| Topic: |
Science > Physics |
| User: |
"Patti" |
| Date: |
14 Jul 2005 09:40:04 PM |
| Object: |
E=mc^2, Inertia, Pair Production, why? |
In 1905, Einstein wrote a paper called "Does the Inertia
of a Body Depend on Its Energy Content?". The idea is
summarized as:
1. the old definition of work (W=Fd), combined with
2. the new fact, nothing can go faster than the speed
of light expressed by F=(ma)/[(1-v2/c2)^3/2]
3. the work goes into making the body heavier. Therefore
4. work adds to the inertia of a body and by implication
inertia has energy and to make it concrete
5. the relationship between energy and inertia is
E=mc^2
6. but remember... nobody really knows what inertia
is - or why objects have it in the first place
This was in 1905.
Particle accelerators began operating decades later.
From E=mc^2, M=E/c^2. This means if you can give enough
energy (photons + electric field for example). You
can literally create matter out of pure energy.
Isn't it odd how Einstein formula could have predicted
it. This shows Einstein must be a super genius and one
of a kind.
But what does inertia.. which has a lot to do with the
equation of E=W+mc^2 (where work is zero) relate to
pair production and actual precipitations of particles??
Albert argues that as you give an object more and more
energy, instead of going faster and faster it gets
heavier and heavier. So if you gave a rocket
1 x 10^1000 foot pounds of thrust, it would stil be
going less than the speed of light. So Einstein
thought that if work goes into giving the body more
inertia.. then inertia must contain energy. What
Albert is saying is that even if work = zero. If you
don't put in any work at all, then the electron still
has an energy equal to e=mc^2
Decades later, Particle Accelerators have been
precipitating particles out of pure energy. My
question is.. What is Inertia relationship to the
energy inherent in matter?? How could Einstein equation
produced in 1905 foresee all of the accelerator
results?
Einstein is such a genius I can't understand how
some of you plan to outsmart him and reworking all
his equations.
Patti
.
|
|
| User: "" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
15 Jul 2005 12:38:35 AM |
|
|
Patti wrote:
6. but remember... nobody really knows what inertia
is - or why objects have it in the first place
Indeed, but this is also true of almost everything else in physics:
nobody really knows what energy is, or what a particle is. However, we
can still take measurements of quantities that we can observe, even if
we don't know what they really are. We can then *define* quantities in
terms of their (mathematical) relationships to each other and to
observables. You don't need to know what inertia "really is" in order
to perform calculations involving it. What's important is that those
calculations will result in predictions of things that can be observed.
The mathematical model may be no more than a metaphor for what reality
really is, but it can still mirror its workings. If its results
parallel what happens in the real world then we call it a good theory.
If it deviates then we go back to the drawing board. Einstein's genius
was to accept that light *really does* travel at the same speed for all
observers (instead of trying to find a mechanism to explain it away),
and then to examine the implications thereof without prejudice. One of
those implications was the result e=mc^2.
Decades later, Particle Accelerators have been
precipitating particles out of pure energy. My
question is.. What is Inertia relationship to the
energy inherent in matter?? How could Einstein equation
produced in 1905 foresee all of the accelerator
results?
The annoying but true answer is because it's a good theory. Think of it
this way: if you're going to construct a physical theory that is to be
accurate, it must account for everything that has been observed up till
now. It must not contradict past observations. You must tie all your
variables together in such a way that they mimic the *currently* known
behaviour of the universe. By 1905, Newton's laws were failing in that
respect because of this speed of light business. Special relativity
took account of it (ignoring gravity for the moment).
Now, it seems unlikely that there will be very many mathematically
inequivalent ways of doing this. So if it works correctly for what's
gone before then the chances are fair that it will correctly predict
things that haven't been thought of yet, simply because there can only
be so many different ways of putting it together. e *must* be equal to
mc^2 if the rest of the theory is to work properly.
--
Mike.
.
|
|
|
| User: "Ian Parker" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
15 Jul 2005 03:00:24 AM |
|
|
Mass and Weight are proprtional for one simple reason. A mass
accelerates in a gravitational field because space is curved. Gravity
is simply d(2).../dt(2)
If space is curved it follows that every mass in free fall will follow
a geodesic curve. This curve MUST be the same foor every mass.
.
|
|
|
| User: "" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
15 Jul 2005 03:57:00 AM |
|
|
Ian Parker wrote:
Mass and Weight are proprtional for one simple reason. A mass
accelerates in a gravitational field because space is curved. Gravity
is simply d(2).../dt(2)
If space is curved it follows that every mass in free fall will follow
a geodesic curve. This curve MUST be the same foor every mass.
Well, yes, because this is how GR works. But I rather think you missed
the thrust of the OP's question (which concerned SR and the equivalence
of mass and energy): OP was expressing wonderment that a paper written
way back in 1905 could play such a pivotal role in predicting the
results of experiments that were all but inconceivable at the time of
writing.
My answer (badly expressed, I admit) was that it wasn't the case that
Einstein had some miraculous vision of mass and energy, but rather that
he doggedly followed his postulates to their conclusion; and, moreover,
that there cannot be very many different sets of (reasonably simple)
postulates from which one can derive an SR-like theory that is
consistent with 1905 data. Einstein chose a simple set, and out popped
e=mc^2.
--
Mike.
.
|
|
|
|
|
|
| User: "" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
16 Jul 2005 01:37:59 PM |
|
|
Patti wrote:
In 1905, Einstein wrote a paper called "Does the Inertia
of a Body Depend on Its Energy Content?".
This was in 1905.
