1 Nicolaas Vroom | Rigid rotating disc | Sunday 15 february 2015 |
2 Jonathan Thornburg | Re :Rigid rotating disc | Sunday 15 february 2015 |
3 Gerry Quinn | Re :Rigid rotating disc | Sunday 15 february 2015 |
4 Gregor Scholten | Re :Rigid rotating disc | Sunday 15 february 2015 |
5 Tom Roberts | Re :Rigid rotating disc | Wednesday 18 february 2015 |
6 Jos Bergervoet | Re :Rigid rotating disc | Wednesday 18 february 2015 |
7 Gregor Scholten | Re :Rigid rotating disc | Friday 20 february 2015 |
8 Nicolaas Vroom | Re :Rigid rotating disc | Friday 20 february 2015 |
9 Jos Bergervoet | Re :Rigid rotating disc | Saturday 21 february 2015 |
10 Nicolaas Vroom | Re :Rigid rotating disc | Tuesday 24 february 2015 |
11 Nicolaas Vroom | Re :Rigid rotating disc | Tuesday 24 february 2015 |
12 Phillip Helbig | Re :Rigid rotating disc | Tuesday 24 february 2015 |
13 Gregor Scholten | Re :Rigid rotating disc | Wednesday 25 february 2015 |
14 Gregor Scholten | Re :Rigid rotating disc | Wednesday 25 february 2015 |
15 Nicolaas Vroom | Re :Rigid rotating disc | Wednesday 25 february 2015 |
16 Jos Bergervoet | Re :Rigid rotating disc | Thursday 26 february 2015 |
17 Mike Fontenot | Re :Rigid rotating disc | Thursday 26 february 2015 |
18 Gregor Scholten | Re :Rigid rotating disc | Saturday 7 march 2015 |
19 Tom Roberts | Re :Rigid rotating disc | Thursday 12 march 2015 |
20 Tom Roberts | Re :Rigid rotating disc | Thursday 12 march 2015 |
21 Roland Franzius | Re :Rigid rotating disc | Thursday 12 march 2015 |
22 Mike Fontenot | Re :Rigid rotating disc | Tuesday 17 march 2015 |
23 Nicolaas Vroom | Re :Rigid rotating disc | Wednesday 18 march 2015 |
24 Nicolaas Vroom | Re :Rigid rotating disc | Thursday 19 march 2015 |
25 Phillip Helbig | Re :Rigid rotating disc | Thursday 19 march 2015 |
26 Nicolaas Vroom | Re :Rigid rotating disc | Saturday 21 march 2015 |
27 Phillip Helbig | Re :Rigid rotating disc | Sunday 22 march 2015 |
28 Tom Roberts | Re :Rigid rotating disc | Thursday 26 march 2015 |
29 Roland Franzius | Re :Rigid rotating disc | Thursday 26 march 2015 |
30 Nicolaas Vroom | Re :Rigid rotating disc | Tuesday 31 march 2015 |
31 Nicolaas Vroom | Re :Rigid rotating disc | Wednesday 1 april 2015 |
32 Tom Roberts | Re :Rigid rotating disc | Friday 3 april 2015 |
1) How fast can you rotate a "rigid" disc of a radius of 1 km? When you consider that the max speed of the circumference is 1% of c or 3000km/sec then this is approx 500 revolutions per second.
[[Mod. note -- In general a rotating object will break up (i.e., the internal stresses caused by the rotation will exceed the material's structural strength) if its tip velocity exceeds (up to a factor of order unity) the speed of sound in the object. For most solids the sound speed is between 1 and 10 km/s. -- jt]]
2) a more difficult question is: is there length contraction in respect to the radius? You can "easily" detect that when you have a grid in the rest frame and the disc "floats" above this grid centered around the axis of rotation.
[[Mod. note -- This is known as the Ehrenfest paradox: http://en.wikipedia.org/wiki/Ehrenfest_paradox
A key point to consider when thinking about the Ehrenfest paradox is precisely what do we mean by the term "rigid"? The "standard" definition is Born rigidity http://en.wikipedia.org/wiki/Born_rigidity But it turns out using that definition, a (Born-)rigid object can't rotate (with respect to an inertial reference frame). In other words, a rotating object can't be (Born-)rigid. -- jt]]
3) For a discussion see http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox#Rotating_disc IMO if there is length contraction in the radius than there also should be length contraction in the circumference as measured in the rest frame. 4) Suppose your disc is rotating at its maximum speed in a rest frame. Which is the maximum speed v you can give this rotating disc? IMO almost nothing.
[[Mod. note -- In what reference frame is v to be measured? -- jt]]
Nicolaas Vroom http://users.pandora.be/nicvroom/
There's a very nice discussion of this problem in our newsgroup FAQ: http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html
--
-- "Jonathan Thornburg [remove -animal to reply]"
> |
1) How fast can you rotate a "rigid" disc of a radius of 1 km? When you consider that the max speed of the circumference is 1% of c or 3000km/sec then this is approx 500 revolutions per second. |
Simple geometry tells you that if the disk continues to occupy the same location (in the coordinates of a distant rotating observer) the material at the circumference will be stretched in terms of a local 'quasi-inertial' coordinate system.
[By 'quasi-inertial' I mean ignoring the rotation as a whole, and just considering the region to be moving inertially along a tangent, as if the disc had suddenly lost structural integrity.]
Of course, real materials cannot be rigid, and this is a *consequence* of the fact that they obey the laws of physics with regard to force transmission etc. For precisely this reason, thought experiments involving the interaction of perfectly rigid objects under the laws of physics leads to innumerable paradoxes, in relativity and elsewhere!
> | 2) a more difficult question is: is there length contraction in respect to the radius? |
I'm not sure what exactly is meant by question 2. If the disc is rigid, there clearly cannot be any length contraction of any region in its own frame.
