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Relative
2011-Jun-01, 03:28 PM
I made a couple of thought experiments which leaded to some questions, I'd like to discuss or being helped with:
Thought experiment 1:
If I have a buddy living on the moon, and I would touch him on his chest with a solid stick I'm holding in my hand with a length of 380.000 km in the moment I light a torch, would he feel this touch before he sees the light? And, if it is considered to be a relativistic stick, so the momentum due to my move cannot travel faster than light, does this mean, that the "information" of momentum cannot travel faster than light? Therefore, if (just a little) time is needed to transfer momentum information from one atom or molecule to the next, could this be indication for a space (or spacetime) quantization?
If this stick is made of a conducting material, what would happen then, if at the same time I send an electric signal? a) Light of the torch comes in first, than electric signal depending on conductivity, afterwards momentum? b) Each of which at the same time, but for what reason then light through an "empty space", so with no obstacle at all, travels at the same speed like momentum through solid matter (comparatively "full of obstacles")?
Thought experiment 2:
I've been looking for an answer on this, but there is contradictory information available. Imagine a "relativistic" Newton's cradle with a lenght of the distance Earth-Moon. Does the momentum travel at speed of sound, or is it depending on the materials density? So after what amount of time the last sphere on the moon moves, when the first sphere on planet earth makes contact?
Thought experiment 3:
If I'm sitting at the back seat of a 300.000 km long bus, which just starts to move (Im not talking about velocities close to c, just the very opposite) at let's say 1m/s, this is half of walking velocity :-) I will still feel, that this bus started moving (ok, if momentum is NOT travelling at c!) So, if I look at the driver (his picture takes one second to reach my eye), he might still be collecting money from people entering the bus, because he hasn't started to move yet, while I'm already feeling the move.
What about the second while he doesn't. Will his picture be "blurred" somehow, and shouldn't we notice this proportionately in smaller scale?
Reagrds, and thanx for help.

grapes
2011-Jun-01, 03:34 PM
I made a couple of thought experiments which leaded to some questions, I'd like to discuss or being helped with:
Thought experiment 1:
If I have a buddy living on the moon, and I would touch him on his chest with a solid stick I'm holding in my hand with a length of 380.000 km in the moment I light a torch, would he feel this touch before he sees the light? And, if it is considered to be a relativistic stick, so the momentum due to my move cannot travel faster than light, does this mean, that the "information" of momentum cannot travel faster than light? Therefore, if (just a little) time is needed to transfer momentum information from one atom or molecule to the next, could this be indication for a space (or spacetime) quantization?As near as I can tell from your description, the pulse along the stick would travel at most at the speed of sound in the stick.

I don't think the speed of sound is evidence for the quantization of space, though.

macaw
2011-Jun-01, 03:42 PM
I made a couple of thought experiments which leaded to some questions, I'd like to discuss or being helped with:
Thought experiment 1:
If I have a buddy living on the moon, and I would touch him on his chest with a solid stick I'm holding in my hand with a length of 380.000 km in the moment I light a torch, would he feel this touch before he sees the light?

No. Light travels at 300,000,000 m/s. Force in a material travels at the speed of sound (see grapes' post), i.e. at 300 m/s.

Relative
2011-Jun-01, 03:46 PM
Ok. The speed of sound in Iron is 4190 m/s. In other words, if I would touch you with an iron stick which is 4.19 meters long you would feel this after 1/1000 s only?

profloater
2011-Jun-01, 04:04 PM
If it helps with your visualisation, a very, very long stick is still an elastic solid and when you push it, assuming you have constraint to keep it straight, the stick near your end compresses and that compression wave then travels or propagates along the stick at the speed of sound in the stick. Any real stick would actually bend (Euler developed the slenderness rules) and the transverse wave would also propagate along at a different, slower speed.

Jeff Root
2011-Jun-01, 04:07 PM
Forces travel through solid materials at the speed of sound in
that material. The speed of sound in a solid material depends
on the stiffness of the material. Wood is stiffer than rubber;
steel is stiffer than wood. Diamond is the stiffest material I
know of, with the highest sound speed, 12,000 meters per
second. That is 0.00004 c.

Here's a little table of sound speeds in a variety of common
materials:

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/soundv.html

If you push on one end of a rod, the rod resists being pushed.
The atoms in the rod are compressed. The compression moves
through the rod as a pulse moving at the speed of sound. The
atoms move apart again as the force on them is reduced by the
atoms ahead of them moving away.

Nothing about this says anything about the nature of spacetime,
but it is evidence of the quantization of the rod's composition
into individual atoms. Electromagnetic forces are conducted
from one atom to the next at the speed of light as the electron
clouds of adjacent atoms are compressed and distorted by the
changing positions of electrons and protons near them. The
strengths of the forces within atoms and between atoms of a
material, plus the distances between the particles, determine
the material's stiffness. The speed of sound in solid materials
is not closely related to the material's density, as you can see
from the table.

-- Jeff, in Minneapolis

Relative
2011-Jun-01, 04:18 PM
Thanks so far.
This helps me a lot.

Relative
2011-Jun-01, 05:57 PM
Well, thinking it over, I have another question:
For a while, let's get back to the "very long bus" (300,000 km) and imagine it is made of iron (speed of sound, and momentum as supposed in your answers, for iron is 4190 m/s).
Furthermore, let's assume the engine of this bus is located in the front and motion of the bus starts immediately as the driver presses the accelerator. We, located at the back seat, will feel the bus moving (as long as momentum travels at speed of sound as supposed) after about 19.85 hours!! The picture of the driver (speed of light, about 71,600 times higher) should have travelled away meanwhile in a very "blurred" way, because light travels about 2.14^13 m (!) within that time. So what about the picture we see from the dirver, shoudln't it be blurred? Respectively, if we find ourselves in a long bus in reality (we have a couple of them measuring 18 meters!), shoudn't we notice that?
I still can hardly imagine that monentum travels that slow (depending on the material)
For the "Titanic" this woud mean, when its stern moved, its bow hasn't moved for 16/100 s

NEOWatcher
2011-Jun-01, 06:12 PM
The picture of the driver (speed of light, about 71,600 times higher) should have travelled away meanwhile in a very "blurred" way, because light travels about 2.14^13 m (!) within that time.
Think "distorted" instead of blurred.
Any distortion in the look of the bus will only be 1 part in 71600, so the effects will be virtually imperceptable to human eyes.


For the "Titanic" this woud mean, when its stern moved, its bow hasn't moved for 16/100 s
Yep; that could explain why you hear creaks and moans for such large vehicles.
Any; since the acceleration of that ship is so slow compared to the speed of sound, it really didn't noticeably in that 16/100 s anyway.

