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Albertito
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 Posted: Wed Jul 16, 2008 2:21 pm Post subject: Re: Relativistic Dynamics |
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On Jul 13, 5:39 am, Dono <sa...@comcast.net> wrote:
| Quote: |
Sinnce m_0 *d^2x/dt^2=k (constant) is Galilei invariant but not
Lorentz invariant, we have to redefine the impulse in SR as p=
\gamma(v)*m_0*v
We can prove that in the proper frame of the object F :
d(\gamma(v)*v)/dt=\gamma(v)^3*dv/dt
We can also prove (after some computations) that , in a frame F'
moving with constant speed V wrt the frame F:
d(\gamma(v')*v')/dt'=\gamma(v')^3*dv'/dt'
We can further prove that
\gamma(v')^3*dv'/dt'=\gamma(v)^3*dv/dt=k/m_0
This means that by redefining the relativistic impulse as
\gamma(v)*m_0*v , the equations of motion under constant force (F=k)
are Lorentz invariant. So far, so good.
I need some help with the situation when F is NOT constant.
Here are several examples:
1. F= - q*x (common spring)
2. F= -q *sin(theta) (common pendulum)
3. An even nastier case is the case of the torsion pendulum where we
need the relativistic equivalent for the Newtonian p=I*d(theta)/dt
where I is the momentum of inertia . It is not obvious what that
formula would be.
In these particular cases, the fact that the left term of the equation
is invariant (\gamma(v')^3*dv'/dt'=\gamma(v)^3*dv/dt) is of no good,
since the right term is obviously not Lorentz invariant since neither
x, nor theta are Lorentz invariants.
Of course, Hooke law and the pendulum law are laws derived
empirically, so the obvious approach would be to redefine them in
such a fashion that they become Lorentz invariant. Did you see any
literature on this?
|
Dear Dono,
That only proves that SR is wrong. Rather than
defining the impulse as relativistic
p = \gamma(v)*m_0*v,
you should define it as hyperbolic,
p = sinh(v/c)*m_0*c,
then
dp/dt = cosh(v/c)*m_0*dv/dt,
It is very easily to prove (after some computations)
that, in a frame F' moving with constant speed V wrt
the frame F:
dp'/dt' = cosh(v'/c)*m_0*dv'/dt',
such that
dp'/dt' = dp/dt = k, constant force (F=k),
thus
cosh(v'/c)*dv'/dt' = cosh(v/c)*dv/dt = k/m_0,
is invariant.
Now, you can deal with any situation when F is NOT constant,
because you always will attain the same acceleration,
a = F/m_0,
in any frame. Needless to say for this to be true,
it must be dt' = dt.
Regards |
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Eric Gisse
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| Posted: Wed Jul 16, 2008 2:30 pm Post subject: Re: Relativistic Dynamics |
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On Jul 16, 6:21 am, Albertito <albertito1...@gmail.com> wrote:
[snip crank stupidity]
Stop blathering about how everything should be substituted for sinh/
cosh/whatever. IT DOES NOT WORK. Special relativity is verified for v/
c ~ 1, where your inane little additions would be obviously true if
they had mereit. They aren't and they don't, so give it a rest. |
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Albertito
Guest
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| Posted: Wed Jul 16, 2008 2:58 pm Post subject: Re: Relativistic Dynamics |
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On Jul 16, 3:30 pm, Eric Gisse <jowr...@gmail.com> wrote:
| Quote: |
On Jul 16, 6:21 am, Albertito <albertito1...@gmail.com> wrote:
[snip crank stupidity]
Stop blathering about how everything should be substituted for sinh/
cosh/whatever. IT DOES NOT WORK. Special relativity is verified for v/
c ~ 1, where your inane little additions would be obviously true if
they had mereit. They aren't and they don't, so give it a rest.
|
IT WORKS.
If Special Relativity has been verified for
v/c ~ 1, then so my model has, because of
p = sinh(v/c)*m_0*c
and
p = gamma(v)*m_0*v
are indistinguishable until the third-order
term of v/c. Ok, fucking stupid?
