 0 (some spatial separation).
c t ^ timelike lightlike (with e₁)
: e₂ .'
: . .'
: : ds .': e₃
: : .' : spacelike (with e₁)
: : .' :dt
: :'......: .
:.' e₁ dx e₄
'------------------> x
(I am not entirely sure about writing “ds” as the length of the hypothenuse
here as the metric is only *pseudo*-Euclidean, so it is _not_ that ds² = dt²
+ dx². CMIIW.)
> For timelike intervals, the interval
> is written as
> ds²= (cdt)² - dx² - dy² - dz².
Nonsense.
This is simply the same (Minkowski) metric, but with different signature
(+, −, −, −), so the metric tensor is
( 1 0 0 0)
[η]_µν = diag(1, −1, −1, −1) = ( 0 −1 0 0)
( 0 0 −1 0)
( 0 0 0 −1)
instead.
With this signature, instead:
- spacelike: ds² < 0
- lightlike: ds² = 0
- timelike: ds² > 0
(the arithmetic inverse of the above)
Which, again, you can easily see for the extremal cases dt > 0,
dx = dy = dz = 0; and dt = 0, and at least one of dx ≠ 0, dy ≠ 0, or dz ≠ 0.
If that helps to understand it, assume
∆s² = −(c ∆t)² + ∆x² + ∆y² + ∆z²
= −c² ∆t² + ∆x² + ∆y² + ∆z²
instead, i.e. all events are connected by straight lines in a (flat)
spacetime diagram. Then for given events (corresponding to the diagram
above)
e₁ = (1, 1, 0, 0) = (t₁, x₁, y₁, z₁)
e₂ = (2, 1, 0, 0) = (…)
e₃ = (2, 1 + c, 0, 0) = (…)
e₄ = (1, 5, 0, 0) = (…)
[In time interval ∆t light has traveled from spatial coordinate x₁ = 1
exactly c ∆t units of length, and ∆t = 1 here. So x₃ = x₁ + c ∆t
= 1 + c × 1 = 1 + c.]
we find, for example
∆s²(e₁, e₂) = −c² (t₂ − t₁)² + (x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²
= −c² (2 − 1)² + 0 + 0 + 0
= −c²
< 0 → timelike ∎
∆s²(e₁, e₃) = −c² (t₃ − t₁)² + (x₃ − x₁)² + (y₃ − y₁)² + (z₃ − z₁)²
= −c² (2 − 1)² + (1 + c − 1)² + 0 + 0
= −c² + c²
= 0 → lightlike ∎
∆s²(e₁, e₄) = −c² (t₄ − t₁)² + (x₄ − x₁)² + (y₄ − y₁)² + (z₄ − z₁)²
= −c² (1 − 1)² + (5 − 1)² + 0 + 0
= 0 + 16
= 16
> 0 → spacelike ∎
which was probably intuitively obvious in the case of (e₁, e₂), and (e₁,
e₄), and not as obvious with (e₁, e₃) (without a spacetime diagram); but now
we have *mathematical* *proof* which is *a lot* better than intuition.
PointedEars
--
Q: What did the nuclear physicist order for lunch?
A: Fission chips.
(from: WolframAlpha)
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| From | Thomas 'PointedEars' Lahn <PointedEars@web.de> |
|---|---|
| Date | 2018-03-27 19:57 +0200 |
| Message-ID | <11994181.uLZWGnKmhe@PointedEars.de> |
| In reply to | #453478 |
Thomas 'PointedEars' Lahn wrote: > c t ^ timelike lightlike (with e₁) > : e₂ .' > : . .' > : : ds .': e₃ > : : .' : spacelike (with e₁) > : : .' :dt > : :'......: . > :.' e₁ dx e₄ > '------------------> x > > (I am not entirely sure about writing “ds” as the length of the > hypothenuse here as the metric is only *pseudo*-Euclidean, so it is _not_ > that ds² = dt² > + dx². CMIIW.) However, I am sure that, because I have labeled the axis “c t”, so time is given in units of c, I must label one cathetus “c dt” accordingly, instead. PointedEars -- «Nec fasces, nec opes, sola artis sceptra perennant.» (“Neither high office nor power, only the scepters of science survive.”) —Tycho Brahe, astronomer (1546-1601), inscription at Hven
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| From | numbernumber1964@gmail.com |
|---|---|
| Date | 2018-03-20 13:49 -0700 |
| Message-ID | <9640faaa-34a9-40fc-97c4-b35f8b47a7c5@googlegroups.com> |
| In reply to | #452501 |
Units of time is t (s, min. hr...etc) and the units of space (x,y,z) would be m, ft, cm, ly ....etc.
