What is the Interpretation of Length Contraction in Special Relativity?

  • Thread starter cos
  • Start date
  • Tags
    Rotation
In summary, Weisskopf and Katz discuss the concept of length contraction in the context of special relativity. They present diagrams depicting the visual appearance of a cube in motion, with Weisskopf's showing the cube as a rectangle and Katz's showing it as a square. They also discuss the interpretation of this visual distortion, with Weisskopf stating that objects appear rotated while Katz suggests that it is more of a perspective distortion.
  • #1
cos
212
0
In his book 'An Introduction to the Special Theory of Relativity' (46, East-West, 1964) Robert Katz presents Weisskopf's depiction (Physics Today, 13, 24 1960) of length contraction showing that a cube that is moving past a stationary observer will be 'interpreted' as being tilted toward the observer and raised upwards in its direction of travel whilst a photograph that he takes will not show the cube as being 'bent and rotated'.

Is this what STR shows will take place or is it just Weisskop's 'interpretation' of what STR shows?
 
Last edited:
Physics news on Phys.org
  • #2
cos said:
Is this what STR shows will take place or is it just Weisskop's 'interpretation' of what STR shows?

I'm not sure, but I think Weisskopf's article is a semi-popular exposition of papers published independently in 1959 by Terrell and Penrose. Look up Terrell rotation, or Terrell-Penrose rotation, or Penrose-Terrell rotation.
 
  • #3
cos said:
In his book 'An Introduction to the Special Theory of Relativity' (46, East-West, 1964) Robert Katz presents Weisskopf's depiction (Physics Today, 13, 24 1960) of length contraction showing that a cube that is moving past a stationary observer will be 'interpreted' as being tilted toward the observer and raised upwards in its direction of travel whilst a photograph that he takes will not show the cube as being 'bent and rotated'.
I think it is the other way around: The cube will be measured/interpreted to be just Lorentz contracted along it's movement direction. But a camera/eye will see it rather bent and rotated, but not contracted:
http://www.spacetimetravel.org/bewegung/bewegung5.html
http://www.spacetimetravel.org/fussball/fussball.html
 
  • #4
i think this can vizualised in 3D view since the dimension of any object are relative to speed of the object i will think on it again if u send that picture
 
  • #5
Like A.T., I think the wording in the original post could be better.
The Visual Appearance of Rapidly Moving Objects said:
... We all believed that, according to special relativity, an object in motion appears to be contracted in the direction of motion ... A passenger in a fast space ship, looking out of the window, so it seemed to us, would see spherical objects contracted to ellipsoids. This is definitely not so according to Terrell's considerations ...The reason is quite simple ... The points further away from have emiitted their part of the picture earlier than the closer points ... the eye or the photograph gets a "distorted" picture of the object, since the object has been at different locations when different parts of it have emitted the light seen in the picture.

In special relativity, this distortion has the remarkable effect of canceling the Lorentz contraction so that objects appear undistorted but only rotated.This is exactly true only for objects which subtend a small solid angle.

... This must not by any means be interpreted as indicating that there is no Lorentz contraction. Of course there is Lorentz contraction ...
 
  • #6
George Jones said:
Like A.T., I think the wording in the original post could be better.


Originally Posted by The Visual Appearance of Rapidly Moving Objects, V. S. Weisskopf, Physics Today, Sept. 1960

... We all believed that, according to special relativity, an object in motion appears to be contracted in the direction of motion ... A passenger in a fast space ship, looking out of the window, so it seemed to us, would see spherical objects contracted to ellipsoids. This is definitely not so according to Terrell's considerations ...The reason is quite simple ... The points further away from have emiitted their part of the picture earlier than the closer points ... the eye or the photograph gets a "distorted" picture of the object, since the object has been at different locations when different parts of it have emitted the light seen in the picture.

In special relativity, this distortion has the remarkable effect of canceling the Lorentz contraction so that objects appear undistorted but only rotated.This is exactly true only for objects which subtend a small solid angle.

... This must not by any means be interpreted as indicating that there is no Lorentz contraction. Of course there is Lorentz contraction ...

In that article http://18.181.0.31/afs/athena/course/8/...sskopf.pdf [Broken] Weisskopf (as does Katz' dia c Fig. 2-8.1) depicts the observer's view as well as his photograph showing a square face of the cube A B C D with, as a rectangular extension, the left face A B E F fig.1 Relativistic.

Katz wrote that the photographer then interprets that photograph as representing a rotated cube. Weisskopf, above, wrote that objects appear rotated although his fig.1 Relativistic shows that it is not.

On what basis does Katz' photographer interpret a cube that is not rotated as being rotated?

On what basis does Weisskopf's observer see an non-rotated cube as being rotated?
 