The difference with earlier posts is that I
already know how to derive my model from first
principles.
Regards, you nitwit. |
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Dono
Guest
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| Posted: Wed Jul 16, 2008 3:03 pm Post subject: Re: Relativistic Dynamics |
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On Jul 16, 7:21 am, AlbertShito <albertito1...@gmail.com> wrote:
| Quote: |
Now, you can deal with any situation when F is NOT constant,
because you always will attain the same acceleration,
a = F/m_0,
in any frame. Needless to say for this to be true,
it must be dt' = dt.
|
Bzzt, no.
Back with your head in the toilet. |
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Albertito
Guest
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| Posted: Wed Jul 16, 2008 3:32 pm Post subject: Re: Relativistic Dynamics |
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On Jul 16, 3:30 pm, Eric Gisse <jowr...@gmail.com> wrote:
| Quote: |
On Jul 16, 6:21 am, Albertito <albertito1...@gmail.com> wrote:
[snip crank stupidity]
Stop blathering about how everything should be substituted for sinh/
cosh/whatever. IT DOES NOT WORK. Special relativity is verified for v/
c ~ 1, where your inane little additions would be obviously true if
they had mereit. They aren't and they don't, so give it a rest.
|
Do you need this USENET group as a pulpit from
which to read relativist Gospel lessons and deliver
sermons? If so, you are not that good as relativist
priest, you need to read more of your Einsteinian Bible.
Tom Roberts, for example, can preach better than you.
Fortunately, you can do it better than Dono. I would
say that Tom Roberts is a genuine priest, you're just
a sacristan, and Dono a simple acolyte  |
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Eric Gisse
Guest
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| Posted: Wed Jul 16, 2008 3:58 pm Post subject: Re: Relativistic Dynamics |
|
|
On Jul 16, 6:58 am, Albertito <albertito1...@gmail.com> wrote:
| Quote: |
On Jul 16, 3:30 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Jul 16, 6:21 am, Albertito <albertito1...@gmail.com> wrote:
[snip crank stupidity]
Stop blathering about how everything should be substituted for sinh/
cosh/whatever. IT DOES NOT WORK. Special relativity is verified for v/
c ~ 1, where your inane little additions would be obviously true if
they had mereit. They aren't and they don't, so give it a rest.
IT WORKS.
|
How do you know?
| Quote: |
If Special Relativity has been verified for
v/c ~ 1, then so my model has, because of
p = sinh(v/c)*m_0*c
and
p = gamma(v)*m_0*v
are indistinguishable until the third-order
term of v/c. Ok, fucking stupid?
|
No.
c = 1, v = 0.95:
sinh(v) = 1.13
1/sqrt[1-v^2] = 3.2
You FORGET that gamma diverges as v/c --> 1. Your model is a failure.
Next time you try to model a new "theory" based on matching special
relativity in Taylor expansions, try computing something once in
awhile and think about the behavior of the function.
| Quote: |
The difference with earlier posts is that I
already know how to derive my model from first
principles.
|
Its' a crap model that massively diverges from observation. Who cares
if you can derive it from first principles or not?
| Quote: |
Regards, you nitwit. |
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Albertito
Guest
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| Posted: Wed Jul 16, 2008 4:58 pm Post subject: Re: Relativistic Dynamics |
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|
On Jul 16, 4:58 pm, Eric Gisse <jowr...@gmail.com> wrote:
| Quote: |
On Jul 16, 6:58 am, Albertito <albertito1...@gmail.com> wrote:
On Jul 16, 3:30 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Jul 16, 6:21 am, Albertito <albertito1...@gmail.com> wrote:
[snip crank stupidity]
Stop blathering about how everything should be substituted for sinh/
cosh/whatever. IT DOES NOT WORK. Special relativity is verified for v/
c ~ 1, where your inane little additions would be obviously true if
they had mereit. They aren't and they don't, so give it a rest.
IT WORKS.
How do you know?