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| From | Keith Stein <keithstein111@gmail.com> |
|---|---|
| Date | 2018-03-21 07:26 +0000 |
| Message-ID | <BOnsC.289789$K43.179624@fx31.am4> |
| In reply to | #453352 |
On 20/03/2018 20:49, numbernumber1964@gmail.com wrote: > Units of time is t (s, min. hr...etc) and the units of space (x,y,z) would be m, ft, cm, ly ....etc. Just so numbernumber. I understand that. But i still don't understand what a meter-second, a foot-minute, a centimeter-hour, or a ly-year is. If there is anyone out there who does know, please don't tell me, sometimes IGNORANCE IS BLISS eh! keith stein
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| From | numbernumber1964@gmail.com |
|---|---|
| Date | 2018-03-22 15:28 -0700 |
| Message-ID | <286e82ea-d8f4-4a4c-bea4-7456cec41dbf@googlegroups.com> |
| In reply to | #452501 |
How could this be so difficult the unit of space time are units of the length (m, cm, ft....etc) and time (sec. minuite....etc.)...
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| From | Thomas Heger <ttt_heg@web.de> |
|---|---|
| Date | 2018-03-23 09:57 +0100 |
| Message-ID | <fhjtr0F4180U1@mid.individual.net> |
| In reply to | #453524 |
Am 22.03.2018 um 23:28 schrieb numbernumber1964@gmail.com: > How could this be so difficult the unit of space time are units of the length (m, cm, ft....etc) and time (sec. minuite....etc.)... > It is not the question of difficulty. The question is, which kind of units are appropriate and why. The units of length and time are not really fitting, since 'length' is referring to a subset called 'space'. I tried to show, that complex numbers (actually: complex four vectors) would fit. (Such number are also called 'bi-quaternions'.) The relation between complex numbers and spacetime is visible in the similarities between an Argand diagram and a Minkowski diagram. But we need to rearrange things a bit. E.g. the observer is 'self-centred' and time local. Then time is measured by an arbitrary observer (for instance: humans on planet Earth), which measure their own local time. They actually perform kind of imaginary motion along the timeline. The term 'spacelike' is then used for 'parallel flight' of other observers along other timelines, but on the same hyperplane of the present. The distance to such spots cannot be measured in meters, since 'length' is already used for something else. It is used for distance in space and the term 'space' is used for our universe. This universe has a time-component and further away means also longer ago. The distances to spots in that universe is measured in light-years. And a small fraction of a light-year is called 'meter', which therefore shares this time-dependent concept with the light-year. But how do you measure distances over the hyperplane of the present? (Certainly not in meters) TH
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| From | xip1415926@gmail.com |
|---|---|
| Date | 2018-03-25 18:54 -0700 |
| Message-ID | <a0399b7a-eb40-4bf5-a419-20690db549d7@googlegroups.com> |
| In reply to | #453549 |
On Friday, March 23, 2018 at 4:57:08 AM UTC-4, Thomas Heger wrote: > The question is, which kind of units are appropriate and why. In 1920 Appendix-1 ( Bartleby.com ): Einstein has collinear axes X and X′. Axis X′ is in motion relative to axis X at speed v. g = gamma Quote: Two points on axis X′ which are separated by a distance x′ = 1 when measured on axis X′ are thus separated in our snapshot by the distance: Δx = 1/g. Unquote. “Distance x′ = 1” spans 1 unit on moving axis X′. A snapshot of this unit is taken from stationary axis X. The camera is fast enough to freeze the action and faithfully reproduce moving unit distance so it can be evaluated on stationary X. Unit distance so discovered on X′ is found on axis X to have size 1/g, which size is X unit size of 1 reduced by the factor 1/g. You cannot write an equation and Einstein doesn’t. Wrong: Δx = 1/g · x On the right hand side, x = 1, and on the left hand side Δx is less than 1. You cannot write x < x. Wrong: x′ = 1/g · x If x′ and x are sizes of units, the equation renders the phenomenon of unit length, but each x has value 1, ie x′ = 1 and x = 1, and the equation is invalid.
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| From | numbernumber1964@gmail.com |
|---|---|
| Date | 2018-03-23 10:48 -0700 |
| Message-ID | <4e5a9f0e-3cbe-4fb0-9fb9-bea5cf99929f@googlegroups.com> |
| In reply to | #452501 |
The question is, which kind of .units are appropriate and why. The units of length and time are not really fitting, since 'length' is referring to a subset called .'space'. ____________________________________ Your brains must be really fried, like an ol meth addict. I've been arguing with complete idiots "units of length and time are not fitting" HA HA AH HA HA>>>>>>>>>>>almost time to take your idiot pill.
