Is length contraction an actual occurrence or merely an optical illusion?

[smithnya]

Hello everyone.

I was thinking about length contraction in Special Relativity last night. I looked up information on the internet, and from what I understand, length contrtaction has never been measured (I'm not completely sure if I simply failed to find information to the contrary). So my question is: Is length contraction an actual occurrence or merely an optical illusion?

 

[Bloodthunder]

It has been verified indirectly before.

http://en.wikipedia.org/wiki/Length_contraction#Experimental_verifications

Length contraction is an actual occurrence.

 

[bobc2]

Hello everyone.

I was thinking about length contraction in Special Relativity last night. I looked up information on the internet, and from what I understand, length contrtaction has never been measured (I'm not completely sure if I simply failed to find information to the contrary). So my question is: Is length contraction an actual occurrence or merely an optical illusion?

smithnya, One way of thinking about the length contraction is to not consider that an object contracts at all. Rather, think of the universe as 4-dimensional occupied by 4-dimensional objects that extend billions of miles along a 4th dimension. Different observers (moving at relativistic speeds relative to each other) "live" in different 3-dimensional cross-sections of the 4-dimensional universe and therefore have different cross-section views of the same 4-dimensional object. The object itself, being 4-dimensional, does not do any contracting itself--it's just that different 3-D lengths would be measured by different observers just because of the different views of the same unchanging objective 4-D object.

Brian Greene's book (and video) depict the analagous slicing a loaf of bread at different angles yielding different widths of bread slices. So, it depends on the cross-section angle one uses for slicing the bread. The relative speeds of different observers determines the angle that the "bread" will be sliced (the angle of the 3-D cross-section of the 4-D object).

 

[smithnya]

smithnya, One way of thinking about the length contraction is to not consider that an object contracts at all. Rather, think of the universe as 4-dimensional occupied by 4-dimensional objects that extend billions of miles along a 4th dimension. Different observers (moving at relativistic speeds relative to each other) "live" in different 3-dimensional cross-sections of the 4-dimensional universe and therefore have different cross-section views of the same 4-dimensional object. The object itself, being 4-dimensional, does not do any contracting itself--it's just that different 3-D lengths would be measured by different observers just because of the different views of the same unchanging objective 4-D object.

Brian Greene's book (and video) depict the analagous slicing a loaf of bread at different angles yielding different widths of bread slices. So, it depends on the cross-section angle one uses for slicing the bread. The relative speeds of different observers determines the angle that the "bread" will be sliced (the angle of the 3-D cross-section of the 4-D object).

Ok, I think I understand better. Then essentially a measurement at different speeds would be analogous to a measurement of the cross-sectionof the loaf of bread at different angles? So let me ask something else: does the concept of length contraction then imply that it accours at any speed and not simply at relativistic speeds?

 

[ghwellsjr]

Length contraction is just as much an actual occurrence as time dilation is. Neither are optical illusions. Nobody doubts the reality of time dilation because there is experimental evidence for it. However, a moving clock would not keep the same time if it traveled in different orientations if length contraction did not occur hand in hand with time dilation.

For example, a moving light clock where the beam is bouncing at right angles to the direction of motion experiences no length contraction but if it were rotated so that the beam is bouncing along the direction of motion, it needs length contraction in order to "tick" at the same rate.

 

[harrylin]

Hello everyone.

I was thinking about length contraction in Special Relativity last night. I looked up information on the internet, and from what I understand, length contrtaction has never been measured (I'm not completely sure if I simply failed to find information to the contrary). So my question is: Is length contraction an actual occurrence or merely an optical illusion?

Combine Kennedy-Thorndike:

http://en.wikipedia.org/wiki/Kennedy–Thorndike_experiment

with the fact that time-dilation has been positively measured,
and you obtain a positive answer.

Cheers,
Harald

PS I now see that this was already mentioned by ghwellsjr; anyway I gave a reference for it. :-)

 

[bobc2]

Ok, I think I understand better. Then essentially a measurement at different speeds would be analogous to a measurement of the cross-sectionof the loaf of bread at different angles?

Yes, you've got it.

So let me ask something else: does the concept of length contraction then imply that it accours at any speed and not simply at relativistic speeds?

Yes. The contraction is so small with the every day speeds we normally observe that you cannot detect it witht he naked eye. Someone here will probably give you the algebraic equation for computing the contracted length for an object moving at any velocity, v. You can calculate how small or how large the contracted length is if you insert a small velocity or a very large velocity into the formula.

