Re: Simple length problem - for Todd, Harald, thinkers
- From: "Todd" <nospam@xxxxxxxxxx>
- Date: Sun, 2 Jul 2006 22:07:51 -0500
"David" <dseppala@xxxxxxxxxxxxx> wrote in message news:h9pga21makhgtnodo1h5v6upr6bsf7u01h@xxxxxxxxxx
On Sun, 2 Jul 2006 16:42:33 -0500, "Todd" <nospam@xxxxxxxxxx> wrote:
I am suggesting that there is some range of stretching where indeed
"David" <dseppala@xxxxxxxxxxxxx> wrote in message
news:qf6ga21rq2958niftna17dtq7nkbmtvh4n@xxxxxxxxxx
Todd, lets look at and agree on some basic properties of materials. I
want to make sure I understand the simple cases as explained in SR. In
SR problems instead of using high velocities and everyday distances, I
look at things using everyday velocities and very, very long lengths
(this is what Dirk calls my immortal fumble).
Let's say that a rod of a given material, length and diameter can be
stretched a bit and when the force that causes the stretching is
removed the rod returns to its original length. Posters in this group
have indicated that speed the rod will return to its original length
is the speed of sound for the material. Let's assume that is correct.
Let's agree that there is some length such that if the rod is
stretched beyond this critical length, the rod will not return to its
original length when the force is removed. The rod will remain at a
length longer than this critical length due to changes in chemical
bonds. This is a well known behavior of materials.
Now, let's say we have a rod of diameter D composed of N atoms. Lets
say this rod is extremely long and there is a line of people holding
this rod along the x-axis. Let's say the rod is stretched to its
critical length. Call that length L. Lets say there is a conveyer
belt moving with velocity V along the x-axis that has an identical rod
of N atoms on it that is also stretched to its critical length.
Now at time t0, when one end of the rod on the conveyer belt is at the
same point in space as one end of the rod the people are holding,
everyone simultaneously steps onto the moving conveyer belt while
holding the rod. This rod accelerates to velocity V. According to
SR, this rod is now longer than the identical conveyer belt rod. The
rest frame observers said the conveyer belt was shorter than the rest
frame rod, and when eveyone stepped onto the conveyer belt this very
long rod didn't suddenly contract to the same length as the conveyer
belt rod (since that occurs at the speed of sound and for rods 100
light-years in length that would take tens of thousands of years).
Observers on the conveyer belt said that the rod started out shorter
but was stretched when everyone stepped onto the conveyer belt because
one end stepped onto the conveyer belt before theo ther end.
So observers in both frames agree that the original rest frame rod is
now stretched beyond its critical elastic limit and cannot be returned
to its original length. So now let's say one nano-second after time
t0, all of these people holding the rod simultaneously, as measured by
their clocks (the original rest frame times) step back into their
original frame while holding still holding this rod. Now this rod is
the same length that it originally was since everyone only traveled a
distance of one-nano second time V (I used V = 3 meters/second).
But now we have a conflict with what we agreed on. We agreed that the
rod was initially stretched to its critical length L and any further
stretching would cause it to remain stretched beyond L. We could not
do anything to return the rod to its original length if it was
stretched beyond this critical length.
Why can't you apply compressional forces to bring the rod back to its
original length?
you can bring the rod back to its original length. But I am also
suggesting that there is some critical length where stretching beyond
this length changes the chemical bonds and that compression will not
restore it to its original length. We can take a steel spring,
stretch it to its critical length and release the force causing the
stretching and the spring will return to its natural unstretched
length. However there is some critical length we can stretch the
spring beyond and when the stretching force disappears the spring will
not return to its original length. You can try to reverse the steps,
but the stretched spring won't return to its original shape. The same
thing happens if it is a steel rod and not spring shaped. There is a
critical length beyond which the rod will not return to its original
length with mere compression. The chemical bonds have been changed
and you need more than just compression to reverse the process. Some
materials will fracture if they are stretched too far. Trying to
compress the materal to reverse the process will not remove the
fracture.
So when everyone steps onto the conveyer belt with some materials,
the rod will simply fracture, and stepping off the conveyer belt back
into the original frame will not make that fracture disappear.
