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Groups > sci.physics.relativity > #430648 > unrolled thread

Interstellar Travel and time taken for the trip. (No time dilation for the Earth)

Started bygehan.ameresekere@gmail.com
First post2017-09-01 03:25 -0700
Last post2017-09-07 07:32 -0700
Articles 6 on this page of 86 — 15 participants

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Contents

  Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-01 03:25 -0700
    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Dirk Van de moortel <dirkvandemoortel@hotspam.not> - 2017-09-01 13:23 +0200
    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) "Paul B. Andersen" <relativity@paulba.no> - 2017-09-01 14:15 +0200
      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-01 06:09 -0700
    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) rotchm <rotchm@gmail.com> - 2017-09-01 06:20 -0700
      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-01 07:05 -0700
      Re: Interstellar Travel and time taken for the trip. (No time  dilation for the Earth) The Starmaker <starmaker@ix.netcom.com> - 2017-09-01 12:40 -0700
        Re: Interstellar Travel and time taken for the trip. (No time   dilation for the Earth) The Starmaker <starmaker@ix.netcom.com> - 2017-09-02 12:19 -0700
    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Odd Bodkin <bodkinodd@gmail.com> - 2017-09-01 19:37 +0000
    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-02 03:26 +0200
      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) xxein1x1@gmail.com - 2017-09-02 22:34 -0700
        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) xxein1x1@gmail.com - 2017-09-02 22:48 -0700
        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-03 10:18 +0200
          Energy (was: Interstellar Travel and time taken for the trip. (No time dilation for the Earth)) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-03 15:52 +0200
            Re: Energy (was: Interstellar Travel and time taken for the trip. (No time dilation for the Earth)) Ethel Ocallaghan <unlgclo@awlwaac.ag> - 2017-09-03 13:56 +0000
              The problem of crackpots (was: Energy) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-03 17:32 +0200
      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-03 18:43 -0700
        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-03 18:55 -0700
          Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-03 19:03 -0700
            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 08:22 +0200
              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-04 23:32 -0700
              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 04:11 -0700
                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Gary Harnagel <hitlong@yahoo.com> - 2017-09-05 05:06 -0700
                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-05 05:17 -0700
                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Gary Harnagel <hitlong@yahoo.com> - 2017-09-05 05:26 -0700
                      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Istrátora Metiku <untw@nwpovu.un> - 2017-09-06 12:42 +0000
                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 22:11 -0700
                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 14:33 +0200
                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-06 00:33 +0200
                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 22:48 -0700
                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Istrátora Metiku <untw@nwpovu.un> - 2017-09-06 13:03 +0000
                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 22:46 -0700
                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-06 13:04 +0200
                      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 05:05 -0700
                        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-06 05:25 -0700
                        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-07 02:10 +0200
                          Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 20:40 -0700
                            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-07 13:15 +0200
                              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-07 05:42 -0700
                              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-07 21:56 -0700
                              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-07 21:58 -0700
          Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 07:57 +0200
            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-04 23:19 -0700
              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 03:38 -0700
                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-05 04:52 -0700
                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 22:08 -0700
            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 03:58 -0700
              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 14:22 +0200
            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 14:03 +0200
          Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 08:26 +0200
            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 04:12 -0700
        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-04 06:42 +0200
          Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-04 05:35 -0700
            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-04 21:49 +0200
              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-04 19:35 -0700
                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 07:41 +0200
                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 03:53 -0700
                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-05 14:15 +0200
                      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 22:17 -0700
                        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-06 12:44 +0200
                          Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 05:19 -0700
                            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-06 15:34 +0200
                              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 08:53 -0700
                                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-06 18:02 +0200
                                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 21:02 -0700
                                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-07 11:31 +0200
                                      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Erika Milling <kak@kiilwgil.lc> - 2017-09-07 15:46 +0000
                                      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-07 21:44 -0700
                            Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-06 16:01 +0200
                              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-06 07:11 -0700
                              Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 08:57 -0700
                                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 09:01 -0700
                                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-07 02:25 +0200
                                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 20:49 -0700
                                      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-07 11:42 +0200
                                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-07 01:23 -0700
                                      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-07 02:01 -0700
                                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Odd Bodkin <bodkinodd@gmail.com> - 2017-09-06 12:56 -0500
                                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) mlwozniak@wp.pl - 2017-09-06 12:44 -0700
                                  Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-06 20:36 -0700
                                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-07 12:04 +0200
                                    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Odd Bodkin <bodkinodd@gmail.com> - 2017-09-07 12:14 +0000
                                Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-06 20:12 +0200
    Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) bigal95210@gmail.com - 2017-09-05 15:48 -0700
      Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) gehan.ameresekere@gmail.com - 2017-09-05 22:49 -0700
        Re: Interstellar Travel and time taken for the trip. (No time dilation for the Earth) "Dono," <sa_ge@comcast.net> - 2017-09-07 07:32 -0700

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#431448

FromThomas 'PointedEars' Lahn <PointedEars@web.de>
Date2017-09-07 12:04 +0200
Message-ID<2045122.1UYkAi07OO@PointedEars.de>
In reply to#431420
gehan.ameresekere@gmail.com wrote:

> On Wednesday, September 6, 2017 at 11:26:53 PM UTC+5:30, Odd Bodkin wrote:
>> First of all, the observation is not "based on a calculation". It is a
>> direct measure of angular displacement by watching the azimuth and
>> zenith angles of a star change. The angular displacement is a direct
>> measurement of the bend. There is absolutely zero dependence on any
>> theory for the bend MEASUREMENT.
> 
> Agree, it was a measurement and more accurate measurements made during
> solar eclipses that confirmed the theory.

