The relativistic equation can be converted to one for direct
calculation of relativistic velocity

v = c * sqrt(1 - ((m c^2)/E)^2)


Hi,

To derive a formula for the relativistic velocity of a particle I began
with

E = m(gamma - 1)
= m(1/sqrt(1-v^2/c^2) - 1)

The end result was that
v = c*sqrt(1-(1+E/m)^(-2))

which is not the same as the one that you posted. After some
rearrangements of our equations, an inner term of mine is

1 + E/m

and yours is

1+ E/(mc^2)

I assume the difference between your result and mine is due to units.
In the forumla E = m(gamma - 1), are c=1 units being used? and if so,
how can I convert it to SI units (MKS)?

Thanks for the help!


P.S

I'm not sure why, but for various values of E, my calculator gives
the same result, which is equal to 3x10^8. Might this be due to
precision of my calculator?

Thanks again!

"Max" wrote in message
oups.com...
The relativistic equation can be converted to one for direct
calculation of relativistic velocity

v = c * sqrt(1 - ((m c^2)/E)^2)


Hi,

To derive a formula for the relativistic velocity of a particle I began
with

E = m(gamma - 1)
= m(1/sqrt(1-v^2/c^2) - 1)

The end result was that
v = c*sqrt(1-(1+E/m)^(-2))

which is not the same as the one that you posted. After some
rearrangements of our equations, an inner term of mine is

1 + E/m

and yours is

1+ E/(mc^2)

I assume the difference between your result and mine is due to units.
In the forumla E = m(gamma - 1), are c=1 units being used? and if so,
how can I convert it to SI units (MKS)?

Thanks for the help!


P.S

I'm not sure why, but for various values of E, my calculator gives
the same result, which is equal to 3x10^8. Might this be due to
precision of my calculator?

Thanks again!
Not exactly... it's due to the precision of the operator.
The problem you have is choosing the wrong value for c.
You see, the time for light to go from A to B is equal to the time
it takes to go from B to A.
So, for example, if it takes 1 unit of distance to go from A to B
then it takes -1 unit of distance to go from B to A, right?
So you should have used -1 instead of 1 for c. Everyone knows
-1 = 1, and since time doesn't go backwards... well... 1/1 = 1,
but you should have used c = -1/1 = -1.
Androcles.

I have _no_ idea what you mean!

Max a écrit :
The relativistic equation can be converted to one for direct
calculation of relativistic velocity

v = c * sqrt(1 - ((m c^2)/E)^2)

Hi,

To derive a formula for the relativistic velocity of a particle I began
with

E = m(gamma - 1)

= m(1/sqrt(1-v^2/c^2) - 1)

The end result was that
v = c*sqrt(1-(1+E/m)^(-2))

which is not the same as the one that you posted. After some
rearrangements of our equations, an inner term of mine is

1 + E/m

Maybe it would help if you started with the correct formula for
kinetic energy

E = mc^2(gamma - 1)

But you can derive v from gamma itself if you wish

gamma = 1/sqrt(1-(v^2/c^2))

1/gamma^2 =1-(v^2/c^2)

v^2/c^2 = 1-1/gamma^2

v^2 = c^2 (1-1/gamma^2)

v = c sqrt(1-1/gamma^2)

and since E=gamma mc^2, gamma=E/mc^2

so,

v = c sqrt(1-1/(E/mc^2))

or finally

v = c sqrt(1-(mc^2/E)^2)

and yours is

1+ E/(mc^2)

I think mine was v = c * sqrt(1 - ((m c^2)/E)^2)

I assume the difference between your result and mine is due to units.
In the forumla E = m(gamma - 1), are c=1 units being used?

No. the kinetic energy formula is as I mentionned above, and
the speed of light is not 1, but 2.99792458 E8 m/s

Don't listen to desk corner theoreticians who play with the units.
You will only end up getting mixed up. Stick to MKS values from any
trustable source (NIST for example) for all fundamental values
and you will be ok.

and if so, how can I convert it to SI units (MKS)?

It is in MKS. Energy is in joules mass is in kg, velocity is
in m/s

Thanks for the help!