It does inspire an interesting thought experiment, though, which may be along the lines you were thinking of. What if we made a massive circular 'flywheel' corresponding to the outer rim of your disc? The material is tough and minimally elastic in terms of tension (but very compressible). It is constrained somehow to rotate around a central axis, but it is possible for it to shrink in radius if the stresses on it demand this. What happens if we continuously apply torque to the axle, spinning it faster and faster?
I would predict that initially the measured speed of the rim would increase to a substantial fraction of c. After that the radius will shrink proportional to the relativistic length contraction that a distant observer would expect based on the relative speed of elements of the rim. The exact degree of radial contraction would vary with the elasticity, but the speed of the rim not so much. (More stretchable materials would contract less quickly.)
You could keep putting energy into the system indefinitely as far as special relativity is concerned, but at some point gravitational forces would have to be considered, and eventually it would collapse into a black hole.
- Gerry Quinn
--- This email has been checked for viruses by Avast antivirus software. http://www.avast.com
> | 2) a more difficult question is: is there length contraction in respect to the radius? |
AFAIK the mostly agreed solution of this so-called Ehrenfest paradoxon is:
The material of the disk itself is not length-contracted, since this is not possible without destroying the disk. However, this has the effect that seen from a disk-riding observer, the disk material seems to be stretched, since the yardsticks of this observer undergo a length contraction. The result is that for the disk-riding observer, the circumference of the disk is stretched, i.e. is greater then 2pi r, where r is the disk radius. This means that the disk-riding observer observes a non-Euklidian spatial geometry for the disk.
[Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. Also, one must take into account the light-travel time from different points of the object. While this was confusing even to experts several decades ago, it has now been cleared up in the technical, though not in all of the popular, literature. See, for example, http://casa.colorado.edu/~ajsh/sr/contraction.html#cartwheel and check out the Lorentz-contracted cartwheel. -P.H.]
This becomes clearer if one considers not a solid disk, but rather a bunch of radial hairs in the form of a disk: as the rotation rate increases the individual hairs become further apart, as measured by a comoving observer at the end of some hair.
Of course in practice no material is anywhere close to being strong enough for this to be important or measurable.
Tom Roberts
> | Nicolaas Vroom wrote: |
>> |
2) a more difficult question is: is there length contraction in respect to the radius? |
> |
AFAIK the mostly agreed solution of this so-called Ehrenfest paradoxon is: The material of the disk itself is not length-contracted, since this is not possible without destroying the disk. However, this has the effect that seen from a disk-riding observer, the disk material seems to be stretched, since the yardsticks of this observer undergo a length contraction. |
No, "seen from a disk-riding observer" is wrong. This observer will not see his own yardstick contracted. You have to invoke a stationary observer for that! And that observer will also see that distance markers along the circumference of the disk still are unchanged compared to the stationary circumference circle (otherwise the disk would not fit on the original circle, which it does in the situation we are describing).
This in turn means that also the disk-riding observer will see the mismatch between his yardstick and the markers (worldlines of markers cannot coincide in one frame and have mismatch in another). But the disk-riding observer will explain this as a correct yardstick and a stretched disk.
To judge the mechanical stresses in the disk the disk- riding observer is best positioned. In his inertial frame he sees the material of the disk at rest (albeit with some rotation and in a gravity field). The fact that the disk seems stretched to hime means that there really is a mechanical stretching force in the material.
...
> | circumference of the disk is stretched, i.e. is greater then 2pi r, where r is the disk radius. This means that the disk-riding observer observes a non-Euklidian spatial geometry for the disk. |
If he uses a disk-fixed coordinate system, that is.. Another option for his coordinates would be an inertial frame with the momentary speed of his point on the rim.
-- Jos
>> |
AFAIK the mostly agreed solution of this so-called Ehrenfest paradoxon is:
The material of the disk itself is not length-contracted, since this is not possible without destroying the disk. However, this has the effect that seen from a disk-riding observer, the disk material seems to be stretched, since the yardsticks of this observer undergo a length contraction. |
> |
No, "seen from a disk-riding observer" is wrong. This observer will not see his own yardstick contracted. |
I did not write that the observer sees his own yardstick contracted. I wrote his yardstick is contracted (seen from an inertial frame in which the disk is rotating, but not translating). As the disk-riding observer sees his own yardstick non-contracted, i.e. having normal length, he instead measures the circumference of the disk being stretched, when he measures the circumference using his yardstick.
> | You have to invoke a stationary observer for that! |
That is exactly what I did. Without mentioning it explicitly because I thought that would be clear.
> | Nicolaas Vroom wrote: |
> > |
2) a more difficult question is: is there length contraction in respect to the radius? |
> |
AFAIK the mostly agreed solution of this so-called Ehrenfest paradoxon is: The material of the disk itself is not length-contracted, since this is not possible without destroying the disk. However, this has the effect that seen from a disk-riding observer, the disk material seems to be stretched, since the yardsticks of this observer undergo a length contraction. The result is that for the disk-riding observer, the circumference of the disk is stretched, i.e. is greater then 2pi r, where r is the disk radius. This means that the disk-riding observer observes a non-Euklidian spatial geometry for the disk. [Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
> | popular, literature. See, for example, http://casa.colorado.edu/~ajsh/sr/contraction.html#cartwheel and check out the Lorentz-contracted cartwheel. -P.H.] |
The first question to answer what type of material is rigid and what
is non-rigid.
AFAIK rigid material does not experience length contraction.
The only way to find this out is by performing real experiments.
Please visit:
http://users.telenet.be/nicvroom/wik_Born_rigidity.htm#ref2
What this shows are three outcomes of almost the same experiment.
In fact this is the most simple experiment to demonstrate length contraction
without any clocks.
