Exploring Length Contraction in Higher Dimensions: A Scientific Inquiry

[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

 

[PAllen]

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.

 

[Einstein's Cat]

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!

 

[Ibix]

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.

 

[Einstein's Cat]

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?

 

[Ibix]

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.

 

[Mister T]

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.

 

[Einstein's Cat]

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?

 

[Ibix]

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.

 

[Drakkith]

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.