If Special Relativity has been verified for
v/c ~ 1, then so my model has, because of
p = sinh(v/c)*m_0*c
and
p = gamma(v)*m_0*v
are indistinguishable until the third-order
term of v/c. Ok, fucking stupid?
No.
c = 1, v = 0.95:
sinh(v) = 1.13
1/sqrt[1-v^2] = 3.2
You FORGET that gamma diverges as v/c --> 1. Your model is a failure.
Next time you try to model a new "theory" based on matching special
relativity in Taylor expansions, try computing something once in
awhile and think about the behavior of the function.
The difference with earlier posts is that I
already know how to derive my model from first
principles.
Its' a crap model that massively diverges from observation. Who cares
if you can derive it from first principles or not?
Regards, you nitwit.
|
You do not even know how to evaluate simple
functions, fuckhead!
In order to test how much both functions
diverge, you must consider this way
c = 1, v = 0.95:
sinh(v/c)*c = 1.09948,
and
v/sqrt[1-v^2] = 3.04243,
(multiply v/sqrt[1-v^2] by v, ok?)
I can't remember any experimental test
where the beta tested were v/c = 0.95 or
even slightly lower. You should be aware
that the respective Taylor expansions are
sinh(v/c)*c = v(1+v^2/6c^2 + v^4/120c^4 +... )
v/sqrt[1-v^2] = v(1+v^2/2c^2 + 3v^4/8c^4 + ... )
Are you claiming that it can be experimentally
discriminated v^2/6c^2 from v^2/2c^2, for a beta
v/c = 0.85? The discrepancy is small
(v^2/6c^2): v^2/2c^2) = 1/3 ,
in that second-order term. What about the error
bars, eh? Don't lie me more, troll!
Perform an estimation of error bars on both
functions if you can,
c = 1, v = 0.95 ± dv,
m_0 = 1,
(we can even leave this mass m_0 without uncertainty,
for simplicity's sake)
p1 = sinh(v/c)*m_0*c
p2 = m_0*v/sqrt[1 - v^2/c^2].
It is elementary calculus, don't panic, you
only have to differentiate the above functions.
After that estimation of error bars, you will
be able to see how those error bars make
p1 and p2 experimentally indistinguishable.
Next time, try to be a little more rigorous in your
replies and computations, I'm not that stupid as you
think I am. |
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Eric Gisse
Guest
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| Posted: Wed Jul 16, 2008 9:08 pm Post subject: Re: Relativistic Dynamics |
|
|
On Jul 16, 8:58 am, Albertito <albertito1...@gmail.com> wrote:
| Quote: |
On Jul 16, 4:58 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Jul 16, 6:58 am, Albertito <albertito1...@gmail.com> wrote:
On Jul 16, 3:30 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Jul 16, 6:21 am, Albertito <albertito1...@gmail.com> wrote:
[snip crank stupidity]
Stop blathering about how everything should be substituted for sinh/
cosh/whatever. IT DOES NOT WORK. Special relativity is verified for v/
c ~ 1, where your inane little additions would be obviously true if
they had mereit. They aren't and they don't, so give it a rest.
IT WORKS.
How do you know?
If Special Relativity has been verified for
v/c ~ 1, then so my model has, because of
p = sinh(v/c)*m_0*c
and
p = gamma(v)*m_0*v
are indistinguishable until the third-order
term of v/c. Ok, fucking stupid?
No.
c = 1, v = 0.95:
sinh(v) = 1.13
1/sqrt[1-v^2] = 3.2
You FORGET that gamma diverges as v/c --> 1. Your model is a failure.
Next time you try to model a new "theory" based on matching special
relativity in Taylor expansions, try computing something once in
awhile and think about the behavior of the function.
The difference with earlier posts is that I
already know how to derive my model from first
principles.
Its' a crap model that massively diverges from observation. Who cares
if you can derive it from first principles or not?
Regards, you nitwit.
You do not even know how to evaluate simple
functions, fuckhead!