P.S

I'm not sure why, but for various values of E, my calculator gives
the same result, which is equal to 3x10^8. Might this be due to
precision of my calculator?

Thanks again!

You are welcome.

André Michaud

Max:
I have _no_ idea what you mean!

Consider that a plus. If you ever get the idea that you do know
what he means, it will proably be too late for psychiatry to be of
any help.

Repetitive areshole-up-in-the-air-five-times-a-day "Bilge the Al Qaeda spy
and
dubious islamic ****head" blared in
message
...


[snip crap]
You are still a snipping, arrogant, illiterate, innumerate, illogical,
**** without a scrap of logic in you, you whining little toad.
You don't have an inkling about mathematics or physics
and live in the vain hope some moron will think you are clever,
Mr SmartArse who pretends he understands relativity and
doesn't have a clue how to synchronize his watch to Cassini
time.
Modern physics:
http://www.androcles01.pwp.blueyonde...ynchronize.htm

Hey dumb****! Do you know how to move sideways or up?
http://www.androcles01.pwp.blueyonder.co.uk/how_to3.jpg

tau = (t-vx/c²)/sqrt(1-v²/c²)
tau = (t-uy/c²)/sqrt(1-u²/c²)
tau = (t-wz/c²)/sqrt(1-w²/c²)
xi = (x-vt)/sqrt(1-v²/c²)
eta = (y-ut)/sqrt(1-u²/c²)
zeta= (z-wt)/sqrt(1-w²/c²)

Right or wrong, dumb****?
If one is right they all are, if one is wrong they all are,
pathetic ****head.
For v = 0.866c, u = 0.866c, w = 0.866c the resultant velocity is
sqrt( 3/4 + 3/4 +3/4) = 1.5c
Right or wrong, ****forbrains?

Einstein said
eta = y,
zeta = z
because he did not know how to move sideways or up,
anencephalous cretin.


[quote]
we establish by definition that the "time" required by a crab to travel
from A to B equals the "time" it requires to travel from B to A.
[end quote]
Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein can prove nothing can go faster than a crab.

Oops!... Did I say 'a crab'? Sorry...'light'.


"In agreement with experience we further assume the quantity
2AB/(t'A-tA) = c,
to be a universal constant--the velocity of light in empty space." --
Einstein.

In agreement with experience and without any assumption,
BA = -AB,
2AB = AC,

[AB +BA]/(t'A-tA) = 0
Hence c = 0 in Einstein's math.

Observation:
http://www.britastro.org/vss/gifc/00918-ck.gif
Explanation:
http://www.ebicom.net/~rsf1/sekerin.htm (fig 3)

(Or stars explode twice in three months, which is stupid).

In agreement with experience and without any assumption,
you remain a snipping, arrogant, illiterate, innumerate, illogical,
incompetent **** without a scrap of logic in you,
you whining little toad.
You don't have an inkling about mathematics or physics
and live in the vain hope some moron will think you are clever,
Mr SmartArse who pretends he understands physics and
doesn't have a clue how to synchronize his watch to Cassini
time.
Modern physics:
http://www.androcles01.pwp.blueyonde...ynchronize.htm

**** off, useless tord!


tau = (t-vx/c²)/sqrt(1-v²/c²)
tau = (t-uy/c²)/sqrt(1-u²/c²)
tau = (t-wz/c²)/sqrt(1-w²/c²)
xi = (x-vt)/sqrt(1-v²/c²)
eta = (y-ut)/sqrt(1-u²/c²)
zeta= (z-wt)/sqrt(1-w²/c²)
If one is right they all are, if one is wrong they all are.
Carry three watches or do not move sideways or ride an elevator.