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| From | Thomas Heger <ttt_heg@web.de> |
|---|---|
| Date | 2018-03-25 19:03 +0200 |
| Message-ID | <fhq33dFfveeU1@mid.individual.net> |
| In reply to | #453588 |
Am 23.03.2018 um 18:48 schrieb numbernumber1964@gmail.com: > > The question is, which kind of .units are appropriate and why. > > The units of length and time are not really fitting, since 'length' is > referring to a subset called .'space'. > > ____________________________________ > > > > Your brains must be really fried, like an ol meth addict. I've been arguing with complete idiots "units of length and time are not fitting" HA HA AH HA HA>>>>>>>>>>>almost time to take your idiot pill. > > 'Space' and 'time' are concepts to describe experiences we have in everyday life. Spacetime is not an everyday experience. But we can try to estimate, how that might look like. Only problem: we cannot see spacetime, only assume something similar would exist. And we are limited to a certain observation point (vicinity of planet Earth) and cannot move around the universe like 'Starship Enterprise'. To illustrate the problem, lets use an example: imagine, that everything we could see from the world is the picture in a microscope. You can observe everything, but magnified by - say - a factor of 100. Now you come to a large build (say the Eiffel Tower) and want to find out, how that might look like. You peep through the microscope and wander, what the **** you are observing. We could guess and try to compare our guesses with what we can see. If the picture somehow match our ideas, we are happy, otherwise not. So we need to make assumptions about how our very tiny fragment of the real world would extend into the larger realms. There we must not extend our own concepts into the large scale, but need to find something possible in the large scale, which would look like our observations on the small scale. IOW: space and time (as we know them) are a subset of something larger, which has other main features (that we do not know, but want to find out). TH
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| From | xip1415926@gmail.com |
|---|---|
| Date | 2018-03-26 06:39 -0700 |
| Message-ID | <2cd6e7c0-2e1b-4860-b094-787f1223a69d@googlegroups.com> |
| In reply to | #453820 |
On Sunday, March 25, 2018 at 1:03:45 PM UTC-4, Thomas Heger wrote: > > The question is, which kind of units are appropriate and why. ++++ In 1920 Appendix-1 ( Bartleby.com ): Einstein has collinear axes X and X′. Axis X′ is in motion relative to axis X at speed v. g = gamma Quote: “Two points on axis X′ which are separated by a distance x′ = 1 when measured on axis X′ are thus separated in our snapshot by the distance: Δx = 1/g.” Unquote. “Distance x′ = 1” spans one unit on moving axis X′. A snapshot of this unit is taken from stationary axis X. The camera is fast enough to freeze the action and faithfully render moving unit “x′ = 1” to the viewer on stationary X. Unit distance so discovered by the camera is found by the viewer on axis X to have size x = ( 1/g ) · 1 or Δx = ( 1/g ) · 1 in terms of X-units. It is not an equation. You cannot write an equation and Einstein doesn’t. Einstein writes: “Δx = 1/g.” An equation has a dependent variable on the left hand side and an independent variable on the right hand side. No such independent variable appears. Einstein’s expression is just a right-to-left assignment operator such as you have in a programming language. An attempt might be: Δx′ = 1/g · Δx, so that now you have variables on each side. It doesn’t work. The deltas are mixed messages. On the r.h.s Δx is a unit of length on X which is Δx = 1. On the l.h.s we must have a similar understanding of delta, and that is a unit of length on X′ which is Δx′ = 1. The equation is then: 1 = 1/g · 1, obviously wrong. The confusion boils down to Δx′, an item which Einstein declines to use. Is it value of a unit of length, Δx′ = 1, or is it the phenomenon of a unit of length, Δx′ = 1/g ?? Ambiguities of this sort plague the entire Special Theory.