In each experiment there is one train at rest and one is moving.
In each case the train has a cargo and either the train or the cargo is
rigid (or non rigid)
In Figure 1 only the train (NR) is undergoing length contrain.
In Figure 2 both train and cargo are undergoing length contraction
(Implying that the concept rigid versus non-rigid is not realistic)
In Figure 3 only the cargo (NR) is undergoing length contraction.
To understand (rigid) discs please visit: http://users.telenet.be/nicvroom/wik_Ehrenfest_paradox.htm#ref2 Here we discuss 2 possible outcomes of what happens with a rotating disc Figure 2A shows the disc at rest in a reference frame. (Also can be used to demonstrate a rotating disc without any length contraction Figure 2B shows a rotating disc which size stays the same but the markers parallel with the circumference are length contracted. Figure 2C shows both length contraction in size and radius. Also this experiment does not require any clocks nor any moving observer.
Hopes this helps
Nicolaas Vroom
> | On 2/15/15 2/15/15 1:01 PM, Gregor Scholten wrote: |
>> |
Nicolaas Vroom wrote: |
>>> | 2) a more difficult question is: is there length contraction in respect to the radius? |
> | Yes to all of that. The important thing to note is that there is enormous strain in the material of the disk, not only radially (due to the internal force required to maintain the disk's outer radius as it rotates), but also circumferentially (due to the distortion one might ascribe to "length contraction", |
This raises the practicle question: which one of these two effects will win if the disk has some elasticity which will allow its radius to be stretched (by centrifugal effect) or to be contracted (by circumferential stress).
Is there a fixed ratio between these opposing effects? Or can the contraction win for some value of disk size and rotation speed? (One would expect centrifugal expansion to win for simple laboratory-sized experiments..)
> | but is really due to the circumference remaining 2*pi*R while its length to the rotating observer is larger). |
Remaining 2*pi*R _for the stationary observer_, you mean. (Be careful with absolute claims in relativity.)
-- Jos
> | [Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
> | Also, one must take into account the light-travel time from different points of the object. |
> | While this was confusing even to experts several decades ago, it has now been cleared up in the technical, though not in all of the popular, literature. |
> | See, for example, http://casa.colorado.edu/~ajsh/sr/contraction.html#cartwheel and check out the Lorentz-contracted cartwheel. -P.H.] |
Nicolaas Vroom
> | This raises the practicle question: which one of these two effects will win if the disk has some elasticity which will allow its radius to be stretched (by centrifugal effect) or to be contracted (by circumferential stress). |
The only way to answer this question is by performing different experiments with different materials. If the outcome is different than you can see how difficult this whole issue is. When you introduce concepts like stress and elasticity the whole issue becomes a physical problem. This raises the question to what extend when you study only length contraction (of a rod) is stress involved. For example does it make a difference if you push or pull an object.
> > | but is really due to the circumference remaining 2*pi*R while its length to the rotating observer is larger). |
> |
Remaining 2*pi*R _for the stationary observer_, you mean. (Be careful with absolute claims in relativity.) |
IMO when you study length contraction you should only (?) do this from the viewpoint of one frame.
Nicolaas Vroom
> | Op zondag 15 februari 2015 19:01:05 UTC+1 |
> > |
[Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
> |
What do you mean not real? Do you mean it is not physical? Is Time Dilation real i.e. physical? |
It is not real in that no stress or strain on the object results. Consider: it depends on relative velocity. More than one observer can look at the object with different relative velocities, and see different length contractions. Which one is real? The object doesn't even have to know it is being observed.
[appearance of rapidly moving objects]
> > | While this was confusing even to experts several decades ago, it has now been cleared up in the technical, though not in all of the popular, literature. |
> | What do you mean by cleared up? |
There is an article by Terrell.
>>> | [Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
>> |
What do you mean not real? Do you mean it is not physical? Is Time Dilation real i.e. physical? |
> |
It is not real in that no stress or strain on the object results. Consider: it depends on relative velocity. More than one observer can look at the object with different relative velocities, and see different length contractions. Which one is real? |
The one that occurs in the applied inertial frame. If you denote only frame-independent phenomena as "real", then you are right, Lorentz contraction is not real then.
> | [Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
What do you mean with "is not real"? Length contraction is real in that sense that in an inertial frame S, relative to which a body is moving, the length of the body is shorter than in the body's rest frame S'.
In addition, length contraction is not the way how the moving body appears. Take e.g. a moving ball. Lorentz contraction makes it ellipsoid-shaped, however, when watching the moving ball, one sees it still bullet-shaped, due to effects of light propagation. Those effects are described here:
http://www.tempolimit-lichtgeschwindigkeit.de/fussball/fussball.html
The page is in German, those who do not speak German may just have a look on the pictures. The top-most sequence of three pics show how a ball would appear if one just takes the Lorentz contraction into account, but no light propagation effects. The next three pics (up to down) show how the ball appears for three different velocities (<< c, 0.9 c, 0.99 c) when taking the light propagation effects into account (bullet-shape is kept, but surface structures are distorted).
The last picture where the ball appears stretched results from taking light propagation into account, but no Lorentz contraction (i.e. how the ball would appear in Newtonian physics).
> | Also, one must take into account the light-travel time from different points of the object. While this was confusing even to experts several decades ago, it has now been cleared up in the technical, though not in all of the popular, literature. See, for example, http://casa.colorado.edu/~ajsh/sr/contraction.html#cartwheel and check out the Lorentz-contracted cartwheel. |
What exactly is to be checked out there?
> |
In article |
> > > |
[Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
> > | What do you mean not real? Do you mean it is not physical? Is Time Dilation real i.e. physical? |
When you observe a sun eclipse in reality, dependent about the distance from the moon to the earth it is possible to see the limb of the Sun around the Moon. As such the moon appears larger and smaller. This is all a visible illusion and physical there is no difference in size involved.