Relative
2011-Jun-01, 07:25 PM
Ok, but as far as I know, things travelling at a gaining speed seen from an external reference frame should become "shorter". So, what about the bus that has its engine at the front, and the back seat passenger feels the move after about 20 hours. Isn't this one getting "stretched" somehow, although gaining speed?

grapes
2011-Jun-01, 07:39 PM
Ok, but as far as I know, things travelling at a gaining speed seen from an external reference frame should become "shorter". So, what about the bus that has its engine at the front, and the back seat passenger feels the move after about 20 hours. Isn't this one getting "stretched" somehow, although gaining speed?It's getting stretched in the same manner that a rubber band is stretched--it is not a relativistic stretching. :)

NEOWatcher
2011-Jun-01, 07:53 PM
Ok, but as far as I know, things travelling at a gaining speed seen from an external reference frame should become "shorter". So, what about the bus that has its engine at the front, and the back seat passenger feels the move after about 20 hours. Isn't this one getting "stretched" somehow, although gaining speed?

Like Grapes said. It's a physical stretching, not a relativistic stretching. (molecules bumping into each other or being pulled apart)
I also said "stretch", but that will depend on whether you are pushing or pulling it.
Think of a train leaving a station. It will get longer as it leaves because each train car will not move until the slack in it's coupler has it's slack taken up.

All that is before relativity distorts it's view.

Relative
2011-Jun-01, 08:10 PM
Like Grapes said. It's a physical stretching, not a relativistic stretching. (molecules bumping into each other or being pulled apart)
I also said "stretch", but that will depend on whether you are pushing or pulling it.
Think of a train leaving a station. It will get longer as it leaves because each train car will not move until the slack in it's coupler has it's slack taken up.

All that is before relativity distorts it's view.

That is quite a good picture! But imagine all trains are having no slack in their couplers by nature, because all af them are driving away from us. So, you will only feel a "delay" if you PUSH them from behind, until all of these slacks are gone, and, therefore, you are in direct contact with the locomotive (vTrain=c)
On the other hand, if you PULL a train, where all the slacks already have gone, you will not feel a delay in the last car, even if this train itself has zero speed (Imagine a model train with all slacks eliminated and standing still on the track. In one direction you'll have "delay" in motion, in the opposite direction there's no delay at all...)

NEOWatcher
2011-Jun-01, 08:14 PM
But imagine all trains are having no slack in their couplers by nature, because all af them are driving away from us.
I can see what you are saying, but equating it to the molecular bonds, each coupler will individually be in a different state of slack. You will end up with an average slack of one half the available movement in the coupler.

macaw
2011-Jun-01, 08:15 PM
Well, thinking it over, I have another question:
For a while, let's get back to the "very long bus" (300,000 km) and imagine it is made of iron (speed of sound, and momentum as supposed in your answers, for iron is 4190 m/s).
Furthermore, let's assume the engine of this bus is located in the front and motion of the bus starts immediately as the driver presses the accelerator. We, located at the back seat, will feel the bus moving (as long as momentum travels at speed of sound as supposed) after about 19.85 hours!!

Well, it is as realistic as your bus of 300,000km. How realistic is that?



The picture of the driver (speed of light, about 71,600 times higher) should have travelled away meanwhile in a very "blurred" way, because light travels about 2.14^13 m (!) within that time.

No massive object can travel at the speed of light. So, your "what ifs" aren't possible.





So what about the picture we see from the dirver, shoudln't it be blurred? Respectively, if we find ourselves in a long bus in reality (we have a couple of them measuring 18 meters!), shoudn't we notice that?

No, we shouldn't and we don't.



I still can hardly imagine that monentum travels that slow (depending on the material)
For the "Titanic" this woud mean, when its stern moved, its bow hasn't moved for 16/100 s

What you can or cannot imagine is unimportant, what the physical reality is, is.

macaw
2011-Jun-01, 08:17 PM
That is quite a good picture! But imagine all trains are having no slack in their couplers by nature, because all af them are driving away from us. So, you will only feel a "delay" if you PUSH them from behind, until all of these slacks are gone, and, therefore, you are in direct contact with the locomotive (vTrain=c)
On the other hand, if you PULL a train, where all the slacks already have gone, you will not feel a delay in the last car, even if this train itself has zero speed (Imagine a model train with all slacks eliminated and standing still on the track. In one direction you'll have "delay" in motion, in the opposite direction there's no delay at all...)

This is false. You are not asking questions, you are developing ATMs against basic mainstream mechanics.

Jeff Root
2011-Jun-01, 08:28 PM
The analogy with the train is a really good idea! The connections
between atoms and molecules are just like coupler connections
between train cars, but because the atomic connections are so
much tighter, the force travels through them much faster.

-- Jeff, in Minneapolis

Relative
2011-Jun-01, 08:32 PM
Well, it is as realistic as your bus of 300,000km. How realistic is that?
As I was saying, this also applies to dimensions we are used to. We can buy a 4.19 meters long iron stick at our local do-it-yourself-supplier, and to measure 1/1000 sec is no problem today. But to see, whether the end of the stick is "blurred" or "distorted" is beyound our abilities. (We cannot even determine the 24 single frames of a movie :-))
I DID NOT invent ToR, so don't blame me for having "unrealistic" thoughts, they are just implemented by that theory, I still try to understand, so if I think, the bus (even a common length) is getting strechted, when it has its engine in the front instead of its back, this has nothing to do with ATM so far

Relative
2011-Jun-01, 08:44 PM
I can see what you are saying, but equating it to the molecular bonds, each coupler will individually be in a different state of slack. You will end up with an average slack of one half the available movement in the coupler.

Ok. Let's assume a train with an "average" slack in the couplers as supposed. Wouldn't you agree that pushing the train makes it shorter, and pulling it makes it longer though?

macaw
2011-Jun-01, 09:01 PM
I DID NOT invent ToR, so don't blame me for having "unrealistic" thoughts, they are just implemented by that theory,

This type of statement proves that you are indeed attempting to develop an ATM under the guise of asking questions.
The problem is not with ToR, is with your understanding of it.


I still try to understand, so if I think, the bus (even a common length) is getting strechted, when it has its engine in the front instead of its back,

The stretching/compression effect has nothing to do with relativity, it is all classical mechanics.