In order to test how much both functions
diverge, you must consider this way
c = 1, v = 0.95:
sinh(v/c)*c = 1.09948,
and
v/sqrt[1-v^2] = 3.04243,
(multiply v/sqrt[1-v^2] by v, ok?)
|
Yea my bad, didn't notice the v. Reading is, as always, fundamental.
Doesn't change my conclusions, however.
| Quote: |
I can't remember any experimental test
|
You haven't looked - that's why. Calculate the velocity of the protons
in the Tevatron - protons have a mass of 938 MeV, and they have a
kinetic energy of 1 TeV. Kinetic energy is mc^2 [gamma - 1]. If you
don't get an answer close to 1, you are doing it wrong.
| Quote: |
where the beta tested were v/c = 0.95 or
even slightly lower. You should be aware
that the respective Taylor expansions are
|
GodDAMN you love your shiny Taylor expansion so fucking much you don't
understand the limitations of the series.
| Quote: |
sinh(v/c)*c = v(1+v^2/6c^2 + v^4/120c^4 +... )
v/sqrt[1-v^2] = v(1+v^2/2c^2 + 3v^4/8c^4 + ... )
Are you claiming that it can be experimentally
discriminated v^2/6c^2 from v^2/2c^2, for a beta
v/c = 0.85? The discrepancy is small
|
Keeping 3 terms of a divergent series and claiming equivalence to high
order is stupid. Plot the functions on the domain v (= [0,1) and
you'll SEE what I'm talking about. Or babble some more about Taylor
expansions and completely refuse to calculate a number - whichever.
| Quote: |
(v^2/6c^2):v^2/2c^2) = 1/3 ,
in that second-order term. What about the error
bars, eh? Don't lie me more, troll!
|
Divergent series, persistent idiot.
lim v--->c sinh(v/c) ---> 1
lim v--->c v/sqrt[1-v^2/c^2] ---> \infty.
Go ahead. Plug in a value for v into the _actual functions_, not your
truncated series.
[...]
| Quote: |
Next time, try to be a little more rigorous in your
replies and computations, I'm not that stupid as you
think I am.
|
I think you are a person of limited mental ability who has found a new
toy when he finally got around to learning first or maybe second
semester calculus. I'm not impressed - I know first semester calculus
too, and so do most educated people in here.
Your angle is obvious - you hate relativity and you'll do whatever it
takes to supplant it. Doesn't matter if the new model is any
combination of wrong, stupid, nonsensical, or silly - just as long as
it isn't relativity. You seem to think that just because you can match
a few terms in a Taylor expansion you have a valid competitor to
relativity - which is WRONG. Not only are you wrong on matching the
series' but you are completely missing the point about what makes
relativity so important in modern physics. |
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Dono
Guest
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| Posted: Wed Jul 16, 2008 9:51 pm Post subject: Re: Relativistic Dynamics |
|
|
On Jul 16, 9:58 am, AlbertShito <albertito1...@gmail.com> wrote:
| Quote: |
You should be aware
that the respective Taylor expansions are
sinh(v/c)*c = v(1+v^2/6c^2 + v^4/120c^4 +... )
v/sqrt[1-v^2] = v(1+v^2/2c^2 + 3v^4/8c^4 + ... )
|
Albertshito,
The above Taylor expansions are valid ONLY for v/c<<1. Pick up a
calculus book, Albertshito.
What happens when you get higher speeds?
This is what happens when you play too much with your dick when you
are 16: you grow up dumb like Juanshito |
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Albertito
Guest
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| Posted: Thu Jul 17, 2008 8:56 am Post subject: Re: Relativistic Dynamics |
|
|
On Jul 16, 10:08 pm, Eric Gisse <jowr...@gmail.com> wrote:
| Quote: |
On Jul 16, 8:58 am, Albertito <albertito1...@gmail.com> wrote:
On Jul 16, 4:58 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Jul 16, 6:58 am, Albertito <albertito1...@gmail.com> wrote:
On Jul 16, 3:30 pm, Eric Gisse <jowr...@gmail.com> wrote:
On Jul 16, 6:21 am, Albertito <albertito1...@gmail.com> wrote:
[snip crank stupidity]
Stop blathering about how everything should be substituted for sinh/
cosh/whatever. IT DOES NOT WORK. Special relativity is verified for v/
c ~ 1, where your inane little additions would be obviously true if
they had mereit. They aren't and they don't, so give it a rest.