> | It is not real in that no stress or strain on the object results. Consider: it depends on relative velocity. More than one observer can look at the object with different relative velocities, and see different length contractions. |
How do you perform such an experiment in the most simple way in the reality? Why are there more observers involved? IMO it should be possible just by using two trains one at rest and one moving to demonstrate length contraction as described in: http://users.telenet.be/nicvroom/wik_Born_rigidity.htm#ref2 Ofcourse the outcome could be negative implying length contraction is not real. In case the observer at rest observes length contraction you could also use a video camera and demonstrate the same.
> | Which one is real? The object doesn't even have to know it is being observed. |
> | [appearance of rapidly moving objects] |
> > | What do you mean by cleared up? |
> |
There is an article by Terrell. |
IMO terrell rotation is considered visible illusion. See: http://en.wikipedia.org/wiki/Terrell_rotation "a receding object would appear contracted, an approaching object would appear elongated" See also: http://users.telenet.be/nicvroom/terrell.htm
Nicolaas Vroom
> | Op zaterdag 21 februari 2015 22:12:17 UTC+1 schreef Jos Bergervoet: |
>> |
This raises the practicle question: which one of these two effects will win if the disk has some elasticity which will allow its radius to be stretched (by centrifugal effect) or to be contracted (by circumferential stress). |
> |
The only way to answer this question is by performing different experiments with different materials. |
If you do not believe the theory of relativity or the theory of elastic deformation, _then_ your only way to answer the question is by performing experiments. (But this may not be the situation for the audience you are addressing here..)
> | If the outcome is different than you can see how difficult this whole issue is. |
Different from what? (The outcome, I mean!)
> | When you introduce concepts like stress and elasticity the whole issue becomes a physical problem. |
But not fundamentally different from designing a skyscraper, or any mechanical structure.
-- Jos
> | [...] If you denote only frame-independent phenomena as "real", then you are right, Lorentz contraction is not real then. |
Good comment. Many people DO regard anything that is frame-dependent to be "not real". I don't subscribe to that belief: I think that length contraction and time dilation (and, more generally, simultaneity) are all real for a given observer. I certainly don't regard them to be any kind of "illusion" or "meaningless appearance".
-- Mike Fontenot
> | The first question to answer what type of material is rigid and what is non-rigid. AFAIK rigid material does not experience length contraction. The only way to find this out is by performing real experiments. Please visit: http://users.telenet.be/nicvroom/wik_Born_rigidity.htm#ref2 What this shows are three outcomes of almost the same experiment. In fact this is the most simple experiment to demonstrate length contraction without any clocks. In each experiment there is one train at rest and one is moving. |
You are considering linear motion there, i.e. translation, not rotation like for the rotating disk. For linear motion, it is immediately clear that length contraction always occurs, independent from the properties of the material. This result follows from Lorentz transformation, or, what might be easier to understand, from considering a Minkowski diagram, like this one:
http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction#The_nature_of_length_contraction
The brown line marks the length of the rod in the rod's rest frame (x,t), the red line the length of the rod in an inertal frame (x',t') which is moving relative to the rod. Due do Minkowski metric of spacetime, the red line is shorter than the brown line, not longer as one might assume when looking at the diagram.
The reason why the rod's length in the frame (x',t') is given by the red line which is rotated against the brown line is the relativity of simultaneity: in the rod's rest frame (x,t), two events are simultaneous when they are on the same x coordinate line, however, in the frame (x',t'), two events are simultaneous when they are on the same x' coordinate line.
You see, it is completely irrelevant whether the rod is made of rigid material or of a non-rigid one. It's just a question of intersections of the worldlines of the rod's front and back and spatial coordinate lines.
> |
In each case the train has a cargo and either the train or the cargo is
rigid (or non rigid)
In Figure 1 only the train (NR) is undergoing length contrain. In Figure 2 both train and cargo are undergoing length contraction (Implying that the concept rigid versus non-rigid is not realistic) In Figure 3 only the cargo (NR) is undergoing length contraction. |
Just apply the above mentioned Minkowski diagram: if both, train and cargo have constant length in the train's rest frame, it immediately follows that both, train and cargo, are Lorentz contracted in a frame in which the train is moving.
For rotation, like a rotating disk, however, things are much more complicated.
> | To understand (rigid) discs please visit: http://users.telenet.be/nicvroom/wik_Ehrenfest_paradox.htm#ref2 Here we discuss 2 possible outcomes of what happens with a rotating disc Figure 2A shows the disc at rest in a reference frame. (Also can be used to demonstrate a rotating disc without any length contraction Figure 2B shows a rotating disc which size stays the same but the markers parallel with the circumference are length contracted. Figure 2C shows both length contraction in size and radius. |
There are two inertial frames that we can apply here: - the frame of a stationary observer, in which the disk is rotating, but not translating, let's denote this frame S - a frame the is locally co-moving with a disk riding observer, let's denote this frame S'
The frame of the disk-riding observer itself is no inertial frame, since it is co-rotating and therefore accelerated.
Since S and S' are moving relative to each other, they must disagree in the length of a local section of the disk's circumference, since this section is at rest in S', but moving in S. And as well, they must disagree in the length of a nearby rod that is at rest in S'.
From this follows that both solutions, 2B and 2C, are possible:
- For 2B, the disk's circumference and the nearby rods are contracted in S, whereas in S', both, the local circumference section and the rod are non-contracted. Let R denote the original radius of the disk from when the disk was not rotating, and r the radius of the rotating disk. It follows that in S, the radius is r and the circumference 2pi r. However, in the co-rotating non-inertial frame, the radius is r, too, but the circumference is 2pi R > 2pi r, making the spatial geometry in this frame non-Euklidian.