Relative
2011-Jun-01, 09:19 PM
Dear macaw,

to avoid misundertanding. I love ToR! But, like many others, I have problems to understand it, and, of course, this leads to some questions (which might look a little cynical to you). But, cynicism and developing an ATM (by the way, I don't actually know at what point) are two very, very different animals...

pzkpfw
2011-Jun-01, 09:23 PM
Let's knock off the side discussion of whether this is ATM or not. Macaw, please don't make these accusations in thread, they are off topic. Relative, asking follow up questions is fine, but you do start to sound a little like you are pushing for the answer you want. Please be careful.

Relative
2011-Jun-01, 09:32 PM
Thanx pzkpfw,
before today I didn't even know (or there was different information available) how fast momentum travels. By now, I understand it is travelling at speed of sound. Sorry for answering "too fast" without thinking it over or to the end. It has nothing to do with I want a certain answer, it was rather some way of "disbeleive" in common sense, sorry...

grapes
2011-Jun-02, 03:39 AM
before today I didn't even know (or there was different information available) how fast momentum travels. By now, I understand it is travelling at speed of sound. And it gets complicated. The speed of sound varies. Shock waves are basically impulses that a traveling faster than the speed of sound in front of the wave, so yeah it gets complicated. The thing to take away from this discussion is that nothing you do here is going to be transmitted to the moon instantly, no matter how you set it up phyically.

Rather than disbelieve the physics, let the physics guide your understanding. There's plenty out there that no one understand! :)

chornedsnorkack
2011-Jun-02, 08:06 AM
Consider that the whole country of Japan moved by about 3 m recently. Well, not 3 m everywhere - the country actually expanded in the process.

It took a few minutes. So within these few minutes the country accelerated to the speed of a few centimetres per second, then decelerated to a halt (well, to a speed to a few centimetres per year).

But that momentum did not travel instantly: the waves had a speed of a few kilometres per second. So in western Japan, you could be at rest and watch the news as to how the eastern Japan was accelerating and expanding, and watch the waves propagating as they approached and reached the observer....

NEOWatcher
2011-Jun-02, 11:58 AM
Ok. Let's assume a train with an "average" slack in the couplers as supposed. Wouldn't you agree that pushing the train makes it shorter, and pulling it makes it longer though?
Yes; but you seem to want to equate that to relativity.

Let me throw a little refinement into the analogy too.
The molecular bonds will tend to reach an equilibrium. In the analogy, this would equate to a spring inside the coupler. This will set up an oscillation of distance between cars. As soon as the acceleration (push/pull) stops, those couplers will bring that train back to an average length. This also sets up a wave of varying distances between cars.

Let's try this. (a series of dots represents the couplers)
Train at non relativistic rest (or coasting)
------------....------------....------------
Train at non relativistic acceleration (in this case - pull)
------------.....------------.....------------
Train at non relativistic acceleration (in this case - push)
------------...------------...------------
Train at relativistic speed (coasting)
----..----..----..----
Train at relativistic spead accelerating (pull)
----...----...----...----
Train at relativistic spead accelerating (push)
----.----.----.----
(Ignore the actual number of dots or dashes, They don't match any actual ratio and are provided as a visual reference only)

neilzero
2011-Jun-02, 12:04 PM
Not only that, but portions of Japan would over shoot, so corrections would occur repeatedly, such that a single movement produces a slow vibration at most other locations = after shocks. Neil

Shaula
2011-Jun-02, 12:14 PM
Not only that, but portions of Japan would over shoot, so corrections would occur repeatedly, such that a single movement produces a slow vibration at most other locations = after shocks. Neil
That is not what aftershocks are. At all. Most aftershocks happen days after the main quake. In a day the waves could have crossed Japan something like 400 times.

Jeff Root
2011-Jun-02, 04:25 PM
Ok. Let's assume a train with an "average" slack in the couplers
as supposed. Wouldn't you agree that pushing the train makes it
shorter, and pulling it makes it longer though?
I'm very curious to learn where you plan to go with the answer to
this question. Everyone will agree that the answer is "yes", and
that it applies to anything that is pushed or pulled.

As NEOWatcher suggested, springs instead of couplers make
a better analogy to the bonds between atoms and molecules.
Obviously pushing compresses the springs and pulling stretches
the springs, and removing the external force allows the springs
to return to their normal length.

-- Jeff, in Minneapolis

chornedsnorkack
2011-Jun-02, 04:57 PM
Yes; but you seem to want to equate that to relativity.


While elasticity and waves are allowed by classical mechanics, they are optional.

In classical physics, stiffness is an arbitrary number, and so is speed of sound derived from it. There is no reason in classical physics why some object might not be perfectly rigid and transmit force instantly (thus infinite speed of vibrations), or have speed of sound faster than light.

Not the case in relativity. Since nothing can move faster than light, there is a rigid upper bound on the stiffness of any substance, whether it is subject to sudden blow or static force.

But a question here: in relativity, a body with rest mass not only cannot move faster than light but also cannot move exactly at the speed of light.

Is it theoretically possible for a medium (with rest mass even when unstressed) to have a speed of sound which is exactly equal to light speed?

profloater
2011-Jun-02, 05:14 PM
Like others I am not sure what you are really driving at so I will confuse it further. In a struck piano string the impact of the hammer travels along the string at the speed of sound in steel, as both a longitudinal wave and a slower transverse wave. the waves bounce at the ends and return causing complex harmonics of both types of waves and the sound produced has an initial strike followed by a ringing set of tones we know as a piano sound. If the string were really very long like to the moon, exactly the same would happen but the strike sound would go on for longer as the wave travelled toward the end, no relativity involved but still very complex sets of vibrations in the solid. (And it would take a long time to reach the moon). If you sent an electrical signal up the wire it would still be slower than c because the speed of light in a solid is slowed down by a series of interactions with the atoms.

Jeff Root
2011-Jun-02, 05:44 PM
Is it theoretically possible for a medium (with rest mass even
when unstressed) to have a speed of sound which is exactly
equal to light speed?
Just like your comments about elasticity and waves in
classical mechanics, the speed of sound can be anything if
you only consider classical mechanics, which doesn't have
anything relevant to say about the real limitations that exist.
The speed is determined by the interactions between charged
particles, which are described by quantum electrodynamics,
so outside of classical mechanics. Essentially, the speed
of sound is determined by the speed at which one particle
can respond to a force applied to it by another particle. So
you look at various materials composed of various different
particles and find out empirically what those speeds are.
As I mentioned, the highest sound speed I know of is the
speed of sound in diamond, 12,000 meters per second, or
0.00004 c.

-- Jeff, in Minneapolis

grapes
2011-Jun-02, 08:03 PM
Is it theoretically possible for a medium (with rest mass even when unstressed) to have a speed of sound which is exactly equal to light speed?I think that's so, for an infinitely rigid material.