Likewise, when the material is something that doesn't fracture, but is
stretched beyond its critical limit, it will not return to its
original length. In the steel rod case the shape will change. The
diameter of the rod will be reduced as the length is stretched. There
is some point in the stretching where the chemical bonds change enough
that compression won't return the rod to its original diameter.
There are many chemical properties which once done cannot be undone
by reversing the same steps. Stretching of materials past their
elastic limit is one such property.
Sure. But that just means that when the rod is brought back from the belt frame to the original rest frame it will not be in the same physical condition it was in at the very start of the experiment, even though it will be the same length as it started. I see no problem here.
Look at Einstein's theory using a rod that is a few hundred light
years long and use a very low velocity like 3 meters / second as the
difference in the two frames.
From the original rest frame view, when everyone steps on to the
conveyer belt simultaneously as measured in the rest frame, they say
that in just a fraction of a second all the chemical bonds increase
their spacing along the x-axis by some small amount. This occurs in
Einstein's theory because the length of the rod can't instaneously
change (which is easy to show) but the atoms must be smaller due to
their velocity V. The length contraction of individual atoms occurs
over the width of each atom and can travel that distance very quickly.
Let's say that happens at either the speed of sound or the speed of
light. But since the rod is over 100 light-years in length, when
everyone simultaneously steps onto the conveyer belt, the rod that
everyone is holding is now 3 or so meters longer than the identical
rod that has always been in the conveyer belt frame. The size of the
individual atoms change almost instaneously, but we have to wait at
least 100 years for the length to change (if things travel at the
speed of light) to be equal in length of the non-accelerated rod, or
maybe tens of thousands of years if the effect occurs at the speed of
sound (as changes in chemical bonds do). So observers in this
original rest frame see the chemical bonds stretched almost
instaneously.
Yes. But in order for this to happen, there must have been an *external* force applied to *each atom* in order for each atom to undergo identical, *simultaneous* accelerations from the viewpoint of the rest frame. This is hard to imagine in practice, but, hey, it's your thought experiment. Think about the simpler example of the two blocks connected by a long elastic cord. To accelerate each block simultaneously in the rest frame, an external force must be applied to each block separately. The rest frame sees no change in distance between the blocks as they accelerate, but they would note that stress waves begin to travel along the cord in both directions as soon as the blocks begin accelerating. These waves begin at each end of the cord simultaneously in the rest frame and propagate toward the opposite end. Since these stress waves travel at only the speed of sound, portions of the cord near the midpoint of the cord might not feel the effect of the acceleration of the blocks until well after the blocks have finished their acceleration.
What do observers in the conveyer belt see? They see one end of
the rod accelerated (decelerated) before the other end - say with the
lengths and speeds this time difference is one second. They say the
rod had been shorter than their 100+ light-year rod before everyone
stepped on the conveyer belt. And now its a meter longer than their
identical 100+ light-year rod. They say the individual atoms have
increased in size, and since this was over a very small distance for
each atom, this happened almost instantaneously for each individual
atom, so within a second or so all the atoms increased in size. And
within a second or so the length of the rod stretched. But to have
the rod increase in length from being shorter than their rod to being
longer than their rod, this effect has to propagate through all the
chemical bonds. Somehow, these observers have to measure that some
effect relating to the chemical bonds was able to propagate over a
length of 100+lightyears in just a second or two. That cannot happen.
David
No, nothing has to propagate through the chemical bonds in order to account for why the rod gets longer in the moving frame. The external force applied to each atom is responsible for changing the distance between the atoms. Again, think of the two blocks connected by a cord. From the moving frame point of view, the external forces are not applied simultaneously. Naturally they see the distance between the blocks increase during the acceleration of the blocks. They agree with the rest frame that there are stress waves in the cord that begin propagating from each end of the cord when that end begins accelerating. These stress waves have nothing to do with why the distance between the blocks increased according to the moving frame. Observers in this frame are not puzzled at all about the fact that the distance between the blocks increased in much less time than stress waves can propagate from one end of the cord to the other. Even if there were no cord at all, the distance between the blocks would increase from the point of view of the moving frame.
Todd
[Snip]
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