Is relativistic effect of length contraction physically unreal ?

In summary: Frame 10) to the object in frame 1 would show that the object in Frame 10 measured shorter then the object in Frame 1 because in Frame 10 the object would be measured against a gradient of reference frames where the denser layers correspond to shorter distances. So... if you imagine a square with the universe inside it and imagine that each frame of reference corresponds to a different distance from the center of the square, then the density of the universe would be different in different frames of reference.
  • #1
feynmann
156
1
Is relativistic effect of length contraction physically "unreal"?

One guru indicate that Length contraction has nothing to do with compression.
It is more correct to view length contraction as a rotation in space time.
If we rotate a box filled with gas or perfect fluid, clearly its density does not change.
Suppose the box is accelerated to speed close to the speed of light. Its length will be shorten due to Lorentz contraction. My question is this: Will the density of the box increase with its speed?

Length contraction has nothing to do with compression. Remember that the observer moving with the rod measures the same length at all times so nothing is being compressed.

It is more correct to view length contraction as a rotation in space time. Have a friend hold a meter stick some distance way from you perpendicular to the line between the 2 of you. From a distance do a measurement. Now have your friend rotate the meter stick 45deg, measure it again. Now from your view point it is shorter then it was before. :
 
Physics news on Phys.org
  • #2


feynmann said:
It is more correct to view length contraction as a rotation in space time.
A rotation in spacetime, not space. (That bit with the meterstick was just an analogy.)
If we rotate a box filled with gas or perfect fluid, clearly its density does not change.
Why would it?
Suppose the box is accelerated to speed close to the speed of light. Its length will be shorten due to Lorentz contraction. My question is this: Will the density of the box increase with its speed?
Sure. (According to an observer seeing it move.)
 
  • #3


feynmann said:
Will the density of the box increase with its speed?
How do you define the density of a moving object? (If you use standard definitions then yes)
 
  • #4


feynmann said:
It is more correct to view length contraction as a rotation in space time.
A rotation in space is a linear map [itex]x\mapsto Rx[/itex], where R satisfies [itex]R^TR=1[/itex] and can be made to go 1 by continuously changing the parameters that R depends on (3 euler angles). A restricted (i.e. homogeneous, proper and orthochronous) Lorentz transformation is a map [itex]x\mapsto\Lambda x[/itex], where [itex]\Lambda[/itex] satisfies [itex]\Lambda^T\eta\Lambda=\eta[/itex], and can be made to go 1 by continuously changing the parameters that [itex]\Lambda[/itex] depends on (3 euler angles and 3 velocity components). So you can view it as a rotation if you'd like, but it's clearly a generalization of that concept.

[tex]\eta=\begin{pmatrix}-1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\\ \end{pmatrix}[/tex]
 
  • #5


My question is this: Will the density of the box increase with its speed?

Seems like an increase in density is related to length contraction as well as relativistic mass increase?

Dalespam posted:
How do you define the density of a moving object? (If you use standard definitions then yes)

Could you explain this? I suspect there is a subtley I don't see...in other words, why might one consider a "non standard" definition...
 
  • #6


Naty1 said:
Could you explain this? I suspect there is a subtley I don't see...in other words, why might one consider a "non standard" definition...
Well, it's like anything else in relativity, you can define different meanings for the same terms and come out with different conclusions. For example, you can say "mass" and you can mean "rest mass" or "relativistic mass". You can also say "length" and you can mean "coordinate length" or "proper length" or even "spacetime interval". So something like mass/length³ can mean a lot of subtly different things and thus there is a lot of wiggle-room for different definitions in a word like "density" in relativity.
 
  • #7


feynman, suppose we imagine that the entire universe was contained within an area of a finite square "Imagine a square". The interior of the square is the universe. Now draw a line down the middle of the square and imagine that to the left of the line is homogenous matter and that to the right of the line is empty space. now imagine that the entire portion of empty space is a gradient of reference frames (think like... a beaker with a series of fluids, let's say 10 of them of varying densities from greatest to least density). Each of these different layers corresponds to a different frame of reference. Within each frame of reference we understand the concept of 1 meter and 1 meter equals 1 meter so long as we are measuring within that frame of reference. But... If I were to measure an object, which measured 1 meter while measured by a meter stick within a mutual frame of reference (Frame of reference 1) then they would both appear the same length. But... comparing the measurement of another object a particular frame of reference (frame of reference 2) with a meter stick from another frame of reference (frame of reference 3), the object which is in frame of reference 2 would not measure 1 meter RELATIVE to this other frame of reference (frame of reference 3).

"Warped space" is comprised of a continuous "density" gradient of space-time. Where each gradation is a particular reference frame only there are an infinite amount of them.
 
  • #8


Dalespam, thanks for your post #6...
 
  • #9


You're welcome!

Hopefully, the OP will define the density of a moving object and then the thread can proceed.
 