Relative
2011-Jun-03, 09:03 AM
Thanks a lot for all your replies,


And it gets complicated. The speed of sound varies. Shock waves are basically impulses that a traveling faster than the speed of sound in front of the wave, so yeah it gets complicated!
Yes. I guess, it would also be nice to know whether there is some sort of „supersonic bang“ when the momentum exceeds the specific speed of sound in a material. Does anybody know something about this?




Let's try this. (a series of dots represents the couplers)
Train at non relativistic rest (or coasting)
------------....------------....------------
Train at non relativistic acceleration (in this case - pull)
------------.....------------.....------------
Train at non relativistic acceleration (in this case - push)
------------...------------...------------
Train at relativistic speed (coasting)
----..----..----..----
Train at relativistic spead accelerating (pull)
----...----...----...----
Train at relativistic spead accelerating (push)
----.----.----.----
(Ignore the actual number of dots or dashes, They don't match any actual ratio and are provided as a visual reference only)

That’s very good. I hope, finally, I got it know... ☺


I'm very curious to learn where you plan to go with the answer to
this question.

Well, actually this was for a better understanding of momentum at first, which includes the question of pushing or pulling (at least imho).
The question behind, however, is a little different, and I would like to include chornedsnorkack’s question

Is it theoretically possible for a medium (with rest mass even when unstressed) to have a speed of sound which is exactly equal to light speed?
Basically, that is a good one.
Furthermore, we discover that each material has its specific speed of sound (at which momentum travels). So is momentum some kind of wave like sound, or is sound some kind of momentum?
On the other hand, if this material is a conductor, the electric field within it travels at speed of light, no matter whether its distance between each atom/molecule (or the coupler/spring distance or its stiffness) varies from another material. It seems strange to me, that all this has no influence.
Especially, as the electric field has to pass a „bulk of obstacles“on its way by traveling through a material compared to speed of light in a vacuum (!).
Or is an electric signal sent via a cable slightly slower than c? (I’m not talking about the speed of electrons themselves, to avoid confusion)

Relative
2011-Jun-03, 09:09 AM
I just noticed, that some answers to my last post already came in meanwhile, while I was writing it...
Thank you

chornedsnorkack
2011-Jun-03, 09:43 AM
Just like your comments about elasticity and waves in
classical mechanics, the speed of sound can be anything if
you only consider classical mechanics, which doesn't have
anything relevant to say about the real limitations that exist.
The speed is determined by the interactions between charged
particles, which are described by quantum electrodynamics,
so outside of classical mechanics. Essentially, the speed
of sound is determined by the speed at which one particle
can respond to a force applied to it by another particle. So
you look at various materials composed of various different
particles and find out empirically what those speeds are.
As I mentioned, the highest sound speed I know of is the
speed of sound in diamond, 12,000 meters per second, or
0.00004 c.
-- Jeff, in Minneapolis

Yes, at low pressures.

At high pressures, speed of sound will be heavily affected by Fermi repulsion of neutrons, as well as strong force repulsion.

What are the highest speeds of sound which have been directly observed? They must be relativistic, but presumably not exactly equal to the speed of light....

Grey
2011-Jun-03, 12:35 PM
Furthermore, we discover that each material has its specific speed of sound (at which momentum travels). So is momentum some kind of wave like sound, or is sound some kind of momentum?I'd say neither. Momentum is a property of an object. For nonrelativistic speeds, it's the product of the mass and the velocity. In a sound wave, momentum is transferred from one particle to the next, through some kind of medium. But calling the speed of sound in a material "the speed of momentum" seems like it's not quite understanding what momentum is.


Or is an electric signal sent via a cable slightly slower than c? (Im not talking about the speed of electrons themselves, to avoid confusion)An electric signal sent via cable does indeed travel a little slower than the speed of light.

Jeff Root
2011-Jun-03, 04:33 PM
The speed of an electric field through a conductor is difficult
to calculate. It appears to be easier to measure the speed
than to calculate it from first principles. These two Wikipedia
articles explain a bit about it. In the first article, look for the
section titled 'Drift speed'.

http://en.wikipedia.org/wiki/Electric_current
http://en.wikipedia.org/wiki/Velocity_factor

-- Jeff, in Minneapolis

Relative
2011-Jun-03, 05:12 PM
In a sound wave, momentum is transferred from one particle to the next, through some kind of medium. But calling the speed of sound in a material "the speed of momentum" seems like it's not quite understanding what momentum is.
Well, likewise the term "speed of sound" seems slightly misleading then. It should rather be "momentum propagation speed" or something similar for each specific medium, right?

caveman1917
2011-Jun-04, 12:17 AM
Well, likewise the term "speed of sound" seems slightly misleading then.

Why? We're already using it for air at atmospheric pressure.
You see lightning before you hear it because the speed of light is higher than the speed of sound, it seems a bit odd to say that you see it first because the speed of light is higher than the "momentum propagation speed".

Tensor
2011-Jun-04, 01:17 AM
Why? We're already using it for air at atmospheric pressure.
You see lightning before you hear it because the speed of light is higher than the speed of sound, it seems a bit odd to say that you see it first because the speed of light is higher than the "momentum propagation speed".

Especially since light also has momentum, which propagates at a much higher speed than sound in air.

John Mendenhall
2011-Jun-04, 03:40 AM
While elasticity and waves are allowed by classical mechanics, they are optional.

In classical physics, stiffness is an arbitrary number, and so is speed of sound derived from it. There is no reason in classical physics why some object might not be perfectly rigid and transmit force instantly (thus infinite speed of vibrations), or have speed of sound faster than light.

Not the case in relativity. Since nothing can move faster than light, there is a rigid upper bound on the stiffness of any substance, whether it is subject to sudden blow or static force.

But a question here: in relativity, a body with rest mass not only cannot move faster than light but also cannot move exactly at the speed of light.

Is it theoretically possible for a medium (with rest mass even when unstressed) to have a speed of sound which is exactly equal to light speed?

Ha! Easy one. No. Violates SR. See the Wiki article on 'Born Rigidity'.

caveman1917
2011-Jun-04, 04:06 AM
Especially since light also has momentum, which propagates at a much higher speed than sound in air.