No, it was just one of the observations:

<https://en.wikipedia.org/wiki/Tests_of_general_relativity#Classical_tests>

>> Secondly, if Einstein had not found his error, somebody else would have.
>> Einstein is not solely responsible for all results in relativity -- far
>> from it. When an idea starts to show some interesting merit, then
>> scientist from all over start to work on the same thing, improving and
>> correcting where necessary.
> 
> If somebody else found the error, they would be famous, not Einstein.

You have no idea what you are talking about.

> It is hard to predict what path science could have taken if its course was
> affected by random events.

It is not, and it was not.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#431459

FromOdd Bodkin <bodkinodd@gmail.com>
Date2017-09-07 12:14 +0000
Message-ID<oord6o$191b$1@gioia.aioe.org>
In reply to#431420
<gehan.ameresekere@gmail.com> wrote:
> On Wednesday, September 6, 2017 at 11:26:53 PM UTC+5:30, Odd Bodkin wrote:
>> 
>> First of all, the observation is not "based on a calculation". It is a 
>> direct measure of angular displacement by watching the azimuth and 
>> zenith angles of a star change. The angular displacement is a direct 
>> measurement of the bend. There is absolutely zero dependence on any 
>> theory for the bend MEASUREMENT.
> 
> Agree, it was a measurement and more accurate measurements made during
> solar eclipses that confirmed the theory.
> 
>> 
>> Secondly, if Einstein had not found his error, somebody else would have. 
>> Einstein is not solely responsible for all results in relativity -- far 
>> from it. When an idea starts to show some interesting merit, then 
>> scientist from all over start to work on the same thing, improving and 
>> correcting where necessary.
>> 
>>> 
> 
> If somebody else found the error, they would be famous, not Einstein. 

Oddly enough this is not so.  The originator often gets credit even if
mistakes get made. 

> It is hard to predict what path science could have taken if its course
> was affected by random events.
> 
> 
> 



-- 
Odd Bodkin -- maker of fine toys, tools, tables

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#431370

FromThomas 'PointedEars' Lahn <PointedEars@web.de>
Date2017-09-06 20:12 +0200
Message-ID<4086702.Rb8q5NZCej@PointedEars.de>
In reply to#431354
gehan.ameresekere@gmail.com wrote:

> On Wednesday, September 6, 2017 at 7:31:29 PM UTC+5:30, Thomas
> 'PointedEars' Lahn wrote:
>> That might be considered cruel by those affected, but is actually good
>> so. Science works by falsification: relentlessly weeding out
>> *inconsistent* ideas and *demonstrably* false models about the world.
> 
> You do realize that if Einstein had not had the time to correct his error
> in predicting the bending of starlight around the sun, if the observation
> had been done earlier, based on the wrong calculation, Einstein would have
> been labeled as a failure and maybe a crackpot?

First of all, to which “wrong calculation” are you referring?  (Einstein 
made several statements that he corrected in later papers, as evidenced by 
the number of occurrences of “Corrections” in 
<http://einsteinpapers.press.princeton.edu/> p.)
 
> Also, the experiment which made world headlines and made Einstein famous

Famous in the general public’s perception due to the “world headlines”.
He had the support of the scientific community long before that *because 
what he said made sense to begin with*.

That is also evidenced by his membership in the Prussian Academy of Sciences 
since 1913, *2 years before* he presented general relativity to that body; 
you just would not get invited into those circles if they would not take you 
and your work seriously.  His papers had been selected for publication in 
the journal of the Academy („Sitzungsberichte“) since 1905 already.

<http://bibliothek.bbaw.de/kataloge/literaturnachweise/einstein/literatur.pdf>

    [The National Geographic Channel series “Genius” tells the story that
     Max von Laue traveled, at the behest of Max Planck, from Berlin to
     Berne in 1906 to visit Einstein in the Swiss Patent Office to offer him
     Planck’s support (whose 1900 idea of quanta Einstein had used in 1905
     to explain the photoelectric effect – the work for which he was awarded
     explicitly the Nobel Prize in Physics 1921).  Von Laue is shown not
     only surprised to find a young man instead of a seasoned fellow, but
     is also presented, to his amazement, by Einstein with yet another
     revolutionary discovery that Einstein has made in the meantime: his
     “afterthought” to SR that “light carries mass”, now known to the
     general public as “E = m c²”.

