I've been set a question at basic degree level, the word limit is
1000, however I don't require a 1000 word essay, just a full answer I
can pad out. The question is:
A sceptical friend challenges you about Einstein's theory as follows:
"I have read a little about the theory and it seems fundamentally
wrong. For example, the most famous equation from special relativity
tells us that energy and mass are equivalent, the relation being that
energy = mass x c^2. I read an article about an experiment at CERN in
Geneva where two protons, each travelling at a speed of 0.9997c but in
opposite directions, collided head-on and managed to create a new
particle, the W boson. However, I found in a book that the mass of the
proton if about 1.7x10^-27kg whilst the W boson has a mass of
1.3x10^-25kg. Since the protons together have much less mass than the
W boson, Einstein's equation suggests that there is more energy after
the collision than before. However, I also read that conversation of
energy is one of the most fundamental principles in physics. Doesn't
Einstein's famous equation lead to a conflict between the experiment
and this important principle?
As another example, it is surely a basic requirement of any physical
theory that all observers must agree on the outcome of a physical
process, even though they might disagree on the precise times and
locations of particular space-time events. Now suppose i build a
garage that is 4 m long and buy a car that is 5 m long. Obviously the
car will not fit inside. However, if I drive into the garage at a
speed of 0.6c then relativity theory tells me that the car will appear
shorter to an observer at rest next to the garage, due to the Lorentz
contraction. Specifically i will appear to have a length 5m x
TheSqrRoot(1-0.6^2) = 4m and so will, in principle, fit inside! I
could, for example, fit both ends of the garage with spring-loaded
doors that open and shut very rapidly. If sensors on the doors caused
them to close momentarily when the car was completely inside, the 5m
long car could, in principle briefly be housed inside the 4m garage
without crashing into either door! Fine, but now imagine the view from
the driver's seat of the car. Since special relativity states that all
observers in states of uniform motion relative to each other
experience the same basic laws of physics and so cannot tell, in an
absolute sense, whois moving and who is stationary, the car must
appear still to be 5m long to hte driver. To the driver, it is the
garage that will appear to be shortened, such that its length is now
3.2m. From this point of view the car cannot possibly fit into the
garage and the spring-loaded doors will cause a very messy accident.
Only once of these points of view can be correct - either the car gets
mangled or it doesn't. Hence the theory is logically inconsistent.
Anyway, I cannot see the practical use of Einstein's theory as i
cannot think of a single piece of technology, in use today, whose
performance is affected because Einstein's theory is correct and
Newton's is wrong."

How would you respond to your friend's objections?

Personally I have always regarded Einstein as one prize bullsh*tter

Most good solutions are simple
A 'simple solution' that is 98% incomprehensible - is a pretty good con

You say: 
.. conversation of energy ...

but you probably mean 

conservation  or conversion perhaps?

Really frde (does that mean Fred?)

Could I say (using the same logic) that poetry of Paul Verlaine
http://www.tonykline.co.uk/Browsepages/French/Verlaine.htm

is total con, because I never studied french -
 and after trying to read them in original I conclude 
 that they are  98% incomprehensible  ????

Considerable independent evidence has been found to support many of
Einsteins ideas, I can't say rigorously as the math is over my head
and I have not examined the details of the confirmation. A few of the
people who think Einstein is mostly wrong are very well educated in
appicable fields, but most of the decenters are like frde and/or
cracked pots.   Neil

In the W Boson experiment, the kinetic energy is reduced  by about
99%, apparently becoming mass of the W boson. My guess is this tends
to confirm that energy can become mass which was also part of
Einstein's theory.  Neil

Your friend has confused rest mass and relativistic mass.
If you want a practical use for Einstein's theory, look at GPS -
relativistic effects have to be taken into account to get the
positional accuracy.  Less practical, but more direct, look at
experiments where an atomic clock has been flown at high speed and
high altitude and then compared to its stationary twin.  The 2 clocks
show different times, exactly as predicted by Einstein.

Ian G.