Good point, hadn't thought of that :)

Grey
2011-Jun-04, 11:15 AM
Good point, hadn't thought of that :)Exactly. Momentum can be transferred between objects by various mechanisms, so thinking about compression or sound waves as being equivalent to momentum or momentum transfer seems to be a little bit off.

cjl
2011-Jun-04, 08:16 PM
Another thing to note is that the sound speed is the speed of a compression wave in a material in the limiting case where the amplitude of the compression wave goes to zero. Large amplitude compression waves travel faster than the "sound speed" in a material.

astromark
2011-Jun-04, 08:37 PM
Ultra sound impulse waves.. Are used to make clear images of the different densities of materials. Brain scans or rock strata.
The wave motions travel at different rates through different densities.. call it sonar or ultra sound and into microwave signals..
Its a science of its own.

Ken G
2011-Jun-04, 08:45 PM
Another point to consider is "dispersion", which is when the speed of sound is different for different frequency. This significantly distorts the sounds you hear underwater, for example, when you are a large distance from the source.

Ken G
2011-Jun-04, 08:49 PM
Another thing to note is that the sound speed is the speed of a compression wave in a material in the limiting case where the amplitude of the compression wave goes to zero. Large amplitude compression waves travel faster than the "sound speed" in a material.
That would surprise me, I'd have expected large perturbations to travel slower. The traveling speed is the group speed, and we think of things like "breaking waves" as an example of a steepening of a front because the phase speed is overtaking the group speed. Also, large-scale oscillations (like pendulums) tend to oscillate at a slower frequency, which also suggests a slowing wave when the amplitude is large. I don't say you're wrong, merely that your claim surprises me, so tell me more.

Relative
2011-Jun-04, 09:14 PM
Ok. I'd like to make (or try to make) a summary, at least for my understanding, of the last answers.
If we compare speed of sound and speed of light, don't we observe the following differencies:
speed of light is an intrinsic property of light itself (it is even supposed to be a natural constant!). So light has a speed. This doesn't apply to speed of sound.
Sound itself (or a sound wave) has no speed at all. Likewise, in a vacuum, it is equal to zero, so it doesn't even exist.
It requires a "medium", so it is rather a specific property of the latter than a property of the first.
It seems to me, like we are mistaking cause and effect.
If we look at the specific melting point of a material, heat is the cause, and melting is the effect. We name the intrinsic property of a material (melting point) after the effect, not after the cause.
If we push an iron stick, it is supposed that the momentum we apply travels "at speed of sound". To me the opposite is the case. A sound wave basically travels at same the speed, at which mometum is transferred to the next atom/molecule/object. You state, "momentum can be transferred between objects by various mechanisms". But this obviouslyis a property of the material, not of the different ways (one of which sound) it can be applied to it! If I push an iron stick forward (in a vacuum), there is no sound heard. It has nothing to do with sound. It just needs the same time as something we call "speed of sound"?

Shaula
2011-Jun-04, 11:07 PM
Sounds waves are longitudinal compression waves. They are an intrinsic mechanical property of the material. It has to be compressed and stretched, which can only be done at a rate related to the stiffness of the material. That is why the speed of propagation of the impulse as you describe it is the same as the speed of sound. Those two facts are why sound speed and light speed are so different. And yes, sound travels at the same speed as a mechanical displacement (which you call momentum transfer) - because that is exactly what it is. When light travels in a medium no part of the medium has to move - when sound does some part of the medium must move to support it.

Relative
2011-Jun-05, 12:27 AM
As it was mentioned here a several times. Is everybody aware of the difference between hardness and stiffness or densitity of a specific material (I don't know, maybe this misundertsanding is just due to the the fact that I'm not a native English speaker...)

When light travels in a medium no part of the medium has to move
Well, that's actually the first time I hear about that light has no influence on a medium. Where is your source for that fundamental perception??

Tensor
2011-Jun-05, 02:45 AM
Well, that's actually the first time I hear about that light has no influence on a medium. Where is your source for that fundamental perception??

There's a difference between having an influence on a medium and the requirement that part of the medium has to move. While light can move through a medium without requiring part of that medium move (Think of it this way, what moves in a vacuum?), light can interact with something within what it is moving through (think of gas or dust within the vacuum).

One of the main problems with the idea of an Aether ( the supposed substance that provided a medium for light to wave), was that it has to be so stiff that light could move at ~300.000 kps and yet be vacuous enough that it had no effect on the movement of astronomical bodies.

Ken G
2011-Jun-05, 06:19 AM
If I push an iron stick forward (in a vacuum), there is no sound heard. It has nothing to do with sound. It just needs the same time as something we call "speed of sound"?I believe this is the crux of your problem. If I push one end of a stick in a vacuum, the sound travels through the stick, not the vacuum. The medium of sound here is the stick. Indeed, if I sing into one end of the stick, my voice reaches the other end at essentially the same speed as a push on one end of the stick would reach the other end-- the vacuum around the stick isn't doing anything in either case. Sound is a push, it's the same thing, and that's why the speed is the same.

Shaula
2011-Jun-05, 07:01 AM
Well, that's actually the first time I hear about that light has no influence on a medium. Where is your source for that fundamental perception??
As has been said the key word there was has, I very deliberately used it over does. Light can propagate quite happily without inducing bulk movement in a solid. I specifically did not say that light has no effect on a medium because that would be false. Light may be absorbed and re-emitted as it travels but there is no requirement for that to happen. It is is perfectly happy in a vacuum whereas sound waves require a medium. I was trying to get across the large fundamental difference in the method of propagation between the two.

cjl
2011-Jun-05, 08:24 AM
That would surprise me, I'd have expected large perturbations to travel slower. The traveling speed is the group speed, and we think of things like "breaking waves" as an example of a steepening of a front because the phase speed is overtaking the group speed. Also, large-scale oscillations (like pendulums) tend to oscillate at a slower frequency, which also suggests a slowing wave when the amplitude is large. I don't say you're wrong, merely that your claim surprises me, so tell me more.

I will admit that I'm unfamiliar with the behavior of compression waves in a solid, so I could be wrong in that case. However, for a fluid, a finite amplitude wave causes some fluid motion along with the wave. In addition, the fluid in a compression wave is heated adiabatically compared with the initial state of the fluid. As a result, the fluid in the compression wave both has a higher local sound speed (due to the higher temperature) than the bulk fluid around it, and it has some motion in the same direction as the wave. So, at the midpoint of the wave, the pressure disturbance propagates forwards at the local sound speed plus the bulk motion of the fluid. Since this is actually faster than the front of the wave is propagating, a finite amplitude compression wave will tend to "pile up" on itself until it eventually forms a shock wave (and the velocity of a shock is dependent on the pressure jump, and it is faster for larger dp). For expansion waves, exactly the opposite applies. The rear of the expansion wave tends to move slower than the front of the wave, so expansion waves will spread out over time in a fluid. So, the end result is that the wave shape is distorted for a finite amplitude wave in a fluid, with compression waves piling up and expansion waves spreading out, and compression waves end up as a shock traveling above the local sound speed (as shocks tend to do).