IT WORKS.
How do you know?
If Special Relativity has been verified for
v/c ~ 1, then so my model has, because of
p = sinh(v/c)*m_0*c
and
p = gamma(v)*m_0*v
are indistinguishable until the third-order
term of v/c. Ok, fucking stupid?
No.
c = 1, v = 0.95:
sinh(v) = 1.13
1/sqrt[1-v^2] = 3.2
You FORGET that gamma diverges as v/c --> 1. Your model is a failure.
Next time you try to model a new "theory" based on matching special
relativity in Taylor expansions, try computing something once in
awhile and think about the behavior of the function.
The difference with earlier posts is that I
already know how to derive my model from first
principles.
Its' a crap model that massively diverges from observation. Who cares
if you can derive it from first principles or not?
Regards, you nitwit.
You do not even know how to evaluate simple
functions, fuckhead!
In order to test how much both functions
diverge, you must consider this way
c = 1, v = 0.95:
sinh(v/c)*c = 1.09948,
and
v/sqrt[1-v^2] = 3.04243,
(multiply v/sqrt[1-v^2] by v, ok?)
Yea my bad, didn't notice the v. Reading is, as always, fundamental.
Doesn't change my conclusions, however.
|
That's correct, you never read, you never learn from your
mistakes. You have to learn to be a little more modest.
| Quote: |
I can't remember any experimental test
You haven't looked - that's why. Calculate the velocity of the protons
in the Tevatron - protons have a mass of 938 MeV, and they have a
kinetic energy of 1 TeV. Kinetic energy is mc^2 [gamma - 1]. If you
don't get an answer close to 1, you are doing it wrong.
|
Let's see. In my model, Kinetic energy is
T = mc^2 [cosh(v/c) - 1],
thus
v = c arccosh((T/mc^2) + 1) = 7.66585 c.
I got an answer v/c = 7.66585, close to 1,
I'm doing it right, because of
Under SR the domain for v/c is [0,1], and
under my model the domain for v/c is [0, oo].
| Quote: |
where the beta tested were v/c = 0.95 or
even slightly lower. You should be aware
that the respective Taylor expansions are
GodDAMN you love your shiny Taylor expansion so fucking much you don't
understand the limitations of the series.
sinh(v/c)*c = v(1+v^2/6c^2 + v^4/120c^4 +... )
v/sqrt[1-v^2] = v(1+v^2/2c^2 + 3v^4/8c^4 + ... )
Are you claiming that it can be experimentally
discriminated v^2/6c^2 from v^2/2c^2, for a beta
v/c = 0.85? The discrepancy is small
Keeping 3 terms of a divergent series and claiming equivalence to high
order is stupid. Plot the functions on the domain v (= [0,1) and
you'll SEE what I'm talking about. Or babble some more about Taylor
expansions and completely refuse to calculate a number - whichever.
|
Under SR the domain for v/c is [0,1],
under my model the domain for v/c is [0, oo]
| Quote: |
(v^2/6c^2):v^2/2c^2) = 1/3 ,
in that second-order term. What about the error
bars, eh? Don't lie me more, troll!
Divergent series, persistent idiot.
|
v/sqrt[1-v^2] diverges for v ---> c, so its associated
error bar also diverges. Do you know what does it mean,
persistent idiot?
| Quote: |
lim v--->c sinh(v/c) ---> 1
lim v--->c v/sqrt[1-v^2/c^2] ---> \infty.
|
Wrong. In my model the limit is,
lim v---> oo sinh(v/c) ---> oo
| Quote: |
Go ahead. Plug in a value for v into the _actual functions_, not your
truncated series.
|
Go above.
| Quote: |
[...]
Next time, try to be a little more rigorous in your
replies and computations, I'm not that stupid as you
think I am.