 

[smithnya]

Combine Kennedy-Thorndike:

http://en.wikipedia.org/wiki/Kennedy–Thorndike_experiment

with the fact that time-dilation has been positively measured,
and you obtain a positive answer.

Cheers,
Harald

PS I now see that this was already mentioned by ghwellsjr; anyway I gave a reference for it. :-)

Thank you. I appreciate it much.

 

[smithnya]

Yes, you've got it.




Yes. The contraction is so small with the every day speeds we normally observe that you cannot detect it witht he naked eye. Someone here will probably give you the algebraic equation for computing the contracted length for an object moving at any velocity, v. You can calculate how small or how large the contracted length is if you insert a small velocity or a very large velocity into the formula.

Is there any theory as to the mechanism by which length contraction happens that you know of? Length contraction is an alteration of the geometry of matter, isn't it?

 

[ghwellsjr]

Is there any theory as to the mechanism by which length contraction happens that you know of? Length contraction is an alteration of the geometry of matter, isn't it?

You might find something of interest here:

http://en.wikipedia.org/wiki/History_of_special_relativity

 

[bobc2]

Is there any theory as to the mechanism by which length contraction happens that you know of? Length contraction is an alteration of the geometry of matter, isn't it?

Remember, there is no contraction at all of the 4-dimensional object. Again, it's just that the different observers have different 3-D cross-section views of the same 4-D object.

A more fundamental question might be, "Why does each observer's X1 axis always rotate so that a photon world line would always bisect the angle between X1 and X4? This is a very mysterious aspect of special relativity. And along with this is the aspect that the 4-D world lines of all objects are organized (oriented) in a manner such that the laws of physics are the same in every one of the different sequences of 3-D cross-sections.

To emphasize: Each observer moves along his unique world line (along his X4 dimension), observing a continuous sequence of 3-D worlds (observers with motion relative to each other observe different 3-D worlds). Yet, the SAME laws of physics hold true for every observer's sequence of 3-D worlds. The unique aspect of the different Affine coordinate systems with the Lorentz transformation relationships (rotation of X1 such that photon world lines bisect the angle between X1 and X4) makes this magic work.

 

[bobc2]

Here is a fanciful sketch of a 4-dimensional beam. We have a black coordinate system representing a "rest frame" along with a blue coordinate system representing the inertial frame associated with a blue guy moving relative to the rest frame. A beam is moving along with the blue guy. Note that the moving frame and the rest frame have different instantaneous 3-D cross-section views of the 4-dimensional beam. The green hypergeometric men have no problem understanding the situation--they can view all 4-dimensions at once--but we humans can only view one instantaneous 3-D cross-section at one instant of time.

 

[smithnya]

Remember, there is no contraction at all of the 4-dimensional object. Again, it's just that the different observers have different 3-D cross-section views of the same 4-D object.

A more fundamental question might be, "Why does each observer's X1 axis always rotate so that a photon world line would always bisect the angle between X1 and X4? This is a very mysterious aspect of special relativity. And along with this is the aspect that the 4-D world lines of all objects are organized (oriented) in a manner such that the laws of physics are the same in every one of the different sequences of 3-D cross-sections.

To emphasize: Each observer moves along his unique world line (along his X4 dimension), observing a continuous sequence of 3-D worlds (observers with motion relative to each other observe different 3-D worlds). Yet, the SAME laws of physics hold true for every observer's sequence of 3-D worlds. The unique aspect of the different Affine coordinate systems with the Lorentz transformation relationships (rotation of X1 such that photon world lines bisect the angle between X1 and X4) makes this magic work.

Ugghh all of it makes my head spin :) I understand the basic concept, but I'm having difficulty rationalizing and picturing it in my head. Thanks for your explanation nevertheless. It cleared a lot up.

 

[smithnya]

Here is a fanciful sketch of a 4-dimensional beam. We have a black coordinate system representing a "rest frame" along with a blue coordinate system representing the inertial frame associated with a blue guy moving relative to the rest frame. A beam is moving along with the blue guy. Note that the moving frame and the rest frame have different instantaneous 3-D cross-section views of the 4-dimensional beam. The green hypergeometric men have no problem understanding the situation--they can view all 4-dimensions at once--but we humans can only view one instantaneous 3-D cross-section at one instant of time.

Awesome. Thank you so much! This helps me vizualize it.