- For 2C, the nearby rods are contracted in S, but the circumference is not. In turn, in S' the nearby rod is non-contracted, but the local circumference section is expanded. In S, the radius of the disk is R and the circumference 2pi R, whereas in the co-rotating non-inertial frame, the radius is R, but the circumference is > 2pi R, again yielding a non-Euklidian spatial geometry.
So, there are two types of rigidity: one that keeps the length of the local circumference section in S' constant, and in turn results in contraction of the disk's radius, and the other one that keeps the radius constant, but yields an expansion of the local circumference section in S'. A rigidity which would permit for both is impossible in SR.
> | The first question to answer what type of material is rigid and what is non-rigid. |
There is no possible material that is rigid, because that would imply an infinite speed of sound. And, of course, no material ever observed comes close to being rigid.
> | AFAIK rigid material does not experience length contraction. |
This is just plain wrong. "Length contraction" does not affect any physical object, it is a geometrical projection that affects how relatively moving observers MEASURE the object. Such measurements cannot possibly affect the object itself. And, of course, there can be many differently-moving observers who measure different values for the "length contraction" of the object, but it clearly has a single actual length.
Yes, all those sloppy authors that say "moving clocks run slow" and "moving rods get shortened" are WRONG. They ought to say "moving clocks are observed to run slow", and "moving objects objects are observed to be shortened". Because neither the clock nor the rod is affected in any way, but their words say that they are. But my phrases are not perfect, either, as one might interpret them as saying these phenomena are merely appearance, and that isn't correct, either. Bottom line: sound bites cannot capture the subtleties of relativity.
> | The only way to find this out is by performing real experiments. |
First you must understand this correctly by learning what the words you use actually mean. In particular, "length contraction" does not mean what you apparently think it means. You are probably similarly confused by "time dilation".
I always put those two phrases in quotes because those names are very poor, and do not accurately describe the actual phenomena. But they are solidly established historically.
> | [... repetitions of the above mistake] |
Tom Roberts
> | Op zondag 15 februari 2015 19:01:05 UTC+1 |
>> | [Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
> | What do you mean not real? Do you mean it is not physical? Is Time Dilation real i.e. physical? |
The problem is that the words "real" and "physical" are ambiguous, and mean different things to different people (and in different contexts, and...).
For instance, "time dilation" and "length contraction" are not "real" in the sense that they modify or affect the object in question. But they are "real" in the sense that these phenomena can have observable, physical consequences (e.g. pion beams ~ 1 km long exist; electrons moving in wires generate magnetic forces that drive motors).
As I have said so often, understanding subtle concepts like relativity requires precision in thought and word. The above exchange falls woefully short of what is required. For instance, the Moderator's "appears" does not seem to subsume the fact that pion beams ~ 1 km long exist -- if "time dilation" was merely "appearance" they could not exist. So there is more substance here than those words capture....
[Moderator's note: I agree with all you say in this post and the previous one, except, perhaps, here: Adopting your terminology, the correct formulation should be: "pion beams are observed to be ~ 1 km long". If you are referring to the fact that they are observed to travel farther than one would expect from their speed and lifetime, then what is involved is time dilation (from our point of view) and/or length contraction (from their point of view); pions are clocks and rulers just like anything else. -P.H.]
Gregor Scholten said:
> | If you denote only frame-independent phenomena as "real" [...] |
One reasonable meaning of "real" is "serves as a viable and useful model of some physical phenomenon". If that is the meaning used, then only coordinate- independent quantities can be "real" (because coordinates are arbitrary human constructs, and Nature does not use them).
Mike Fontenot said
> | I don't subscribe to that belief: I think that length contraction and time dilation (and, more generally, simultaneity) are all real for a given observer. |
I don't think it makes sense for "reality" to be observer dependent like that. But I also think your words are too ambiguous to be useful.
Tom Roberts
> | On 2/20/15 2/20/15 11:39 AM, Nicolaas Vroom wrote: |
>> | The first question to answer what type of material is rigid and what is non-rigid. |
> |
There is no possible material that is rigid, because that would imply an infinite speed of sound. And, of course, no material ever observed comes close to being rigid. |
But velocities are of no significance in basic theories.
Objects, which, in conventional terms, rotate at highest physical possible velocities are the electrons in high angular momentum states.
Its funny to observe that their speed in the 1-particle projection Dirac space is nearly infinite because the current four vector in spherical relativistic coordinates, as the cofactor of the angular momentum, correctly transforms covariantly in the same way as if the proper speed four-vector of a material point object would be measured in proper time and not coordinate time.
This is of course a rock solid principle of covariantly Lorentz invariant fomulation of questionable physical terms like velocities of basically wavelike phenomena.
--
> |
Mike Fontenot said |
>> | I don't subscribe to that belief: I think that length contraction and time dilation (and, more generally, simultaneity) are all real for a given observer. |
> |
I don't think it makes sense for "reality" to be observer dependent like that. But I also think your words are too ambiguous to be useful. |
I elaborate on my statement in the section entitled "Empirical Determination of the Current Age of a Distant Perpetually-Inertial Person" of my webpage
https://sites.google.com/site/cadoequation/cado-reference-frame
The basic argument is that an observer (inertial OR accelerating) can make elementary observations and elementary calculations about the current age of a distant person, which convey an inherent meaningfulness (and therefore a "realness") for that observer. Exactly what those observations and calculations are cannot be understood in a "sound byte", and anyone interested will need to spend some time with that webpage. And even the webpage itself is too short to fully specify those calculations, and (in particular) to show how the basic argument for inertial observers can be extended to include accelerating observers. For that, the paper
"Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629
is required.