I think you are a person of limited mental ability who has found a new
toy when he finally got around to learning first or maybe second
semester calculus. I'm not impressed - I know first semester calculus
too, and so do most educated people in here.
|
Human beings are all of limited mental ability, but your lack of
modesty does not make you better than me.
| Quote: |
Your angle is obvious - you hate relativity and you'll do whatever it
takes to supplant it. Doesn't matter if the new model is any
combination of wrong, stupid, nonsensical, or silly - just as long as
it isn't relativity. You seem to think that just because you can match
a few terms in a Taylor expansion you have a valid competitor to
relativity - which is WRONG. Not only are you wrong on matching the
series' but you are completely missing the point about what makes
relativity so important in modern physics.
|
I do not hate relativity, I hate dogmas. I'm not competing
against SR. Suppose SR was not invented, and there were only
Galilean relativity, then my approach would be the same.
Relativity has been important in modern physics, but science
needs to advance. The domain of applicability of SR has become
pretty narrow for that necessary advance.
Regards |
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Albertito
Guest
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| Posted: Thu Jul 17, 2008 9:16 am Post subject: Re: Relativistic Dynamics |
|
|
On Jul 16, 10:51 pm, Dono <sa...@comcast.net> wrote:
| Quote: |
On Jul 16, 9:58 am, AlbertShito <albertito1...@gmail.com> wrote:
You should be aware
that the respective Taylor expansions are
sinh(v/c)*c = v(1+v^2/6c^2 + v^4/120c^4 +... )
v/sqrt[1-v^2] = v(1+v^2/2c^2 + 3v^4/8c^4 + ... )
Albertshito,
The above Taylor expansions are valid ONLY for v/c<<1. Pick up a
calculus book, Albertshito.
What happens when you get higher speeds?
This is what happens when you play too much with your dick when you
are 16: you grow up dumb like Juanshito
|
I would summarize it by means of a metaphor,
"SR pretends to capture the infinity and
enclose it into a bottle with a top called
invariant c."
Are you also enclosed into that bottle,
little troll Dono-KarandaShito? |
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Eric Gisse
Guest
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| Posted: Thu Jul 17, 2008 9:16 am Post subject: Re: Relativistic Dynamics |
|
|
Albertito wrote:
[snip]
| Quote: |
under my model the domain for v/c is [0, oo]
|
Another strike against your crappy model. No superluminal speeds have
ever been observed under any circumstances.
Your results from momentum significantly diverge from SR at v ~ c.
It'd be noticed in accelerators if your thoughts had any merit. Go
ahead though - whine more about a series expansion. I laugh as you
match to low order when you are expanding near a singularity in the
function.
[snip] |
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Albertito
Guest
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| Posted: Thu Jul 17, 2008 9:58 am Post subject: Re: Relativistic Dynamics |
|
|
On Jul 17, 10:16 am, Eric Gisse <jowr...@gmail.com> wrote:
| Quote: |
Albertito wrote:
[snip]
under my model the domain for v/c is [0, oo]
Another strike against your crappy model. No superluminal speeds have
ever been observed under any circumstances.
|
Yes, correct. No superluminal speeds have ever been observed.
Do you know why? Because you can't use light to measure
superluminal motion, it is that simple. It is like to use
sonar echoes to measure the speed of supersonic objects,
they would never be observed travelling faster than the
speed of sound.
| Quote: |
Your results from momentum significantly diverge from SR at v ~ c.
It'd be noticed in accelerators if your thoughts had any merit. Go
ahead though - whine more about a series expansion. I laugh as you
match to low order when you are expanding near a singularity in the
function.
|
The reason why it had not been noticed in accelerators is
very simple. The energy-momentum relation
E^2 = (mc^2) + (pc)^2
is generically the same under SR and under my model.
Under SR you have momentum
p = m*v*gamma, and kinetic energy
T = mc^2 [gamma - 1]
This yields total energy
E = mc^2 + T = mc^2*gamma.
