| Topic: |
Science > Physics |
| User: |
"KMyers1" |
| Date: |
10 Jun 2007 05:32:33 AM |
| Object: |
Faster Than Light? |
Consider the following apparent relativistic paradox:
We have two linear particle accelerators set up facing in opposite
directions with a common target T in between. Accelerator A
accelerates a particle to some significant fraction of light, say .99,
and smashes the particle into the target. Accerator B accelerates
another particle to the same fraction of light and smashes its
particle into the same target but from the opposite direction. Now we
remove the target and allow the particles from Accelerators A and B to
smash into each other directly. Since the particle from accelerator A
is definitely moving at .99c in one direction past target T, and
particle B is definitely moving at .99c in the other direction past
target T, I argue that the particles are moving towards each other at
1.98c, in apparent violation of relativistic concepts.
Now I suppose that someone is probably going to say, that even though
the particles from A and B are moving in opposite directions relative
to the same target, each with a velocity of .99c, that their
velocities relative to each other are not additive, and therefore they
do not exceed the speed of light relative to each other. But that
doesn't seem realistic since target T provides a common reference
point for both particles. Anyway, one could argue about this all day
long in theory, but the real question is: Has anyone ever actually
tried an equivalent experiment? And specifically with entire atoms,
not just photons or electrons?
Yeah I know, this has probably already been considered a million
times, but I wanted to ask anyway, just in case...
Kevin M.
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| User: "Dirk Van de moortel" |
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| Title: Re: Faster Than Light? |
10 Jun 2007 06:56:54 AM |
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"KMyers1" <KMyers1@clearwire.net> wrote in message news:1181471553.234287.34610@p47g2000hsd.googlegroups.com...
Consider the following apparent relativistic paradox:
We have two linear particle accelerators set up facing in opposite
directions with a common target T in between. Accelerator A
accelerates a particle to some significant fraction of light, say .99,
and smashes the particle into the target. Accerator B accelerates
another particle to the same fraction of light and smashes its
particle into the same target but from the opposite direction. Now we
remove the target and allow the particles from Accelerators A and B to
smash into each other directly. Since the particle from accelerator A
is definitely moving at .99c in one direction past target T, and
particle B is definitely moving at .99c in the other direction past
target T, I argue that the particles are moving towards each other at
1.98c, in apparent violation of relativistic concepts.
Now I suppose that someone is probably going to say, that even though
the particles from A and B are moving in opposite directions relative
to the same target, each with a velocity of .99c, that their
velocities relative to each other are not additive, and therefore they
do not exceed the speed of light relative to each other. But that
doesn't seem realistic since target T provides a common reference
point for both particles. Anyway, one could argue about this all day
long in theory, but the real question is: Has anyone ever actually
tried an equivalent experiment? And specifically with entire atoms,
not just photons or electrons?
Yeah I know, this has probably already been considered a million
times, but I wanted to ask anyway, just in case...
As measured in the rest frame of either particle, the speed of
the other particle would be something like 0.99995c.
Everything we know about particle physics is consistent with
that and nothing we know about it is consistent with how you
seem to think nature should behave.
Yeah, I know, this has indeed already been answered a million
times, but I wanted to say it anyway, just in case :-)
[followup to sci.physics.relativity]
Dirk Vdm
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| User: "Uncle Al" |
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| Title: Re: Faster Than Light? |
10 Jun 2007 01:28:06 PM |
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KMyers1 wrote:
Consider the following apparent relativistic paradox:
We have two linear particle accelerators set up facing in opposite
directions with a common target T in between.
Colliding particle accelerators. Given any achievable velocities V1
and V2 and any finite lightspeed (e.g., Lorentz Invariance), the bound
on the relative velocities of V1 and V2 as viewed by any inertial
observer cannot exceed
(V1 + V2)/[1 +(V1)(V2)/c^2]
This is transformation of velocities parallel to the direction of
motion. For velocities at an arbitrary angle theta, Jackson gives
u_parallel = (u'_parallel + v)/(1+(v dot u')/c^2)
u_perp = u'_perp/(gamma_v(1+(v dot u')/c^2))
But that
doesn't seem realistic since target T provides a common reference
point for both particles.
No. There is no privileged inertial observer. Anybody off at an
angle sees what SR tells him he will see.
THE EASY WAY: Were there to be internal inconsistencies in SR
(meaning inconsistencies of a purely mathematical logical nature) that
would automatically lead to contradictions in number theory, itself,
and arithmetic, since the mathematics of Minkowski geometry is
equiconsistent with the theory of real numbers and with arithmetic.
THE HARD WAY: Special Relativity is physics on a topologically
trivial Lorentzian manifold with a metric whose curvature tensor is
zero. This is a perfectly diffeomorphism-invariant condition and does
not require any particular coordinate choice. It is invariant under
the full group of diffeomorphisms. The Poincare group is the group of
*isometries* of the metric in special relativity.
The Special Relativity metric is *non-dynamical* (unlike GR). It
defines the coupling *constants* of your theory. If you change the
metric in any nontrivial way you are changing your theory. An
operation can only be called a "symmetry" of a special-relativistic
(non-gravitational) theory if it preserves the metric, and therefore
the symmetry of special-relativistic theories is the Poincare group
only. General Relativity (gravitation) has a dynamic metric.
Has anyone ever actually
tried an equivalent experiment? And specifically with entire atoms,
not just photons or electrons?
Colliding particle accelerators; Relativistic Heavy Ion Collider on
Long Island, NY. Photons at c, electrons or protons deeply asymptotic
to c, or gold nuclei a 99.999c, what's the difference?
Yeah I know, this has probably already been considered a million
times, but I wanted to ask anyway, just in case...
If you have a brilliant idea that contradicts observation, you are
wrong. If you have a brilliant idea that contradicts theory but *not*
observation, somebody should look.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
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| User: "Ben Rudiak-Gould" |
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| Title: Re: Faster Than Light? |
10 Jun 2007 03:05:17 PM |
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KMyers1 wrote:
Since the particle from accelerator A
is definitely moving at .99c in one direction past target T, and
particle B is definitely moving at .99c in the other direction past
target T, I argue that the particles are moving towards each other at
1.98c, in apparent violation of relativistic concepts.
The so-called closing velocity between the particles is 1.98c. If you look
at Einstein's original paper on relativity, you'll see that he uses a
velocity of the form c+v, where v>0, in a relativistic calculation. That's a
closing velocity. The velocities that can't exceed c are those that
represent the change in an object's position with respect to time. There are
only two objects in your thought experiment, and they have velocities of +/-
0.99c, not 1.98c.
-- Ben
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