-- Mike Fontenot
> |
There is no possible material that is rigid, because that would imply an infinite speed of sound. And, of course, no material ever observed comes close to being rigid. |
I agree with you that rigid material (by difinition) does not exists. IMO the reason is that it requires instantaneous communication.
> > | AFAIK rigid material does not experience length contraction. |
> |
This is just plain wrong. "Length contraction" does not affect any physical object, it is a geometrical projection that affects how relatively moving observers MEASURE the object. |
> | Such measurements cannot possibly affect the object itself. |
> | And, of course, there can be many differently-moving observers who measure different values for the "length contraction" of the object, but it clearly has a single actual length. |
IMO it does not make sense to use the results of different observers if they measure different values for the same object.
> | Yes, all those sloppy authors that say "moving clocks run slow" and "moving rods get shortened" are WRONG. They ought to say "moving clocks are observed to run slow", and "moving objects are observed to be shortened". |
Clifford M.Will at page 273 writes (Was Einstein right):
"On the other hand it is rather difficult effect to see experimentally
because it is hard to accelerate macroscopic rods to high enough
velocities to make the effect noticeable."
At page 271 he writes: "The observational evidence for time dilation is overwhelming." My understanding is that in order to demonstrate this you only need one observer and two clocks. The moving clock should run behind when both meet again.
> > | The only way to find this out is by performing real experiments. |
> |
First you must understand this correctly by learning what the words you use actually mean. In particular, "length contraction" does not mean what you apparently think it means. You are probably similarly confused by "time dilation". |
Nicolaas Vroom
> | On 2/24/15 2/24/15 7:35 AM, Nicolaas Vroom wrote: |
> > | Op zondag 15 februari 2015 19:01:05 UTC+1 |
> >> | [Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears. |
> > | What do you mean not real? Do you mean it is not physical? Is Time Dilation real i.e. physical? |
> |
The problem is that the words "real" and "physical" are ambiguous, and mean different things to different people (and in different contexts, and...). For instance, "time dilation" and "length contraction" are not "real" in the sense that they modify or affect the object in question. |
> | But they are "real" in the sense that these phenomena can have observable, physical consequences (e.g. pion beams ~ 1 km long exist; electrons moving in wires generate magnetic forces that drive motors). |
Only physical processes can influence other physical processes.
> | [Moderator's note: etc If you are referring to the fact that they are observed to travel farther than one would expect from their speed and lifetime, then what is involved is time dilation (from our point of view) and/or length contraction (from their point of view); pions are clocks and rulers just like anything else. -P.H.] |
If pions behave (physical) different under different (physical) conditions than if the law that describe these processes is called time dilation than time dilation (as a description of a process) is real.
At the same time physics becomes difficult when in order to describe (study) time dilation also length contraction is involved and when length contraction is described (studied) also time dilation is involved. IMO both should be studied independently of each other and when that is not possible clearly be indicated why. This implies that you should study moving objects i.e. length (contraction) without moving clocks.
Nicolaas Vroom
> > > | AFAIK rigid material does not experience length contraction. |
> > |
This is just plain wrong. "Length contraction" does not affect any physical object, it is a geometrical projection that affects how relatively moving observers MEASURE the object. |
> | What you indirectly indicate (?) that when you have an observer at rest in front of an object/train at rest and a moving object/train which passes directly infront of the object/train at rest that the observer can never observe any (physical) length contraction when both trains are in front of him. (Assuming that both objects have the same length at rest) |
No. Of course length contraction is observed. However, it is just a type of illusion. Nothing happens to the fast-moving object. In SR, one can't even say if an object is fast-moving or not, all that matters is relative motion, hence the name "relativity".
Even mentioning rigidity in this context indicates that one hasn't understood what is being discussed.
> > | Such measurements cannot possibly affect the object itself. |
> | I fully agree. Performing a measurement does not physical change the object being measured. The issue ofcourse is that the apparatus used by the moving observer in order to measure should not undergo any physical change. As such in order to study physics you should not use different relative moving observers. |
The point of SR is that moving observers can agree on invariant quantities.
> > | And, of course, there can be many differently-moving observers who measure different values for the "length contraction" of the object, but it clearly has a single actual length. |
> |
IMO it does not make sense to use the results of different observers if they measure different values for the same object. |
The point of SR is that moving observers can agree on invariant quantities.
> > | Yes, all those sloppy authors that say "moving clocks run slow" and "moving rods get shortened" are WRONG. They ought to say "moving clocks are observed to run slow", and "moving objects are observed to be shortened". |
> |
Clifford M.Will at page 273 writes (Was Einstein right): "On the other hand it is rather difficult effect to see experimentally because it is hard to accelerate macroscopic rods to high enough velocities to make the effect noticeable." |
Both true, but the Will quote isn't relative to the one above.
> | My understanding is that time dilation is a physical effects i.e. that moving clocks run slower. |
In this case there is a difference with respect to length contraction. Yes, if the clocks meet up again, the one which changed its direction (at least one has to change its direction, otherwise they couldn't meet again) most is slower.
Note that in this case, the observers with each clock has a different experience, as the change in direction can be noticed. (Sometimes it is said that this involves acceleration---which it must---and thus needs GR to understand---which it doesn't. It isn't the magnitude of the acceleration, or any integral over it, which matters, but rather the path length.
> | My understanding for length contraction is much less clear. I thought (this is for me a question) that length contraction is also a physical effect. If it is not but implies different "observers" which have all different speeds (using moving clocks which all run differently) relative to the object being measured my solution would be to use only one frame and one set of synchronised clocks. |
Sure, you can do that, but the point of SR is that moving observers can agree on invariant quantities.
