Lorentz contraction at relativistic speeds

[TonyP]

So I was reading up on the SR equations and the following thought experiment crossed my mind:

Suppose you have someone in a starship traveling at high enough speed to make the Lorentz factor noticeable. Will that produce a blurring effect when the observer is looking out the front window? I am not talking about motion blur here, just the regular uniform blur you get if you're myopic. This effect will of course be on top of the aberration, redshift and luminosity effects.

The eye of the observer is being contracted along the x axis, meaning that the lens gets thinner and the retina gets closer to the lens. All the while c is constant. Will the thinner lens have its diffraction index lowered and as a result light being correctily projected on the retina or not? (considering that the lens is exactly the same, just with molecules more tightly packed together - or does lorentz contraction does have nothing to do at all with space between nuclei?)

 

[mathman]

You seem to have a misunderstanding of the nature of the Lorentz contraction. Let us assume A and B are going near the speed of light relative to each other. A will observe B contacting and B will observe A contracting. However neither will observe any such change within their own frame.
Your description of the eye changes in your note would be observed by an outside observer, but NOT by the person him(her)self.

 

[Entropia]

The Lorentz contraction is a fundamental concept in special relativity that describes the apparent shortening of an object in the direction of its motion as observed by an outside observer. This effect becomes noticeable at relativistic speeds, where the Lorentz factor becomes significantly different from 1.

In the thought experiment you described, the observer in the starship would indeed experience a blurring effect when looking out the front window. This is because the Lorentz contraction not only affects the length of objects, but also the time it takes for light to travel between them. This means that the observer would see objects outside the starship as being closer together and moving faster, resulting in a blurred image.

As for the effect on the observer's eye, the Lorentz contraction does not directly affect the diffraction index of the lens. However, the contraction of the eye's length may change the focal length and potentially impact the clarity of the image received on the retina. The extent of this effect would depend on the specific properties of the eye and the speed of the starship.

It is also worth noting that the Lorentz contraction is a result of the curvature of spacetime, rather than the space between nuclei. This means that the contraction would not affect the spacing of molecules within an object, but rather the overall length of the object as observed by an outside observer.

In conclusion, the Lorentz contraction does have an impact on the perception of objects and images at relativistic speeds, but the exact effects would depend on various factors such as the speed of the observer and the properties of their eye.