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| From | Thomas Heger <ttt_heg@web.de> |
|---|---|
| Date | 2018-03-26 21:43 +0200 |
| Message-ID | <fht0q8F5phhU1@mid.individual.net> |
| In reply to | #453884 |
Am 26.03.2018 um 15:39 schrieb xip1415926@gmail.com: > On Sunday, March 25, 2018 at 1:03:45 PM UTC-4, Thomas Heger wrote: > >>> The question is, which kind of units are appropriate and why. > > ++++ > > In 1920 Appendix-1 ( Bartleby.com ): Einstein has collinear axes X and X′. Axis X′ is in motion relative to axis X at speed v. > > g = gamma > > Quote: > > “Two points on axis X′ which are separated by a distance x′ = 1 when measured on axis X′ are thus separated in our snapshot by the distance: Δx = 1/g.” > > Unquote. > > “Distance x′ = 1” spans one unit on moving axis X′. A snapshot of this unit is taken from stationary axis X. The camera is fast enough to freeze the action and faithfully render moving unit “x′ = 1” to the viewer on stationary X. Unit distance so discovered by the camera is found by the viewer on axis X to have size x = ( 1/g ) · 1 or Δx = ( 1/g ) · 1 in terms of X-units. > > It is not an equation. You cannot write an equation and Einstein doesn’t. > > Einstein writes: “Δx = 1/g.” An equation has a dependent variable on the left hand side and an independent variable on the right hand side. No such independent variable appears. Einstein’s expression is just a right-to-left assignment operator such as you have in a programming language. > > An attempt might be: Δx′ = 1/g · Δx, so that now you have variables on each side. It doesn’t work. The deltas are mixed messages. On the r.h.s Δx is a unit of length on X which is Δx = 1. On the l.h.s we must have a similar understanding of delta, and that is a unit of length on X′ which is Δx′ = 1. The equation is then: 1 = 1/g · 1, obviously wrong. > > The confusion boils down to Δx′, an item which Einstein declines to use. Is it value of a unit of length, Δx′ = 1, or is it the phenomenon of a unit of length, Δx′ = 1/g ?? > > Ambiguities of this sort plague the entire Special Theory. > I do agree, but usually do not refer to Einstein or SRT, but to a slightly different version of relativity by Herman Minkowski. Einstein discusses the question of parallel movement with different velocities. But 'parallel movement with different velocities' does not sound like what nature usually does. To overcome such a restriction I prefer a different setup: - time is a local phenomenon and measured by the observer - the observer stays constantly at rest in his own FoR - the observer defines the term 'space' with distances to himself - this 'space' is actually his own past light-cone. - this 'space' and what is visible there is what he calls 'universe' - any observer is of equal rights, hence has his own personal 'universe' The change in velocity is actually a curvature of the worldline (of the observer). Since he is at rest (by definition), he enters a different 'time domain' through acceleration. So: timelines are specific and not necessarily in parallel. They could also have an angle. We could actually see such anomalies. E.g. the so called 'Pioneer anomaly' could be explained as 'curvature of the axis of time' (of the Pioneer craft), because the probe was accelerated (e.g. by a rocket and several planets). TH
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| From | Keith Stein <keithstein111@gmail.com> |
|---|---|
| Date | 2018-03-30 11:00 +0100 |
| Message-ID | <kVnvC.293978$a15.34903@fx22.am4> |
| In reply to | #452501 |
On 13/03/2018 09:06, Thomas Heger wrote: > since a sphere in spacetime has a volume with units of an action. > > > > TH Whereas a cube in spacetime has a volume with units of ?
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| From | Will Bos <sllu@wsws.sb> |
|---|---|
| Date | 2018-03-30 10:52 +0000 |
| Message-ID | <p9l4t9$1022$2@gioia.aioe.org> |
| In reply to | #454273 |
Keith Stein wrote: > On 13/03/2018 09:06, Thomas Heger wrote: >> since a sphere in spacetime has a volume with units of an action. TH > > Whereas a cube in spacetime has a volume with units of ? six, that's a tensor.
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| From | Will Bos <sllu@wsws.sb> |
|---|---|
| Date | 2018-03-30 11:02 +0000 |
| Message-ID | <p9l5fr$1022$5@gioia.aioe.org> |
| In reply to | #454275 |
Will Bos wrote: > Keith Stein wrote: > >> On 13/03/2018 09:06, Thomas Heger wrote: >>> since a sphere in spacetime has a volume with units of an action. TH >> >> Whereas a cube in spacetime has a volume with units of ? > > six, that's a tensor. actually seven, since that's a spacetime.
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| From | Thomas Heger <ttt_heg@web.de> |
|---|---|
| Date | 2018-04-03 06:45 +0200 |
| Message-ID | <figf6iFfvr8U1@mid.individual.net> |
| In reply to | #454273 |
Am 30.03.2018 um 12:00 schrieb Keith Stein: > On 13/03/2018 09:06, Thomas Heger wrote: >> since a sphere in spacetime has a volume with units of an action. >> >> >> >> TH > > Whereas a cube in spacetime has a volume with units of ? The term 'cube' refers to euclidean space and a certain geometric figure. I try to show, that our space is actually a subset of something more complex, which could be perceived as space by an arbitrary observer. So the superset of space + time must be spacetime, which has intrinsic properties, that look like space+ time as seen from within. I assume something similar to 'quaternion field', but with a different construct called 'bi-quaternions' or 'complex four vectors'. This something (termed 'spacetime') is estimated and a model searched, which is kind of possible for nature. These biquaternions fit very well, in my opinion. The description of the idea is in my 'book' (actually a google.doc presentation) and can be found here: https://docs.google.com/present/view?id=dd8jz2tx_3gfzvqgd6 TH
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