I don't know about compression wave propagation in a solid though. If someone does, I'd love to hear about it, as I'm sure it's fascinating.

Ken G
2011-Jun-05, 09:57 AM
In addition, the fluid in a compression wave is heated adiabatically compared with the initial state of the fluid. As a result, the fluid in the compression wave both has a higher local sound speed (due to the higher temperature) than the bulk fluid around it, and it has some motion in the same direction as the wave. OK, those are two effects I hadn't included, thanks for the clear explanation. In solids, there's also a slightly slower transverse type of wave, but we're talking about the longitudinal wave here, like the compressive waves you are explaining. Apparently the transverse wave causes the shaking that is deadly in an earthquake, and that tends to come after the original onset of the faster longitudinal wave.

Relative
2011-Jun-06, 11:40 PM
I just have a simple, maybe stupid, question: After all answers here, momentum is supposed to be transferred at the same speed like sound. But sound contains "more information" (i.e. the sound's frequency and amplitude). If I just push (or move) an iron stick in a vacuum in a straight line (like in a Newton's cradle) no sound will be applied, because it is a straight line, so no frequency or amplitude could be detectect and, therefore, no sound will be heard. If I'm trying to transmit the information of a sound, I'll sooner or later be confronted with the situation to transmit something like a sinus-wave, which is obviously longer than a straight line. So, it should need more time. Right or wrong?

Jeff Root
2011-Jun-07, 12:19 AM
A single push on an iron rod in vacuum creates a single
sound pulse, unless the pulse bounces back from the far
end of the rod and makes it reverberate. If you push the
rod by hitting it hard enough, you would hear the pulse
by putting your head against it. If you push so gently that
you can't hear anything when you put your head against it,
then the pulse either has too low a frequency or too low
an amplitude to be audible.

-- Jeff, in Minneapolis

Relative
2011-Jun-07, 12:25 AM
You are talking about a "frueqency" (too low to be audible). Where does it come from, if I do not apply it?

Jeff Root
2011-Jun-07, 12:39 AM
The "frequency" is the rate at which you apply the single
push, creating a single pulse.

Remember that you are talking about a compression wave.
You push on one end of a long iron bar, which compresses
the atoms at the near end of the bar. The compression
travels down the length of the bar as a pulse, which is a
single wave: compression and decompression.

In the real world, I think a single pulse needs to have a
fairly high amplitude to be audible, but the audibility also
depends on the length -- or frequency -- of the pulse.

-- Jeff, in Minneapolis

Relative
2011-Jun-07, 01:14 AM
How can I apply a SINGLE push at a RATE?

Hornblower
2011-Jun-07, 01:28 AM
How can I apply a SINGLE push at a RATE?You could shove our iron bar hard enough for a few seconds to move it significantly, or you could tap it with a steel hammer. The first case might give it more energy but would not be audible to someone with his ear against the far end. The second would make an audible clank.

pzkpfw
2011-Jun-07, 01:32 AM
Edit: I type too slow...

How fast did you push?

Jeff Root
2011-Jun-07, 01:35 AM
You can push on the rod quickly or slowly.

The push could last a millisecond, or a second, or anywhere
in between, or longer, or shorter. The maximum force you
apply could be high or low, independent of how long the push
lasts. Hit it with a metal hammer and you get one rate. Hit
it with a wooden mallet and you get a lower rate. Push it with
your hand and you get a lower rate yet. Push it so gently that
you can barely feel it, and you'll be pushing at a very, very
low rate, such that the wave will be extremely long and the
frequency extremely low.

-- Jeff, in Minneapolis

Relative
2011-Jun-07, 01:44 AM
Ok. I've to doubleckeck this, when I've more time, so, please, take this into account, while I'm answering quickly.
If we have an iron stick of 210 m and push it forward by 3.6 km/h (half of walking speed): at its end we should hear a noise of 20 Hz, just by moving it around?

Jeff Root
2011-Jun-07, 01:53 AM
You need to specify more than just a speed. Is that the
maximum speed it reaches? The average speed? How
quickly does it reach that speed?

-- Jeff, in Minneapolis

Relative
2011-Jun-07, 02:07 AM
You can push on the rod quickly or slowly.

The push could last a millisecond, or a second, or anywhere
in between, or longer, or shorter.

So, how much time does the contact in Newton's cradle take?
Otherwise, what about the "best case" (physical or theoretical, in which no time is needed?) Or, in other words, do you know the "minimum amount" of time required to transfer momentum, so to be able to determine a rate?

Strange
2011-Jun-07, 07:16 AM
Ok. I've to doubleckeck this, when I've more time, so, please, take this into account, while I'm answering quickly.
If we have an iron stick of 210 m and push it forward by 3.6 km/h (half of walking speed): at its end we should hear a noise of 20 Hz, just by moving it around?

You seem to be mixing up several different things (velocity of movement, frequency, time, velocity of propagation...)

If you want to transmit a signal of 20Hz you will need to move the end of the rod backwards & forwards 20 times a second. The speed at which you move the rod will vary and depend on both frequency and amplitude (how far you move the rod). The speed at which those movements are propagated is constant (with the caveats noted above) and is the speed of sound.

If you move/push the rod just once (in a single direction) then you cannot easily talk about frequency or audibility. The movement will contain a complex mix of frequencies that can only really be understood with Fourier transform. But this movement will still be transmitted at the speed of sound.

Jeff Root
2011-Jun-07, 12:59 PM
If you move/push the rod just once (in a single direction) then you
cannot easily talk about frequency or audibility. The movement will
contain a complex mix of frequencies that can only really be
understood with Fourier transform. But this movement will still be
transmitted at the speed of sound.
A train of back-and-forth movements, such as a sine wave, is
simpler than a pulse in that you can, if you choose, ignore the
details of how the pushing begins and ends. With a single
pulse, you need to consider those details, because the details
are what you are asking about in this thread: How a push on
one end of a rod is converted into motion of the other end.
Even how a push on one end is converted into motion of that
same end involves some of those details.

For a Newton's cradle, I expect that you are interested in the
time from when the far side of the next-to-last ball begins to
move until the last ball is no longer in contact with it and is
moving away from it at full speed. That would depend on the
speed of sound in the steel balls, the elasticity of the steel,
the size of the balls, and probably the speed of the first ball
and some other factors I don't know about.

