[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: starship-design: re: so you want to go faster than light . . .

In a message dated 7/22/00 3:58:44 PM Pacific Daylight Time, 
clmanges@worldnet.att.net writes:

> Gentlemen,
>  If I may quote further from the same book, but _previous_ to the quote I 
> sent
>  last . . .
>  the last equation numbered (43) is: E=m/(sqrt (1-q ^2)). This is followed 
> the
>  statement:
>         "We recognize, in fact, that these components of momentum agree 
> those
>  of classical mechanics for velocities which are small compared to that of 
> light.
>  For large velocities the momentum increases more rapidly than linearly 
> the
>  velocity, so as to become infinite on approaching the velocity of light.
>          "If we apply the last of equations (43) to a material particle at 
> rest
>  (q=0), we see that the energy, E(o), of a body at rest is equal to its 
> Had
>  we chosen the second as our unit of time, we would have obtained
>  (44)            E(o) = mc^2
>          "Mass and energy are therefore essentially alike; they are only 
> different
>  expressions for the same thing. The mass of a body is not a constant; it 
> varies
>  with changes in its energy. We see from the last of equations (43) that E 
> becomes
>  infinite when q approaches 1, the velocity of light."
>  I note here the term "approaching", and I hope it isn't a misfortune of
>  translation. I admit, again, that I don't much comprehend this stuff, but 
> the
>  material I'm quoting should certainly be considered reputable, and looks 
> me to
>  support the commonly held view that, the faster you go, the harder it 
> becomes to
>  go a little faster.

Curious, Was your edition the following or a later translation as Einstein 
did write with a heavy german accent. It does not sound like the Einstein 
works I have read including his correspondence with Burtrend Russel. 

 Einstein, Albert.: THE MEANING OF RELATIVITY. ; Princeton, Princeton U. P., 
1945 (2nd ed.). 135 pp. First printing of this edition. 83561 Science   
Offered for sale by Q.M. Dabney & Co., Inc. at US$25.00


>  Now I'm perplexed. With the present exception of Dr. Jackson (to whom I 
> apologize
>  for calling "Johnson" in my last post), I really didn't expect any 
> on
>  this from this group.
>  Awaiting further enlightenment,

Apology accepted, I am informal so do not require people address me as 
Doctor; However I am much pleased when they do. I have been called much worse 

-Enlightning you as requested-
In the above equation E=m/(sqrt (1-q ^2) as q appraoches one, the amount of 
1-q^2  approaches zero, The square root of zero is + 0 or - 0. M/+-0 is 
undefined and not infinity. Appraching infinity is a valid exptression 
matematically; measured in the real world of physics as a asomtote at c on a 
x,y graph the rapidly rising portion of the graphed exponential curve never 
meets c and at values near c run parrell without touching the asomtope. As a 
real world value of graphs with a top limit  and not a math expression. 
Clarifying- an x,y graph is the horizontal and vertical bisects of a large 
square top and sides of graph (normally not shown). Infinity is not on any 
valid graph, nor is 1/0 defined as infinity.

I could not tell where your words start and the book quote ended.
If indeed Einstein stated as you say or correctly quoted, he was speaking (he 
did not write but dictated most of his works) in an ungarded fashion and the 
editors did not catch the error. 

In his personal written equations he commonly wrote in the paper or 
blackboard margin Energy relativitic and velocity relativistic while he went 
through a chain of calculations using only E and V for ease having previously 
defined his meaning. Later transcribers of his work would see a disconected 
margin note or blackboard note like Erel. Vrel. and not connect it with 
defining the equation variable used. In the set of equations for partical 
rest mass he was considering the Energy relativistic limiting velocity of a 
partical from a partical accelerator which is c. He was not considering the 
energy at that time for a rocket delivering the energy real from a different 
frame of reference.

>  Curtis