Exploring Length Contraction: Mechanisms and Implications in Relativistic Speeds

[keepit]

Given that molecules, atoms, protons, and neutrons are overwhelmingly space (i assume quarks and electrons are more than just fields), when an object reaches relativistic speeds, is length contraction the result of a decrease in the geometric space within the molecules, or is it a decrease in the distance between molecules? What is the underlying mechanism of the contraction and why is it only in the dimension of length (or is it only length contraction)? If it is shrinkage of quarks and electrons could there be enough shrinkage in those particles to account for the amount of length contraction of the object?

 

[haael]

is length contraction the result of a decrease in the geometric space within the molecules, or is it a decrease in the distance between molecules?

Provided there is no absolute space, these sentences are equivalent.

What is the underlying mechanism of the contraction and why is it only in the dimension of length (or is it only length contraction)?

The undelying mechanism is the Minkowski space. The contraction is not only in the dimension of length; time also contracts.

In the Minkowski space distance depends on the perspective. The distance between two points can be seen differently depending on your state.
Imagine a pen laying on a table. When you look at it from the top, it has some length. Now look at it from an angle. It will look shrunken.
In Minkowski space it is much the same. The "angle" is your speed relative to the observed object.

If it is shrinkage of quarks and electrons could there be enough shrinkage in those particles to account for the amount of length contraction of the object?

If quarks and leptons are point objects, then they don't shrink, since they already have zero length. If they are not point-like, then you will see them as shrunken, as well as closer to each other.

 

[ghwellsjr]

Given that molecules, atoms, protons, and neutrons are overwhelmingly space (i assume quarks and electrons are more than just fields),

That's just because in some models they are points occupying no space but that is an oversimplification. Just consider the fact that an electron and a positron can interact to completely annihilate each other. How are you going to illustrate that going from two point particles to no point particles? The same thing holds true for all other particles and antiparticles.

when an object reaches relativistic speeds, is length contraction the result of a decrease in the geometric space within the molecules, or is it a decrease in the distance between molecules?

Like all scenarios applied to Special Relativity, once you specify the locations as a function of time for each particle and subparticle according to an Inertial Reference Frame (IRF), you can see what it looks like in any other IRF by using the Lorentz Transformation process. Special Relativity will not help you determine how the different particles and subparticles interact during the acceleration process since there are other unspecified factors that you need to supply in order to determine what happens in a single IRF. Those kinds of details are extremely complex. Consider that they all are subject to the speed of light and at the molecular level, this is an extremely short period of time and it takes a relatively long period of time to accelerate a particle to relativistic speeds so you have to specify an enormous amount of detail to describe how the process might work. Suffice it to say that the laws and equations describing the process are themselves subject to the Lorentz Transformation (they must remain unchanged when going through the LT process) and that guarantees that whatever happens will be compatible with Special Relativity. In general, you can say at the molecular level, whatever distances there are between the different particles according to their "average" rest frame will be the same in their new "average" rest frame after acceleration to relativistic speed, but how they get from one state to the other is beyond the scope of Special Relativity because you haven't specified the forces that cause the acceleration. I don't think you want to even try that.

What is the underlying mechanism of the contraction and why is it only in the dimension of length (or is it only length contraction)?

There is also Time Dilation. Is that what you are asking about?

If it is shrinkage of quarks and electrons could there be enough shrinkage in those particles to account for the amount of length contraction of the object?

Again, if you specify the locations and times of all the particles in one IRF, the Lorentz Transformation process will tell you the Length Contractions (and Time Dilations) in any other IRF.

 

[Bill_K]

That's just because in some models they are points occupying no space but that is an oversimplification. Just consider that fact that an electron and a positron can interact to completely annihilate each other. How are you going to illustrate that going from two point particles to no point particles? The same thing holds true for all other particles and antiparticles.

You illustrate it, of course, using a Feynman diagram. There is no such thing as "complete" annihilation, George. And they do not go to "no particles". When a particle and and antiparticle annihilate, they are replaced by other particles - photons in some cases, but not always. When a quark and antiquark annihilate, a shower of particles is produced. And when an electron and positron annihilate, a neutrino-antineutrino pair is sometimes produced.

 

[ghwellsjr]

You illustrate it, of course, using a Feynman diagram. There is no such thing as "complete" annihilation, George. And they do not go to "no particles". When a particle and and antiparticle annihilate, they are replaced by other particles - photons in some cases, but not always. When a quark and antiquark annihilate, a shower of particles is produced. And when an electron and positron annihilate, a neutrino-antineutrino pair is sometimes produced.

I was treating massive particles differently from massless particles because they transform differently in Special Relativity.

But my point was that particles are treated as points having no dimensions in some models, including Feynman diagrams, but for the issue that the OP is asking about, we would have to use a more complex model where the particles occupy space and that would be hopelessly complex which is why I discouraged him from taking that approach.

 

[EskWIRED]

In Minkowski space it is much the same. The "angle" is your speed relative to the observed object.

Can you point me to a good, digestible secondary source which discusses this concept in more detail? I've studied special and general relativity, and I feel like I have a good understanding, but this style of explanation is not something I am familiar with. I would really like to get comfortable with this "angle" on the topic.

 

[nitsuj]

Can you point me to a good, digestible secondary source which discusses this concept in more detail? I've studied special and general relativity, and I feel like I have a good understanding, but this style of explanation is not something I am familiar with. I would really like to get comfortable with this "angle" on the topic.

With the Mink spacetime diagrams one axis is time, the other is length, the "graphing" a speed. The "angle" for inertial "things" is 90 degrees. that is the dimensions are orthogonal (with respect to speed, this is zero speed)

you can imagine spatial dimensions in the same sense, Change the time axis on the mink diagram to another spatial dimension and you can see how the orientation of a pencil can be made to make it appear to "contract". Of course you know it's 4D and that the length of the pencil hasn't changed, but is just not represented on the 2D diagram.