> |
In article <755668be-ae5a-4bb4-ab23-452590f15168@googlegroups.com>,
Nicolaas Vroom |
> > |
What you indirectly indicate (?) that when you have an observer at rest in front of an object/train at rest and a moving object/train which passes directly infront of the object/train at rest that the observer can never observe any (physical) length contraction when both trains are in front of him. (Assuming that both objects have the same length at rest) |
> |
No. Of course length contraction is observed. However, it is just a type of illusion. |
> | Nothing happens to the fast-moving object. |
> > > | Yes, all those sloppy authors that say "moving clocks run slow" and "moving rods get shortened" are WRONG. They ought to say "moving clocks are observed to run slow", and "moving objects are observed to be shortened". |
> > |
Clifford M.Will at page 273 writes (Was Einstein right): "On the other hand it is rather difficult effect to see experimentally because it is hard to accelerate macroscopic rods to high enough velocities to make the effect noticeable." |
> |
Both true, but the Will quote isn't relative to the one above. |
> > | My understanding is that time dilation is a physical effects i.e. that moving clocks run slower. |
> |
Note that in this case, the observers with each clock has a different experience, as the change in direction can be noticed. (Sometimes it is said that this involves acceleration---which it must---and thus needs GR to understand---which it doesn't. It isn't the magnitude of the acceleration, or any integral over it, which matters, but rather the path length. |
In principle you can perform the whole experiment without acceleration
and only by using clocks at a constant speed.
That means you need 3 Clocks. Clock A is at rest. Clock B moves away from A.
and Clock C moves back to A.
Clock B is set equal to A when they meet. Clock C is set equal to B (later)
when they meet. The difference between A and C is linear function of the
path way.
However that does not mean that acceleration is not involved. In order
to get moving clocks you always need acceleration and this acceleration
can change the behaviour of the clocks and explain what is observed.
Nicolaas Vroom http://users.telenet.be/nicvroom/history_en.htm#par9
> |
If length contraction is an illusion like Terrell rotation which is also
an illusion no physical change is involved.
The problem in Terrell rotation is in the way of measuring.
IMO there are two issues: 1. Different (moving) observers can measure the length of the same object. In that case there can not be any form of length contraction. If the observers measure a different length than there is a problem in the measuring process i.e tools used. 2. Different (moving) observers can measure the length of each other. That means observer A can measure the length of the train of observer B and Observer B can measure the length of the train of Observer A. This is the case IMO where length contraction could become involved. |
Add a third observer moving at a different speed to the second case. He will observe a different amount of length contraction.
You can't somehow make the effect more real by just restricting yourself to the symmetric case of two observers.
> | My understanding is that time dilation is a physical effects i.e. that moving clocks run slower. |
Not in relativity. In relativity (both GR and SR), "time dilation" is a geometrical projection, and no clock is ever affected.
> | My understanding for length contraction is much less clear. |
Hmmmm. Clarity does not equate to correctness. But in relativity, "length contraction" is also a geometrical projection, and no object is ever affected. It is merely projection onto a different axis than "time dilation"; other than that the two are the same.
> | Only physical processes can influence other physical processes. |
OK, as long as you include geometrical properties and relationships in the set of "physical processes". That is, of course rather unusual, so it would be better to abandon this sound bite.
Example: you can carry a ladder through a narrow doorway in some orientations but not others; if you seek a "cause" for this, ultimately you will be forced to accept geometrical relationships (yes, the ladder collides with the door-frame in some orientations, but WHY does it collide?). Ditto for the "cause" of a bullet putting a hole through the target some times, and sometimes not. Etc.
> | [... other confusions and misconceptions] |
Note, please, that the twin paradox does NOT demonstrate "time dilation". Rather, it demonstrates a DIFFERENT geometrical property: the path length between two points can be different for different paths between them. The two points are the twins separating and rejoining; the stay-at-home twin moves inertially between them, and the traveling twin does not -- the difference in their ages (elapsed proper times) is just the difference in path length for these two paths through spacetime. The fact that the traveling twin moved non-inertially is important; the amount of acceleration is not -- what matters is the total path length.
In short: "time dilation" and "length contraction" are differential relationships valid at individual points; both are simple geometrical projections. Path length, on the other hand, is an integral property and applies to paths, not points.
Tom Roberts
> | On 3/18/15 3/18/15 10:31 AM, Nicolaas Vroom wrote: |
>> | My understanding is that time dilation is a physical effects i.e. that moving clocks run slower. |
> |
Not in relativity. In relativity (both GR and SR), "time dilation" is a geometrical projection, and no clock is ever affected. |
In relativity, the time between two events read off from the hands of a moving clock on given curved worldline by any observer is the length of that arc of the worldline
Period
Never there will arise any dispute between observers concerning proper time intervalls. The synchronisation procedures of their laboratory clocks do not enter the definition.
That fact makes the difference between length contraction determined by passages times of the two ends with clocks at rest, length dialation with two comoving clocks and time dilation. Per definition time dilation is the hand rotation rate ratio of a single moving clock and a single clock at rest. There is no ambiguity in observation of time at rest for of a full round completed on the moving clocks face.
--
Roland Franzius
> | Am 26.03.2015 um 09:07 schrieb Tom Roberts: |
> > | On 3/18/15 3/18/15 10:31 AM, Nicolaas Vroom wrote: |
> >> | My understanding is that time dilation is a physical effects i.e. that moving clocks run slower. |
> > |
Not in relativity. In relativity (both GR and SR), "time dilation" is a geometrical projection, and no clock is ever affected. |
> |
In relativity, the time between two events read off from the hands of a moving clock on given curved worldline by any observer is the length of that arc of the worldline |
That may be true. But what does it practically means when you perform an experiment. Does this imply that the time of two clocks which are the same at the start of an experiment can be different at the end?
> | Period |
> | That fact makes the difference between length contraction determined by passages times of the two ends with clocks at rest, length dialation with two comoving clocks and time dilation. |
This sentence is not clear. Do you always need clocks to determine length contraction?