I wonder how one would go about finding an expert who really
knows about the details. An audio engineer who designs
speakers would be one possibility, but the question is basically
in the realm of materials science and engineering. Condensed
matter physics might be another good subject to try.

-- Jeff, in Minneapolis

dgavin
2011-Jun-07, 07:36 PM
chornedsnorkack,

There is another way to look at this, from the point of view of a spinning disk. It's impossible to spin a disk of any material to the point where it's outer circumfrence reaches light speed.

There is a point (speed verses the electron binding force) as you spin up a rotating disk that the centrifical force on each atom overcomes the electron binding forces, and the disk literally starts spinning atoms off from the outer circumfrence. The faster you keep spining up the disk, the faster it will shed it's atoms and from down deeper in the material. Eventually you reach a point when the shedding atoms from deep inside impact other atoms that haven't shed yet, and it starts a small fission reaction, that blows apart the rest of the disk.

In the case of compression waves like the in stick you are refering two, the faster the compression waves moves though the material, the more likely you are to also get impacts of atoms into atoms that trigger a small fission reaction, that blow the stick apart at that location and prevents further propegation of the compression wave.

So if you had a hypothetical material where the compression waves traveled through it at the speed of light, it would undergo spontanious fission with the lightest touch to it. Even a single atom of Oxygen touching the material would cause it to go into a fission reaction. It's very likely that even a small alteration in gravity on the material would trigger it to fission off.

cjl
2011-Jun-07, 09:36 PM
I believe the highest sound speed in any material (at least any of which I am aware) is degenerate plasma. If I remember right, the sound speed is around 1/3c, though I'm going entirely off of memory here, so I could be way off.

(Just as an interesting and semi-related note)

macaw
2011-Jun-07, 09:39 PM
.

If you move/push the rod just once (in a single direction) then you cannot easily talk about frequency or audibility. The movement will contain a complex mix of frequencies that can only really be understood with Fourier transform. But this movement will still be transmitted at the speed of sound.

Yep, it is the Fourier transform of the step function: \pi \delta{(\omega)}+\frac{1}{j \omega}.

Relative
2011-Jun-10, 07:53 PM
You seem to be mixing up several different things (velocity of movement, frequency, time, velocity of propagation...)

If you move/push the rod just once (in a single direction) then you cannot easily talk about frequency or audibility. The movement will contain a complex mix of frequencies that can only really be understood with Fourier transform. But this movement will still be transmitted at the speed of sound.
That's maybe why we cannot determine the difference in the (single) information on a music Cd, whether a single singer is heard or a mixture of harp, horn and piano playing a classical composition, because it has the same "value", and it is just one moment in time. To determine a sound, you need any "Delta", so time that has elapsed.
That's why I'm confused, how we call a poperty of a material "speed of sound", because this intrinsric property of it has nothing to do with a sound, or motion that travels back and forth, if only a puls is applied in one direction. (At least imho. If "speed of sound" would have been named something like "momentum propagation speed", and "speed of sound" would have been considered to be one effect of it - not THE cause - , I probably wouldn't have started this thread..)

Relative
2011-Jun-10, 08:22 PM
For a Newton's cradle, I expect that you are interested in the
time from when the far side of the next-to-last ball begins to
move until the last ball is no longer in contact with it and is
moving away from it at full speed.

Not at all. I'm talkig about the "time required" to transfer the first (moving) ball's momentum to the first one of the row of "resting" ones. This would be required to determine any "rate" (frequency) , at wich the first ball in that row has been hit.

Strange
2011-Jun-10, 08:51 PM
That's maybe why we cannot determine the difference in the (single) information on a music Cd

What does "the (single) information" mean?


That's why I'm confused, how we call a poperty of a material "speed of sound", because this intrinsric property of it has nothing to do with a sound, or motion that travels back and forth, if only a puls is applied in one direction. (At least imho. If "speed of sound" would have been named something like "momentum propagation speed", and "speed of sound" would have been considered to be one effect of it - not THE cause - , I probably wouldn't have started this thread..)

Strawberries aren't berries. Things are called what they are called and there isn't much you can do about it. In this case, the material property is named after the most obvious effect (the speed of sound) rather than an underlying mechanism.

Strange
2011-Jun-10, 08:55 PM
Not at all. I'm talkig about the "time required" to transfer the first (moving) ball's momentum to the first one of the row of "resting" ones.

Unless I have missed your point, this would be the speed of sound in the material.


This would be required to determine any "rate" (frequency) , at wich the first ball in that row has been hit.

The frequency at which the ball is hit is determined by the length of the string - it is a pendulum so the frequency is inversely proportional to the length of the string. The delay caused by the momentum being transferred through the stationary balls will be insignificant by comparison.

Relative
2011-Jun-10, 09:03 PM
What does "the (single) information" mean?



Strawberries aren't berries. Things are called what they are called and there isn't much you can do about it. In this case, the material property is named after the most obvious effect (the speed of sound) rather than an underlying mechanism.
Single information in this case means, if you are looking at a "sound" in one moemt of time (I actually don't know jow many bits or bytes this means on a music CD), you will just "hear" a click, unabale to determine if or how many instruments have been played or whether it is just the "noise" of wind...
And, in a scientific paper (and we are talking about science here, ain't we?) you'll find that strawberries are no berries. Otherwise, where do you know this from. So, especially in physics science , we should take care. We should talk about Temperatures in K. The average joe still doesn't, and it maybe uncomfortable, so we haven't get used to it. But, at least, in science it is used... :-)

Strange
2011-Jun-10, 09:08 PM
Single information in this case means, if you are looking at a "sound" in one moemt of time (I actually don't know jow many bits or bytes this means on a music CD), you will just "hear" a click, unabale to determine if or how many instruments have been played or whether it is just the "noise" of wind...

Ah, I see. Well, if you took a single sample, you wouldn't even have a click; you would just have single value indicating the (voltage/air pressure) level at that point.

Relative
2011-Jun-10, 09:12 PM
Ah, I see. Well, if you took a single sample, you wouldn't even have a click; you would just have single value indicating the (voltage/air pressure) level at that point.
Yep. And that's why I was asking the question about "how much time" does transfer of momentum take at a "single point" (let's call it the point zero, the "contact point" of two moving masses)...

Strange
2011-Jun-10, 10:31 PM
Yep. And that's why I was asking the question about "how much time" does transfer of momentum take at a "single point" (let's call it the point zero, the "contact point" of two moving masses)...

Well, if you are really talking about a single point, then there is no transfer. I'm really not sure what point you are trying to make.

astromark
2011-Jun-11, 01:54 AM
I think I understand 'Relative' and the question...