Personally I prefer three witches:
Double double, toil and trouble,
Fire burn and Einstein bubble. --- Pop!
Hexenmeister.

srp wrote:

Maybe it would help if you started with the correct formula for
kinetic energy

E = mc^2(gamma - 1)

But you can derive v from gamma itself if you wish

gamma = 1/sqrt(1-(v^2/c^2))

1/gamma^2 =1-(v^2/c^2)

v^2/c^2 = 1-1/gamma^2

v^2 = c^2 (1-1/gamma^2)

v = c sqrt(1-1/gamma^2)

and since E=gamma mc^2, gamma=E/mc^2

so,

v = c sqrt(1-1/(E/mc^2))

or finally

v = c sqrt(1-(mc^2/E)^2)


Thank you for writing a derivation and explaining, as it helped me
greatly. My ambition is to some day be able to even derive the
equations you used to begin with based on Einstein's theory, but using
basic equations is fine for me now I think.



No. the kinetic energy formula is as I mentionned above, and
the speed of light is not 1, but 2.99792458 E8 m/s

Don't listen to desk corner theoreticians who play with the units.
You will only end up getting mixed up. Stick to MKS values from any
trustable source (NIST for example) for all fundamental values
and you will be ok.


The different units make learning relativity for me more difficult. The
equations are simpler, but I understand less and have to memorize
conversions from c=1 to c=2.99...E8 units. I'll follow your advice
about the units. At the moment I've been learning some general
relativity where they measure mass in length! which is even more
confusing when it comes time to solve actual problems and obtain
numerical answers.

Thank you very much André Michaud! I truly appreciate your help and it
has done me a lot of good.

Max a écrit :
srp wrote:

Maybe it would help if you started with the correct formula for
kinetic energy

E = mc^2(gamma - 1)

But you can derive v from gamma itself if you wish

gamma = 1/sqrt(1-(v^2/c^2))

1/gamma^2 =1-(v^2/c^2)

v^2/c^2 = 1-1/gamma^2

v^2 = c^2 (1-1/gamma^2)

v = c sqrt(1-1/gamma^2)

and since E=gamma mc^2, gamma=E/mc^2

so,

v = c sqrt(1-1/(E/mc^2))

or finally

v = c sqrt(1-(mc^2/E)^2)

Thank you for writing a derivation and explaining, as it helped me
greatly. My ambition is to some day be able to even derive the
equations you used to begin with based on Einstein's theory, but
using basic equations is fine for me now I think.

You are proceeding the right way. But I doubt that you will get
much of anywhere if you base your research on Einstein's theories
(both of them) because both SR and GR are based on velocity
(inertial motion) and not on acceleration, which is the real
cause of the presence of energy, a conclusion easily drawn from
Maxwell.

They are closed and can lead to nothing but themselves.

GR moreover, is based on G, which is a pseudo constant in that
it is made up of variables that have constant values only within
the Solar System system while the particulars of the underlying
third law of Kepler go unnoticed when G is applied to other
circumstances.

Both of these defects explain why no progress has been made built
on these theories since they were popularized.

The real foundation is Maxwell, and through him, Coulomb, Gauss,
Ampere, Biot-Savart. The Lorentz force equation is also valuable.

Of course, Newton is a must at the general mechanics level.

Not meaning that Einstein's theories are worthless. They must
be understood. But they are dead ends.

No. the kinetic energy formula is as I mentionned above, and
the speed of light is not 1, but 2.99792458 E8 m/s

Don't listen to desk corner theoreticians who play with the units.
You will only end up getting mixed up. Stick to MKS values from any
trustable source (NIST for example) for all fundamental values
and you will be ok.

The different units make learning relativity for me more difficult. The
equations are simpler, but I understand less and have to memorize
conversions from c=1 to c=2.99...E8 units.

You'll get used to converting. You will have to.

Just keep in mind that in equations where c is made to equal 1,
it means that the real MKS value of c has been integrated into
one of the other constants or variables of the equation (if the
equation is valid, of course). It is a very constructive exercise
to try to discover where it is hiding. The same for all other
constants set to 1.

I'll follow your advice about the units. At the moment I've been
learning some general relativity where they measure mass in length!
which is even more confusing when it comes time to solve actual
problems and obtain numerical answers.

I agree. Needless hardship. Maybe one day you will be instrumental
in bringing sense back into this mess.

Thank you very much André Michaud! I truly appreciate your help and
it has done me a lot of good.

Good luck.

André Michaud