     <http://channel.nationalgeographic.com/genius/videos/genius-recap-chapter-four/>
 
     At least the town and the time of meeting appears to be historically 
     accurate, as corroborated by von Laue’s official biography at the
     German Historical Museum, Berlin: they did meet in 1906, Einstein (then
     only 27 years old) did live and work in Berne at the time, and von Laue
     was Planck’s assistent from 1905 to 1909:

     <https://www.dhm.de/lemo/biografie/max-laue>

     (However, Einstein’s original notes must have looked different than
      depicted.  For example, Einstein used „V“ for the speed of light
      before “On the Relativity Principle and the Conclusions Drawn from
      It”, 1907, and he did not write that equation – not even using V –
      in the 1905 paper as published [but he used words only].

     <http://einsteinpapers.press.princeton.edu/vol2-doc/347>
     <http://einsteinpapers.press.princeton.edu/vol2-doc/468>)]

> were based on observations that at best were 30% correct?

Cite evidence.

Regardless of possible problems in Eddington’s analysis of the data (this 
claim has been debunked by Kennefick 2007, 2009), the observation was 
repeated later with increasing precision:

  · Lick Observatory, 1922, ibid.;
  · van Biesboeck (Yerkes Observatory), 1953;
  · Texas Mauritanian Eclipse Team (University of Texas), 1973;
  · Titov & Girdiuk (Pulkovo Observatory, St. Petersburg, Russia), 2015;
  · Sahu et al. (STSI/HST) 2017 (gravitational microlensing by distant 
    stars).

*All* of them confirmed general relativity.  *Numerous* *other* experiments 
have confirmed it now; most recently, now *three* confirmed observations of 
gravitational waves (LIGO Scientific Collaboration 2016, 2017).

    [You would have known that if you had done proper research *before* you
     made the claim; that’s one more unofficial point for you on the
     Crackpot Index.  With a starting credit of −5, that’s 6 points for you
     in total.  Congratulations.]

In fact, I am curious about the results of the observations performed in 
that regard during the most recent total solar eclipse (Bruns 2017):

<https://eclipse2017.nasa.gov/testing-general-relativity>

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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#431261

Frombigal95210@gmail.com
Date2017-09-05 15:48 -0700
Message-ID<0999a280-bc4c-4d54-ab7d-525476f92210@googlegroups.com>
In reply to#430648
On Friday, September 1, 2017 at 3:25:36 AM UTC-7, gehan.am...@gmail.com wrote:
> In this recent talk on interstellar travel, Ryan Weed talks about interstellar travel using anti-matter propulsion.
> 
> https://www.youtube.com/watch?v=EBebWBjpWIQ
> 
> http://www.wired.co.uk/article/ryan-weed-wired-2015
> 
> Curiously, he ends with the suggestion that long distance travel would not be so attractive because the traveler will be returning to an Earth that exists far in the future.
> 
> But this cannot be. Imagine a ray of light or a beam of light sent to the moon and back, to a reflector on the moon. The time taken from the sending of the beam to its return will be around 1.3 seconds each way.
> 
> Extend this to light sent to a planet 10 light years away, and it takes 10 years for the outbound trip and 10 years for the return trip, as measured by 'clocks and trees on Earth'.
> 
> Any spacecraft, probe, robot, anything that goes out to that planet at the speed of light and comes back will be back in 20 years time.  If not travelling at the speed of light, it will go out and return in a specific time frame, for example at half the speed of light it will take double the time. 
> 
> Now where is the time dilation in that?

 If you're travelling instantaneously at the speed of light, you will be spread like peanut butter on the floor of the ship after going through an infinite acceleration rate.

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#431293

Fromgehan.ameresekere@gmail.com
Date2017-09-05 22:49 -0700
Message-ID<29337327-98e3-4b67-9042-714c1a126ca3@googlegroups.com>
In reply to#431261
On Wednesday, September 6, 2017 at 4:18:13 AM UTC+5:30, bigal...@gmail.com wrote:

>  If you're travelling instantaneously at the speed of light, you will be spread like peanut butter on the floor of the ship after going through an infinite acceleration rate.

I get the same feeling when arguing with 'reativists' :)

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#431467

From"Dono," <sa_ge@comcast.net>
Date2017-09-07 07:32 -0700
Message-ID<08e31b4e-b013-40e0-bed6-f9e138a5ba7b@googlegroups.com>
In reply to#431293
On Tuesday, September 5, 2017 at 10:49:56 PM UTC-7, gehan.am...@gmail.com wrote:
> On Wednesday, September 6, 2017 at 4:18:13 AM UTC+5:30, bigal...@gmail.com wrote:
> 
> >  If you're travelling instantaneously at the speed of light, you will be spread like peanut butter on the floor of the ship after going through an infinite acceleration rate.
> 
> I get the same feeling when arguing with 'reativists' :)

You can't be "arguing". Arguing implies some amount of knowledge. You are totally ignorant, Gehan. 

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