1: Proton collision experiment.
The kinetic energy of the protons, not just their mass, contributes to
the energy available for the creation of new matter.
2: Energy/mass, momentum, and charge are all conserved.  It is not at
all clear on what basis the friend suggests otherwise.
3:The car/garage paradox.
The friend has made the erroneous assumption that the *simultaneous*
closing of both doors in his/her frame of reference is also
simultaneous in the driver's frame of reference.  The friend sees the
car momentarily inside the garage; the driver sees the the door ahead
open again *before* the rear one closes!  (See
http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html)

This reminds me of the story about the person arrested for running a
red light.  He claimed that due to the doppler effect, the light
looked green to him.  His argument was accepted, but he was then
arrested for speeding.

As has been pointed out by others, the GPS system, indeed satellite
navigation and operation in general, requires adjustments beyond those
called for by Newton due to time dilation effects.

> the most famous equation from special relativity
> tells us that energy and mass are equivalent, 
> the relation being that energy = mass x c^2. 

The mass in this equation refers to the effective "relativistic mass",
which is an increasing function of the speed of the object:

m = m0/(1-v^2/c^2)^0.5

where v is the speed of the object, c is the speed of light in vacuo,
and m0 is the rest mass of the object.

If one writes the energy-mass relationship in terms of the rest mass,
the expression is actually:

	E = [p^2*c^2 + (m0*c^2)^2]^0.5

where p is the relativistic momentum of the object, p = v*m (m here is
the relativistic mass, not the rest mass).  See
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c4>

This relationship holds even for objects that have zero rest mass (for
instance, photons).

> I read an article about an experiment at CERN in
> Geneva where two protons, each travelling at a speed 
> of 0.9997c but in opposite directions, collided head-on 
> and managed to create a new particle, the W boson. 
> However, I found in a book that the mass of the
> proton if about 1.7x10^-27kg whilst the W boson has 
> a mass of 1.3x10^-25kg. Since the protons together 
> have much less mass than the W boson, Einstein's 
> equation suggests that there is more energy after 
> the collision than before.

Your friend is confusing relativistic mass and rest mass.  The protons
in the above example have a significant kinetic energy, and that
energy, through the mass-energy relationship, is available for the
creation of rest mass in the form of W-bosons.

Using the full mass-momentum-energy relationship above, with v/c =
0.9997, we have that each proton has an energy of 8.68*10^-25 Joules 
(the rest mass of the proton is 1.673 * 10^27 kg, and c = 2.998
m/sec).  The total energy available in the collision is twice this
(for two protons), which is 1.736*10^-24 Joules.  In your example, the
rest mass of the W-boson is given as 1.3*10^-25 kg (it's actually more
like 1.43*10^-25 kg), so it's rest energy is 1.3*10^-25 kg * c^2 =
1.17*10^-24 Joules.  The total energy available in the collision is
more than enough to create a W-boson, and because energy must be
conserved, the excess energy must be carried off by either the rest
mass or kinetic energy of other particles created in the collision. 
Momentum must also be conserved, and because in the laboratory
reference frame, the total momentum (a vector quantity) is zero
(head-on collision of protons with momenta of equal magnitude but
opposing signs), these other particles must be ejected from the
collision in opposing directions so that the vector sum of their
momenta adds up to zero.

> Now suppose i build a garage that is 4 m long and buy a 
> car that is 5 m long. Obviously the car will not fit inside. 
> However, if I drive into the garage at a speed of 0.6c then 
> relativity theory tells me that the car will appear shorter to 
> an observer at rest next to the garage...[etc.]

This is a well-known apparent paradox that has many explanations on
the web. The resolution of the apparent paradox rest in the fact that
what one observer considers as simultaneous does not correspond to
what the other observer considers as simultaneous (relative
simultaneity).  See, for instance:

<http://en.wikipedia.org/wiki/Ladder_paradox>
<http://www.upscale.utoronto.ca/GeneralInterest/Key/relspec.htm#shrinking%20garage>
<http://wug.physics.uiuc.edu/courses/phys150/fall02/slides/lect14.pdf>
<http://nobelprize.org/physics/educational/relativity/transformations-3.html>
<http://insti.physics.sunysb.edu/~siegel/sr.html>

> I cannot see the practical use of Einstein's theory as i
> cannot think of a single piece of technology, in use today, whose
> performance is affected because Einstein's theory is correct and
> Newton's is wrong.