> | Per definition time dilation is the hand rotation rate ratio of a single moving clock and a single clock at rest. |
Is this number always less than 1?
> | There is no ambiguity in observation of time at rest for of a full round completed on the moving clocks face. |
Tricky sentence.
Nicolaas Vroom
N. David Mermin
"Space and Time in Special Relativity"
McGraw-Hill, 1968
Waveland Press, 1989
ISBN 0-88133-420-0 (paperback)
Even though it's nominally about general relativity, you can also get a lot of insights into special relativity from
Op donderdag 26 maart 2015 09:07:11 UTC+1 schreef Tom Roberts:
> | On 3/18/15 3/18/15 10:31 AM, Nicolaas Vroom wrote: |
> > | My understanding is that time dilation is a physical effects i.e. that moving clocks run slower. |
> |
Not in relativity. In relativity (both GR and SR), "time dilation" is a geometrical projection, and no clock is ever affected. |
Understanding starts by performing experiments.
Experiments with moving clocks are described in "Was Einstein right"
by Clifford M. Will at the pages 54 to 61.
(Chapter The gravitational Red Shift of Light and Clocks)
At page 56 we read: "Thus time dilation makes the flying clock run slowly
relative to the ground clock"
This is in conflict with your claim that "no clock is ever affected"
The next step is to explain this (physical?) behaviour.
> > | My understanding for length contraction is much less clear. |
> |
Hmmmm. Clarity does not equate to correctness. But in relativity, "length contraction" is also a geometrical projection, and no object is ever affected. It is merely projection onto a different axis than "time dilation"; other than that the two are the same. |
The issue is first to what extend you can demonstrate length contraction without moving clocks. At page 273 of the mentioned book is written that these experiments are difficult.
See: http://www.physicsclassroom.com/mmedia/specrel/lc.cfm This document claims: "The object is actually contracted in length as seen from the stationary reference frame. "
> > | Only physical processes can influence other physical processes. |
> |
OK, as long as you include geometrical properties and relationships in the set of "physical processes". That is, of course rather unusual, so it would be better to abandon this sound bite. |
My problem is that if time dilataion nor length contraction are physical processes
they cannot be used to explain other processes.
This raises a whole new issue: How important is SR as a physical law?
> | The fact that the traveling twin moved non-inertially is important; the amount of acceleration is not -- what matters is the total path length. |
It is the acceleration part IMO that is important that the clocks start to behave differently. It is the path length that is important how much the clocks behave different in total
> | In short: "time dilation" and "length contraction" are differential relationships valid at individual points; both are simple geometrical projections. |
Nicolaas Vroom http://users.telenet.be/nicvroom/history_en.htm
> | Op donderdag 26 maart 2015 18:22:14 UTC+1 schreef Roland Franzius: |
>> | [discussion of "tme dilation" vs. path length] |
> | That may be true. But what does it practically means when you perform an experiment. Does this imply that the time of two clocks which are the same at the start of an experiment can be different at the end? |
Yes, of course. Real experiments have been performed that display this difference.
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html (Section 5. Tests of the Twin paradox)
> | Do you always need clocks to determine length contraction? |
The standard way to measure the length of a moving object is to prepare synchronized clocks along its path, all at rest in an inertial frame, and then mark the front and back of the moving object simultaneously in that frame, then measure the distance between marks in that frame. This clearly requires clocks, or some equivalent method of marking/measuring front and rear simultaneously.
>> | Per definition time dilation is the hand rotation rate ratio of a single moving clock and a single clock at rest. |
> |
Is this number always less than 1? |
Yes [#], remembering that it is a differential comparison applied at a single point. Of course that is implicit in a comparison between a single moving clock and a single clock at rest.
[#] This has to do with the structure of Minkowski geometry.
> | Experiments with moving clocks are described in "Was Einstein right" by Clifford M. Will at the pages 54 to 61. (Chapter The gravitational Red Shift of Light and Clocks) At page 56 we read: "Thus time dilation makes the flying clock run slowly relative to the ground clock" This is in conflict with your claim that "no clock is ever affected" |
Will is writing for a general audience in that book, and has taken some shortcuts. He certainly knows this statement is technically incorrect, but apparently figured that to explain the subtleties to a lay audience would take the text too far afield.
> | My problem is that if time dilataion nor length contraction are physical processes they cannot be used to explain other processes. |
That is YOUR problem, not SR's not mine. You need to broaden your horizons: geometry _DOES_ explain certain "physical" facts, such as the ability to carry a ladder through a narrow doorway in some orientations but not others. Geometry also explains "time dilation" and "length contraction", and related physical phenomena (long pion beams, magnetic forces, ...).
> | This raises a whole new issue: How important is SR as a physical law? |
It has proven to be utterly indispensable in modern physics -- EVERY physical theory we have today has SR in its foundations.
> | Is my understanding correct that geometrical projections are something like: If we both slowly move away from each other we both see each other smaller? |
Yes, that is another geometrical effect.
> | If that is the case (exactly) with "time dilation" and "length contraction" than ofcourse both effects are not physical. |
But note that this geometrical effect has physical consequences -- as we move apart we can see each other through smaller apertures.
You attempt to divorce "physical effects" from geometry. THAT IS NOT POSSIBLE. EVERY physical theory has geometry at its base. Newton and Galileo implicitly assumed Euclidean geometry, which pervaded their discussions. Modern physics is based on Minkowskian geometry, not Euclidean; the experimental record fully justifies this change.
You need to broaden your horizons and learn about SR and modern physics. This is not a suitable medium for that -- get some good textbooks and STUDY. You will remain mystified until you do. The moderator gave some good suggestions.
Tom Roberts
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