The general relationship
P^2 - 2MH + z H^2 = 0
M = m + zH
(H = kinetic energy, m = rest mass,
M = total mass, P = momentum)
comes out of the study of the properties of the
Galilei/Poincare'/Euclidean symmetry group, and could have been
inferred any time from the late 19th century onward (particularly since
symmetry groups were the running theme around that time in geometry).
Applying Hamilton's equation (dH/dP = V) gives you the velocity:
2P - 2MV - 2zH^2 + 2zH^2 = 0
or P = MV, V = P/M.
For Galilei, z = 0, and you get
P^2 = 2mH, M = m
which yields the kinetic energy H = P^2/2m and, thus,
P = mv, H = 1/2 mv^2.
For the Euclidean group z < 0, or the Poincare' group, you could define
the total energy E = M/z, and write down
E = H + m/z
E^2 = P^2/z + (m/z)^2;
and you get (in all 3 cases, including Galilei)
M = m/sqrt(1 - zv^2)
P = mv/sqrt(1 - zv^2)
H = mv^2/(1 + sqrt(1-zv^2))
and for Euclid and Poincare'
E = M/z = m/(z sqrt(1-zv^2))
For Euclid (z < -1/K^2), this would yield
E = H - mK^2
E^2 + (PK)^2 = (mK^2)^2,
the rest energy being -mK^2, in terms of the rest mass m, the total
energy decreasing with increasing momentum.
For Poincare' (z = 1/c^2 > 0), this would yield
E = H + mc^2
E^2 - (Pc)^2 = (mc^2)^2,
with the rest energy being mc^2, the total energy going up with
increasing momentum.
.
|
|
|
|
| User: "" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
15 Jul 2005 04:55:51 AM |
|
|
Patti wrote:
In 1905, Einstein wrote a paper called "Does the Inertia
of a Body Depend on Its Energy Content?". The idea is
summarized as:
1. the old definition of work (W=Fd), combined with
2. the new fact, nothing can go faster than the speed
of light expressed by F=(ma)/[(1-v2/c2)^3/2]
3. the work goes into making the body heavier. Therefore
4. work adds to the inertia of a body and by implication
inertia has energy and to make it concrete
5. the relationship between energy and inertia is
E=mc^2
6. but remember... nobody really knows what inertia
is - or why objects have it in the first place
This was in 1905.
Particle accelerators began operating decades later.
From E=mc^2, M=E/c^2. This means if you can give enough
energy (photons + electric field for example). You
can literally create matter out of pure energy.
Isn't it odd how Einstein formula could have predicted
it. This shows Einstein must be a super genius and one
of a kind.
But what does inertia.. which has a lot to do with the
equation of E=W+mc^2 (where work is zero) relate to
pair production and actual precipitations of particles??
Albert argues that as you give an object more and more
energy, instead of going faster and faster it gets
heavier and heavier. So if you gave a rocket
1 x 10^1000 foot pounds of thrust, it would stil be
going less than the speed of light. So Einstein
thought that if work goes into giving the body more
inertia.. then inertia must contain energy. What
Albert is saying is that even if work = zero. If you
don't put in any work at all, then the electron still
has an energy equal to e=mc^2
Decades later, Particle Accelerators have been
precipitating particles out of pure energy. My
question is.. What is Inertia relationship to the
energy inherent in matter?? How could Einstein equation
produced in 1905 foresee all of the accelerator
results?
They can't. Since accelerators don't precipitate
anything, except in physics papers.
And then only if they
have television screens.
Einstein is such a genius I can't understand how
some of you plan to outsmart him and reworking all
his equations.
We already have outsmarted him. Since his equations
are second order tensors, which immediatly
implies that DNA doesn't float in
Twin paradoxes.
Patti
.
|
|
|
| User: "" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
16 Jul 2005 01:45:52 PM |
|
|
wrote:
They [sic] can't. Since accelerators [sic] don't precipitate
anything,
So all those tracks seen in particle accelerator experiments, precisely
matching the characteristics of the respective particles (e.g. their
charges, masses, momenta) are faked. And, while we're on the topic,
the Earth is flat too. Hell, even the sun is flat: it's only curved in
abstract physics papers.
.
|
|
|
| User: "The Ghost In The Machine" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
16 Jul 2005 04:00:05 PM |
|
|
In sci.physics,
<>
wrote
on 16 Jul 2005 11:45:52 -0700
<1121539552.047700.79750@g14g2000cwa.googlegroups.com>:
zzbunker@netscape.net wrote:
They [sic] can't. Since accelerators [sic] don't precipitate
anything,
So all those tracks seen in particle accelerator experiments, precisely
matching the characteristics of the respective particles (e.g. their
charges, masses, momenta) are faked. And, while we're on the topic,
the Earth is flat too. Hell, even the sun is flat: it's only curved in
abstract physics papers.
It's also made out of coal and manganese peroxide, which should
make Ed Conrad happy... :-)
--
#191,
It's still legal to go .sigless.
.
|
|
|
| User: "" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
17 Jul 2005 01:28:35 AM |
|
|
http://www.edconrad.com/ebay/SimplyMagic/sunshine.jpg
.
|
|
|
| User: "The Ghost In The Machine" |
|
| Title: Re: E=mc^2, Inertia, Pair Production, why? |
17 Jul 2005 09:00:09 AM |
|
|
In sci.physics,
<>
wrote
on 16 Jul 2005 23:28:35 -0700
<1121581715.886012.143550@g49g2000cwa.googlegroups.com>:
http://www.edconrad.com/ebay/SimplyMagic/sunshine.jpg
Uh huh. And you got that from precisely where?
--
#191,
It's still legal to go .sigless.
.
|
|
|
|
|
|
|
|
|
Related Articles |
|
|