  • #10


Fredrik said:
A rotation in space is a linear map [itex]x\mapsto Rx[/itex], where R satisfies [itex]R^TR=1[/itex] and can be made to go 1 by continuously changing the parameters that R depends on (3 euler angles). A restricted (i.e. homogeneous, proper and orthochronous) Lorentz transformation is a map [itex]x\mapsto\Lambda x[/itex], where [itex]\Lambda[/itex] satisfies [itex]\Lambda^T\eta\Lambda=\eta[/itex], and can be made to go 1 by continuously changing the parameters that [itex]\Lambda[/itex] depends on (3 euler angles and 3 velocity components). So you can view it as a rotation if you'd like, but it's clearly a generalization of that concept.

[tex]\eta=\begin{pmatrix}-1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1\\ \end{pmatrix}[/tex]

One of the reason that the rotation in spacetime analogy breaks down is that it is not ordinary rotation of coordinates, sine and cosine function. The Lorentz transformation can be seen as a hyperbolic rotation of coordinates in Minkowski space, where the rapidity φ represents the hyperbolic angle of rotation.

Hyperbolic rotation of coordinates:
http://en.wikipedia.org/wiki/Lorentz_transformation#Hyperbolic_trigonometric_expressions

It is more correct to view length contraction as a rotation in space time. Have a friend hold a meter stick some distance way from you perpendicular to the line between the 2 of you. From a distance do a measurement. Now have your friend rotate the meter stick 45deg, measure it again. Now from your view point it is shorter then it was before.
 
Last edited:
  • #11


In other words length contraction is physically real.
 
  • #12


feynmann said:
One guru indicate that Length contraction has nothing to do with compression.
It is more correct to view length contraction as a rotation in space time.
If we rotate a box filled with gas or perfect fluid, clearly its density does not change.
You're omitting an important part of the analogy -- the 'point of view'. No matter how you orient a meterstick in Euclidean space, it will be a meter long. But when we 'observe' the meterstick by making and studying a two-dimensional image (e.g. a photograph, or the image made in our eyes), the orientation of the meterstick affects its size in the image.

The correspondence with space-time is that no matter how you orient (the worldsheet of) something in 4-dimensional space-time, it will look the same. But if we 'observe' the object by looking at a 3-dimensional picture (e.g. by choosing coordinates, and then looking at the 3-dimensional spatial image taken at a particular moment of coordinate time), it's orientation will affect how it looks.


Incidentally, a better analogy with the meterstick is to look at its cross-sections. Suppose you have a 1 m x 3 cm x 1 cm meterstick. (I don't know what dimensions are normal, so I made them up!) Let's orient it so that the 1m axis is pointing North/South, and the 3cm axis is pointing East/West, and the 1cm axis is pointing Up/Down. If you take a 2-dimensional cross section in tne Up/East plane, you will see a 3 cm x 1 cm rectangle. However, if you change your orientation by rotating the plane 30 degrees about the up axis, your cross sections are now 3.5 cm x 1 cm. Voilà, 'length expansion'. (We get expansion instead of contraction because of the sign difference between Euclidean and Minkowski spaces)
 
Last edited:
  • #13


feynmann said:
One of the reason that the rotation in spacetime analogy breaks down is that it is not ordinary rotation of coordinates, sine and cosine function.
The rotation analogy for length contraction works better if you use space-propertime, instead of Minkowski spacetime:
http://www.adamtoons.de/physics/relativity.swf
 

1. Is the relativistic effect of length contraction a real phenomenon?

The relativistic effect of length contraction is a well-established concept in the theory of relativity, which has been extensively tested and confirmed through various experiments and observations. Therefore, it can be considered a real phenomenon in the physical world.

2. How does length contraction occur in the theory of relativity?

According to the theory of relativity, length contraction occurs when an object moves at a high speed relative to an observer. This causes the object to appear shorter in the direction of its motion, as observed by the observer. This phenomenon is a result of the time dilation effect and the constancy of the speed of light.

3. Is length contraction only applicable to objects moving at very high speeds?

Yes, length contraction is a relativistic effect that is only observed at speeds close to the speed of light. At lower speeds, the effect is negligible and cannot be detected. This is because the magnitude of length contraction is directly proportional to the speed of the object relative to the observer.

4. Can length contraction be observed in everyday life?

No, length contraction is only noticeable at speeds close to the speed of light, which is not achievable in everyday situations. The effects of length contraction are only significant for objects moving at speeds of at least 30% of the speed of light.

5. Does length contraction violate the laws of physics?

No, length contraction does not violate any laws of physics. It is a consequence of the theory of relativity, which is a well-established and extensively tested theory. The effects of length contraction are consistent with the principles of special relativity and do not contradict any fundamental laws of physics.

Similar threads

  • Special and General Relativity
Replies
14
Views
221
Replies
63
Views
2K
  • Special and General Relativity
Replies
7
Views
972
  • Special and General Relativity
Replies
2
Views
1K
  • Special and General Relativity
Replies
12
Views
734
  • Special and General Relativity
3
Replies
72
Views
4K
  • Special and General Relativity
Replies
1
Views
501
  • Special and General Relativity
Replies
12
Views
757
  • Special and General Relativity
Replies
11
Views
952
  • Special and General Relativity
Replies
11
Views
1K
Back
Top