A few "practical" examples:

Nuclear energy  - the nuclear binding energy released in nuclear
fission (e.g., power reactors) and nuclear fusion (e.g., "hydrogen"
bombs) is exactly equal to the mass difference between the reacting
nuclei and the product nuclei.

Global positioning system (GPS) - Both depends on the finite and
constant speed of light, and must take into account both special and
general relativistic effects see
<http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html>
and <http://www.metaresearch.org/cosmology/gps-relativity.asp>

Particle accelerators - Particle accelerators in which the particles
have speeds that are a significant fraction of c (e.g., the one used
in your first example above) simply wouldn't work correctly if they
were designed using Newtonian physics.  See
<http://teachers.web.cern.ch/teachers/archiv/HST2002/brochures/bitu/accelerators.htm>

Decay rates of unstable particles - The flux of muons inthe Earth's
atmosphere due to cosmic ray interactions can only be accounted for by
the effects of time dilation on the decay lifetime of these particles.
 See <http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html#c1>

The comments of hfshaw-ga pretty well cover the homework problem as a
question that was originally asked.   (Nicely done hfshaw-ga) I would
caution all of you bright folks out there that when it's pretty
obvious this is someone's grade - you not contribute to the selling of
an education by giving them the answer.  Guide them to the information
and help them to understand it.

Back to the original question - Your friend is a luddite.  The Special
Theory of Relativity (STR) has been well tested, and it was a
testament to Einstein that he suggested several of the early tests as
he presented the work.  As for things that are useful in the real
world due to the STR - well other than understanding the real world -
try the color and luster of gold.   Gold has it's appearence because
the
inner shell electrons (1s) are traveling at about 25 percent of the
speed of light.   http://math.ucr.edu/home/baez/physics/Relativity/SR/gold_color.html
  Now if your friend does not believe in electrons, please tell him to
turn off the light and never use it again.  Or SRT is so wrong -
please no-longer listen to the radio or to ignore the nice cop that
hands you a ticket because you don't believe the doppler shift he used
to measure your speed at 30 mph above the speed limit.    All these
things operate either by a consequence of the effects that SRT
descibes or the physical observations that was used as the assumptions
for SRT.  As for technological considerations, you have to understand
the world first before you can manipulate it.

For what it?s worth I thoroughly applaud ?hfshaw?, ?drimagine?,
?xarqi? and ?iang? comments which were posted as I wrote so I?ll send
anyway. BTW, I was tickled by your ?conversation of energy? typo. I
may use the term :-)

Newton wasn?t ?wrong?, it is simply that his mechanics become
progressively inaccurate at physical extremes. One may not consider
particle accelerators (etc), which rely upon relativistic
considerations, to be a ?practical use? but many would disagree. The
pursuit of knowledge is fundamental to the human spirit and the
ultimate raison d'etre.

The problem you may have with ?logically inconsistent? is because of
flawed logic. There was a time when ?logically?, heavier bodies fell
to earth faster than light ones. Einstein was an awfully clever chap.
Special / General has stood the test of a hundred years. Quantum too,
but like Newtonian, both will eventually be superseded by GUT.

It is a little unfortunate that Einstein is so in the public mind
because much uninformed debate is focused upon his postulates. How
many laymen have heard of Maxwell, arguably more influential upon
modern technology than anyone. He was one of Einstein?s heroes.

Of course relativity is difficult to get one?s head round and I too
have had my scepticism of this and many other mathematical
representations. But in all cases (so far), working through the
theories has confirmed them. What is even more enlightening is that
sometimes one thinks one is exploring a specific avenue, but finds
that the same comprehension is applicable to others. A simple case is
capacitor charge and colliding bodies (elastic and inelastic). Run
through the formulae yourself and you might end up visualising them as
the same thing, which mathematically they are.