Last edited by a moderator:
  • #7
cos said:
In that article http://18.181.0.31/afs/athena/course/8/...sskopf.pdf [Broken]
Doesn't work for me (404 File Not Found)
cos said:
On what basis does Katz' photographer interpret a cube that is not rotated as being rotated?
On what basis does Weisskopf's observer see an non-rotated cube as being rotated?
These statements seem contradictory. It depends what they mean by "interpret" and "see", but the second one seems more correct to me, Although 'rotation' is not exactly correct. It's more a perspective distortion (see links in post #3)
 
Last edited by a moderator:
  • #8
A.T. said:
Doesn't work for me (404 File Not Found)

It connects in other groups but perhaps try 'The Visual Appearance of Rapidly Moving Objects' V.F.Weisskopf, (Physics Today, 13, 24, 1960).

On what basis does Katz' photographer interpret a cube that is not rotated as being rotated?
On what basis does Weisskopf's observer see an non-rotated cube as being rotated?

These statements seem contradictory. It depends what they mean by "interpret" and "see", but the second one seems more correct to me, Although 'rotation' is not exactly correct. It's more a perspective distortion (see links in post #3)

Having printed Weiskopf's article I find that his diagram 'Relativistic Fig. 1' shows that the side of the cube facing the observer, ABCD, is not a square as Katz depicted (and as I wrongly assumed on the basis of the screen image) but is a rectangle.

Weisskopf (and Katz) include in their diagrams the left-hand face of the cube ABEF also as a rectangle however the 'rotation' is obviously nothing more than a perspective distortion created by the aberration of light.
 
  • #9
cos said:
... a cube that is moving past a stationary observer will be 'interpreted' as being tilted toward the observer and raised upwards in its direction of travel...

In STR an observer in a given reference frame is actually a group of many observers all at rest with respect to each other and all with synchronised clocks. There are so many observers, that at any given time there would be one observer right next to a given part of the cube, eg a corner. If they plot the locations of the observers that happen to be right next to a corner at a given time, they would construct a composite measurement of the cube on a map, to be length contracted in its direction of travel, but otherwise undistorted or rotated. This is a measure, rather than what any individual sees. This method of measuring the moving cube elliminates all distortions due to light travel times.
cos said:
... whilst a photograph that he takes will not show the cube as being 'bent and rotated'.

Ok, we should be clear that what a single observer "sees" and what a camera records is essentially the same. In the original Penrose-Terrell analysis, they went so far as to specify a camera with a curved backplate to better simulate a human eyeball. What the eye or camera sees at the time the image is recorded on the back of the camera or eye, is a composition of points on the cube at different times. Light from the trailing edge of an aproaching cube left at a time when the cube was further away, than where the cube was when light left the leading edge of the cube. The end result of the distortion due to light light travel times, is that a moving object appears rotated and stretched. This stretching distortion is largely canceled by actual length contraction, so that so that in the case of a small sphere, the sphere appears neither stretched nor compressed (only rotated) to a single observer. It should be noted that the normal appearance of a moving sphere to a single observer or camera, requires the sphere to be length contracted in the first place.

It would appear that you have misinterpreted Weisskop's 'interpretation', which is consistent with STR.
 
Last edited:

1. What is length contraction in special relativity?

Length contraction in special relativity is the phenomenon where the length of an object appears shorter when it is moving at high speeds relative to an observer. This is a consequence of Einstein's theory of special relativity, which states that the laws of physics are the same for all observers moving at a constant velocity.

2. How does length contraction occur?

Length contraction occurs due to the time dilation effect in special relativity. As an object moves at high speeds, time appears to pass slower for the moving object compared to the observer. This causes the distance between two points on the moving object to appear shorter to the observer.

3. What is the equation for length contraction?

The equation for length contraction is L = L0 / γ, where L is the contracted length, L0 is the rest length of the object, and γ is the Lorentz factor. The Lorentz factor takes into account the velocity of the object relative to the observer and is given by γ = 1 / √(1 - v^2/c^2), where v is the velocity of the object and c is the speed of light.

4. Does length contraction only occur for objects moving at the speed of light?

No, length contraction can occur for objects moving at any speed, as long as it is a significant fraction of the speed of light. However, at speeds much lower than the speed of light, the effect of length contraction is negligible and cannot be observed.

5. How does length contraction affect measurements in experiments?

Length contraction can affect measurements in experiments where the object being measured is moving at high speeds. This can result in a discrepancy between the measured length and the actual length of the object. To account for this, scientists must take into consideration the effects of length contraction when conducting experiments involving high-speed objects.

Similar threads

  • Special and General Relativity
3
Replies
78
Views
3K
  • Special and General Relativity
2
Replies
60
Views
2K
  • Special and General Relativity
Replies
6
Views
1K
  • Special and General Relativity
3
Replies
83
Views
3K
  • Special and General Relativity
Replies
17
Views
2K
  • Special and General Relativity
2
Replies
40
Views
3K
Replies
32
Views
852
  • Special and General Relativity
Replies
33
Views
2K
  • Special and General Relativity
Replies
21
Views
1K
  • Special and General Relativity
Replies
6
Views
3K
Back
Top