# Length contraction inquiry

• B
• Einstein's Cat
In summary, objects with velocity v traveling through 3-dimensional space are not subject to length contraction.

#### Einstein's Cat

Please excuse any stupidity, but I'm under the impression that objects that travel "along" 3- dimensional" space (therefore the objects are three dimensional) with velocity v are subject to length contraction. However would objects of 3+ dimensions and with velocity v still be subject to length contractions when these objects travel "through" 3- dimensional space?

With the term "subject to length contraction" I mean that the length of the object parallel to its one- dimensional motion, would contract.

Many thanks

There is no such thing as 'along' versus 'through' space. More importantly, length contraction is not something that happens to an object. It is a difference between how someone at rest relative to an object measures it versus someone moving relative to the object. All motion is relative, so it is inherently meaningless to talk about who is moving through space.

PAllen said:
There is no such thing as 'along' versus 'through' space. More importantly, length contraction is not something that happens to an object. It is a difference between how someone at rest relative to an object measures it versus someone moving relative to the object. All motion is relative, so it is inherently meaningless to talk about who is moving through space.
I see; thank you for the corrections.

I'll give an analogy for what I mean by "along" and "through" a space.

Say there's a line along a y- axis and that this line is a one- dimensional space. A circle with two degrees of freedom can either travel "along" the space by traveling parallel to the line or "through" the space by traveling perpendicular to the line. In this case the line represents three dimensional space and the circle represents an object of 3+ dimensions.

Let's say there's an obsever, Bob, who's stationary. He sees a 3 dimensional object with velocity v and thus the length of the object parrallel to its one dimensional motion is contracted from his frame of reference. It travels "along" 3- dimensional space.

Next Bob sees an object of 3+ dimensions of the same velocity, v, that travels "through" 3- dimensional space. Would the length parallel to its one dimensional motion be contracted in Bob's frame of reference?

Hopefully this makes the question (more) valid!

I read the OP as meaning travel through space in the sense of an object passing through a 2d plane. In which case we have no evidence that there's anything outside the 3+1 dimensional universe, so there is no formal physical framework in which the question can be framed and it cannot be answered.

Edit: crossed posts with the OP's clarification. I think the above answers the question.

Ibix said:
I read the OP as meaning travel through space in the sense of an object passing through a 2d plane. In which case we have no evidence that there's anything outside the 3+1 dimensional universe, so there is no formal physical framework in which the question can be framed and it cannot be answered.

Edit: crossed posts with the OP's clarification. I think the above answers the question.
So it may not have any physical significance but hypothetically would the length of the 3+ object be contracted?

Einstein's Cat said:
So it may not have any physical significance but hypothetically would the length of the 3+ object be contracted?
I would think that would depend on the rules of geometry obeyed by higher dimensional objects. Since we have no idea if there are more dimensions than the four we know, we don't know what rules they might obey. So, no idea.

Einstein's Cat said:
Please excuse any stupidity, but I'm under the impression that objects that travel "along" 3- dimensional" space (therefore the objects are three dimensional) with velocity v are subject to length contraction.

If the object is moving relative to an observer, then the observer will witness length contraction. But the contraction is only along the line of motion, not in the other two directions.

Mister T said:
If the object is moving relative to an observer, then the observer will witness length contraction. But the contraction is only along the line of motion, not in the other two directions.
Therefore as a 3+ dimensional object travels "through" 3D space there's no one dimensional motion and thus no length contraction; Is this correct?

Einstein's Cat said:
Therefore as a 3+ dimensional object travels "through" 3D space there's no one dimensional motion and thus no length contraction; Is this correct?
We don't know because we don't know if more dimensions than just the four exist, so we don't know how they would behave if they did exist.

EC, your questions are simply not possible for us to answer, as our physical laws only apply to objects within three-dimensional space. Since your question isn't answerable beyond that, I'm afraid I'm going to have to lock this thread.

## 1. What is length contraction?

Length contraction is a concept in special relativity that states that an object's length will appear shorter when moving at high speeds relative to an observer. This phenomenon is a result of time dilation and is a fundamental principle in Einstein's theory of relativity.

## 2. How does length contraction work?

Length contraction occurs when an object moves at a high speed, close to the speed of light. As the object's velocity increases, time slows down for the object relative to an observer. This causes the object's length to appear shorter from the observer's perspective due to the difference in time frames.

## 3. What is the formula for calculating length contraction?

The formula for length contraction is L = L₀/γ, where L is the contracted length, L₀ is the object's rest length, and γ is the Lorentz factor, which is calculated using the object's velocity relative to the speed of light.

## 4. Can length contraction be observed in everyday life?

Length contraction is only noticeable at very high speeds, close to the speed of light. In everyday life, objects and speeds do not reach this magnitude, so length contraction is not observable.

## 5. What are the implications of length contraction?

Length contraction has important implications in our understanding of space and time. It is a fundamental principle in special relativity and helps explain phenomena such as time dilation and the constancy of the speed of light. It also has practical applications in fields such as particle physics and astrophysics.