Understanding the velocity of the wave of motion through the substance is dependant on the density of those masses.

At what velocity does the transfer from one ball to the next occur ? not the transfer through the balls.

Some very fine measurements would reveal the moment velocity is the same as the surface movement momentum.

There is no gap so no transmission is required. Its the same....

Touching the screen of a I-pad... you can not measure any delay... Its this or nothing.

Jeff Root
2011-Jun-11, 05:09 AM
For a Newton's cradle, I expect that you are interested in the
time from when the far side of the next-to-last ball begins to
move until the last ball is no longer in contact with it and is
moving away from it at full speed. That would depend on the
speed of sound in the steel balls, the elasticity of the steel,
the size of the balls, and probably the speed of the first ball
and some other factors I don't know about.
Not at all. I'm talking about the "time required" to transfer the first
(moving) ball's momentum to the first one of the row of "resting"
ones. This would be required to determine any "rate" (frequency) ,
at wich the first ball in that row has been hit.
Yes at all. Probably the only difference between looking at the
last two balls and looking at the first two balls is that my use of
the word "probably" in the quote above changes to "definitely".

The fact that the balls are in a Newton's cradle is irrelevant if
you are talking about only the first two balls. The rate at which
momentum transfers from one ball to another depends in part
on the speed of the first ball. It also depends on the stiffness
and elasticity of the steel (essentially, how easily and quickly
the steel compresses under pressure, and how easily and
quickly it rebounds when the pressure is relieved - elasticity
and resilience being synonymous), the size and masses of the
balls, and of course, the speed of sound in the steel.

The speed of sound in the steel is closely related to the
stiffness and elasticity, but I doubt that knowing the stiffness
and elasticity is sufficient to calculate the speed of sound.

-- Jeff, in Minneapolis

Jeff Root
2011-Jun-11, 05:35 AM
I'm talking about the "time required" to transfer the first (moving)
ball's momentum to the first one of the row of "resting" ones.
Unless I have missed your point, this would be the speed of sound
in the material.
As I've indicated, it is more complicated than that.




This would be required to determine any "rate" (frequency) , at
which the first ball in that row has been hit.
The frequency at which the ball is hit is determined by the length
of the string - it is a pendulum so the frequency is inversely
proportional to the length of the string.
As I think you've realized, he's asking about something else.
The "frequency" is that of the pulse going from the first ball to
the second. I introduced the word "frequency" for this use, and
that may not be the best term. Do you know of a better term?
It is just the inverse of the time interval of the pulse.

-- Jeff, in Minneapolis

Jeff Root
2011-Jun-11, 05:39 AM
A pulse created by a single impact, transferring force in
one direction, is still a sound. It is just a very brief sound.

-- Jeff, in Minneapolis

chornedsnorkack
2011-Jun-11, 06:50 AM
Well, if you are really talking about a single point, then there is no transfer. I'm really not sure what point you are trying to make.

There is transfer at a single point.

When two steel plates collide, what collide is their surfaces (top atom layers).

These come from steady inertial motion to full stop instantly (infinite acceleration). During that instant, their kinetic energy is converted into potential energy of elastic compression, whereupon they shrink.

The pressure is finite (like the speed was finite). Over a finite area, the force is finite; but it causes infinite acceleration of an infinitely small mass of infinitely thin layer of steel at any time.

Such a compression wave of zero thickness travels through steel at exactly the speed of sound, bringing the parts it passes through to halt instantly and shrinking them by a finite and fixed fraction, as kinetic energy is turned into potential.

Also, speed of sound is fully described by stiffness and density.

Shaula
2011-Jun-11, 09:22 AM
These come from steady inertial motion to full stop instantly (infinite acceleration). During that instant, their kinetic energy is converted into potential energy of elastic compression, whereupon they shrink.
Worth noting that that is an approximation of what happens. Infinite acceleration does not physically occur. You are implicitly modelling the steel as a lattice of infinitely stiff components held together by 'springs'.

chornedsnorkack
2011-Jun-11, 02:37 PM
Worth noting that that is an approximation of what happens. Infinite acceleration does not physically occur. You are implicitly modelling the steel as a lattice of infinitely stiff components held together by 'springs'.

Quarks are infinitely stiff.

The electron clouds can and will transfer forces over a few hundred picometres. Thus, nuclei are decelerated from initial speed to standstill in a few hundred or few tens of femtoseconds.

Shaula
2011-Jun-11, 02:57 PM
Which is not infinite acceleration or zero time.

Strange
2011-Jun-11, 03:29 PM
There is transfer at a single point.

If you are transferring energy (or momentum) then it be transferred between one point and another. Despite Jeff's comment, it isn't clear to me that transfer between one ball and the next would be significantly different from transfer between points within one ball.

Cougar
2011-Jun-11, 04:55 PM
The electron clouds can and will transfer forces over a few hundred picometres. Thus, nuclei are decelerated from initial speed to standstill in a few hundred or few tens of femtoseconds.

I only read this last page, wondering how this discussion could go on so long. :) But yes, it seems Relative seeks the more fundamental answer, for which the steel balls and "cradle" are mere analogies. Chorned's answer sounds reasonable, but whatever that "interaction time" is, it's got a definite lower limit of one Planck time. (http://en.wikipedia.org/wiki/Planck_time)

Relative
2011-Jun-11, 10:06 PM
I only read this last page, wondering how this discussion could go on so long. :) But yes, it seems Relative seeks the more fundamental answer, for which the steel balls and "cradle" are mere analogies. .[/url]

Absolutely. If I'm looking at the specific density or "stiffness" values compared to the speed of sound (supposed to be equal to something like "propagation of momentum"), I do not find a proportional or other relation - at least, as far as I have figured out. How can this be?
Example:
Element Mohs Hardness Density Speed of sound
Fe 4 MPa 7.874 g/cm^3 4910 m/s
Cu 3MPa 8.92 g/cm^3 3570 m/s.


Chorned's answer sounds reasonable, but whatever that "interaction time" is, it's got a definite lower limit of one Planck time. (http://en.wikipedia.org/wiki/Planck_time)

Thank you, that "Planck time" helps me a lot. As mentioned in my original post, I was wondering whether there may be some "unit of time" or "unit of space" (or maybe "unit of spacetime") which may also apply to something like propagation speed (or speed of sound).

Just to avoid remarks. I'm not proclaiming an ATM. I didn't think that up myself. There are (scientist) people too who suppose that time, space or spacetime maybe quantisized. I just thought that speed of sound could be - whishful thinking, okay - maybe related to it. Does anybody know about research regarding this?