So my approach now, rather than railing at logical inconsistency, is
?what am I doing wrong?? Healthy scepticism is of course essential but
once one has truly comprehended, the conflicts almost always vaporise.
I have a particular problem with General Relativity which I am
convinced will resolve the Relativity / Quantum incompatibility -- but
most likely I am wrong. Duality is a wonderful tool. You seem to have
an incisive approach so keep at it and all will be revealed.

Best

Hedgie,

The DE in FRDE means Jerry - it is a joke, but one I did not spot until ...

My physics terminated with an 'O' level a very long time ago.

However I have found that I have an unusual ability to pick peoples'
brains and translate 'jargo-speak' into plain English.

Therefore If I find something hard to 'get a handle on' I get suspicious.

I can fully understand that the speed of light is a near constant -
just as the speed of sound is a near constant - the chances are that
the 'photons' or 'waves' are pushing their way through another type of
soup that we cannot yet detect.

I can also understand an 'observed' pseudo Doppler effect on the
physical length of things.
Einstein and railways were rather connected.

Tinkering with Time strikes me as peculiar - nipping out for 10
minutes and finding that 5 years has expired is - well - an
interesting concept.

I would not be convinced unless it were a regularly observed
phenomenon (NASA grants need justification - and scientists /do/
adjust results)
It would be easy to organize a survey of airline staff.

I strongly suspect that 'Einstein' was a cabaret act.

>The DE in FRDE means Jerry - it is a joke, but one I did not spot until ...

Ouch!!

>However I have found that I have an unusual ability to pick peoples'
brains and translate 'jargo-speak' into plain English.

The problem here is that relativity isn't "jargo-speak", it's maths. 
It doesn't translate into English very well, but that doesn't make it
any less valid.  And, as absurd as the predicted effects may seem,
they *are* observed! 100 years on (or 90 if you prefer to focus on
General Relativity) experiments are still being carried out, and the
results still fit the theory.

>I can fully understand that the speed of light is a near constant -

In a vacuum it *is* constant.  That's fundamental to relativity.

>the chances are that the 'photons' or 'waves' are pushing their way
through another type of soup that we cannot yet detect.

That was the "Aether" theory, which was disproved by Michelson and
Morley in 1887.  Their results were part of what lead Einstein to
develop his relativity theories.  Maxwell has already been mention,
but Lorentz and Fitzgerald also did some of the groundwork.

Ian G.

Yes - I remember the Aether stuff

However, we are continually discovering sub atomic 'stuff' 
- 'There are more things in Heaven and Earth than ...'

dear knanmie-ga

I read with much interest your question and with even
greater interest the posted comments. I therefore could
not resist adding my own two cents.

I am sure you can distingish the usual flippant and 
useless comments from some very useful ones 
which explained better than I ever could your friend's 
dilemma (and for free too!)
    
I would further add though that your friend's dilemma
may also be explained by his first eight words:
"I have read a little about the theory" with particular
emphasis on the word little.    
As an old and respected physics lecturer of mine said 
a true understanding of some of the theories of modern
Physics requires both mental effort and a certain level 
of maturity.  

Also asking a researcher to do justice to this type of 
subject in under a 1000 words is both unfair and 
unreasonable. To explain the subject of special 
relativity in whatever context will require as many
words as it takes and that will be in many cases
many thousands of words (and mathematical formula)

There appears to be a trend when certain people will only
accept a 'quick and simple' or 'one soundbite' answer to 
every question. However the real world is a little bit 
more complex.

I am sure your dear friend will take some time to study
and understand better the theories of modern physics
to supplement what has already been discussed in the above 
comments.
There are many excellent web sites out there (which have
already been noted by the other posted comments). There
are also hundreds of books which explain the subject matter
in amazing clarity. I would recommend your friend take
some time to study these 
 
Regards

Mongolia

When you are in movement, the garage would appear longer to you, and
you would think you'd fit...