Under my model you have momentum
p = m*c*sinh(v/c), and kinetic energy
T = mc^2 [cosh(v/c) - 1]
This yields total energy
E = mc^2 + T = mc^2*cosh(v/c).
SR constrains arbitrarily the domain of v within [0, c],
so there is no way to elucidate whether a particle is
actually travelling at superluminal speed.
Since total energy E and c are the same in both models,
we have
cosh(v/c) = gamma(v')
where v can be superluminal, but v' can't.
Regards |
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Eric Gisse
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| Posted: Thu Jul 17, 2008 10:35 am Post subject: Re: Relativistic Dynamics |
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On Jul 17, 1:58 am, Albertito <albertito1...@gmail.com> wrote:
| Quote: |
On Jul 17, 10:16 am, Eric Gisse <jowr...@gmail.com> wrote:
Albertito wrote:
[snip]
under my model the domain for v/c is [0, oo]
Another strike against your crappy model. No superluminal speeds have
ever been observed under any circumstances.
Yes, correct. No superluminal speeds have ever been observed.
Do you know why? Because you can't use light to measure
superluminal motion, it is that simple. It is like to use
sonar echoes to measure the speed of supersonic objects,
they would never be observed travelling faster than the
speed of sound.
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Light is not sound.
For example: the speed of sound is not the same in all inertial
frames.
| Quote: |
Your results from momentum significantly diverge from SR at v ~ c.
It'd be noticed in accelerators if your thoughts had any merit. Go
ahead though - whine more about a series expansion. I laugh as you
match to low order when you are expanding near a singularity in the
function.
The reason why it had not been noticed in accelerators is
very simple. The energy-momentum relation
E^2 = (mc^2) + (pc)^2
is generically the same under SR and under my model.
Under SR you have momentum
p = m*v*gamma, and kinetic energy
T = mc^2 [gamma - 1]
This yields total energy
E = mc^2 + T = mc^2*gamma.
Under my model you have momentum
p = m*c*sinh(v/c), and kinetic energy
T = mc^2 [cosh(v/c) - 1]
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Then your model - is again - crap. This is not "generically the same".
I have already shown you that your expression for momentum is
radically different from SR's, so radically different that it would
have been noticed in the 1930's cyclotron experiments.
If the relativistic expression for momentum was wrong, particle
accelerators would not work.
| Quote: |
This yields total energy
E = mc^2 + T = mc^2*cosh(v/c).
SR constrains arbitrarily the domain of v within [0, c],
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It isn't arbitrary. Its' a consequence of the manifold.
| Quote: |
so there is no way to elucidate whether a particle is
actually travelling at superluminal speed.
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Yea, there is: MEASURE ITS' VELOCITY.
| Quote: |
Since total energy E and c are the same in both models,
we have
cosh(v/c) = gamma(v')
where v can be superluminal, but v' can't.
Regards |
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Eric Gisse
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| Posted: Thu Jul 17, 2008 10:38 am Post subject: Re: Relativistic Dynamics |
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On Jul 17, 1:16 am, Albertito <albertito1...@gmail.com> wrote:
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On Jul 16, 10:51 pm, Dono <sa...@comcast.net> wrote:
On Jul 16, 9:58 am, AlbertShito <albertito1...@gmail.com> wrote:
You should be aware
that the respective Taylor expansions are
sinh(v/c)*c = v(1+v^2/6c^2 + v^4/120c^4 +... )
v/sqrt[1-v^2] = v(1+v^2/2c^2 + 3v^4/8c^4 + ... )
Albertshito,
The above Taylor expansions are valid ONLY for v/c<<1. Pick up a
calculus book, Albertshito.
What happens when you get higher speeds?
This is what happens when you play too much with your dick when you
are 16: you grow up dumb like Juanshito :-)
I would summarize it by means of a metaphor,
"SR pretends to capture the infinity and
enclose it into a bottle with a top called
invariant c."
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-1, epic fail.
Special relativity does not work that way. SR is not a remapping of
[0,\infty) to [0,c).
| Quote: |
Are you also enclosed into that bottle,
little troll Dono-KarandaShito? |
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