Dimensions and Degrees of Freedom

In summary, the conversation discussed the possibility of a fourth dimension in space-time, specifically in relation to our ability to accelerate and change our state of motion. While time is often considered the fourth dimension, it was debated whether a physical fourth dimension is necessary to fully explain our freedom of movement in space.
  • #1
Jimmy
769
38
When considering the three dimensions of space and our freedom of movement in that space, does our ability to change our state of motion (acceleration) imply an existence of a fourth dimension, ie. four space-time dimensions?

Given three dimensions each mutually perpendicular, we can move up, down, left, right, forward and backward. We can also rotate around each axes. Is a fourth axes perpendicular to the other three necessary for going faster and slower?

I know it's often debated whether time is really a physical dimension or just an abstraction. I also know that with regard to 4-D space-time, time isn't a dimension separate from the other three in an absolute sense; it depends on your orientation within space-time.

To summarize my question: is a fourth dimension implicit by the fact that we can accelerate and would it be possible to change the motion of any object without this dimension?
 
Last edited:
Physics news on Phys.org
  • #2
Greetings Jimmy !

Acceleration is not a dimension, and velocity is
not a dimension either. When you describe a body
in a 3D space (normal Cartesian coordinates' systems)
you "break up" its location into the three axes
which you define (as you please). Velocity is then
the change in distance per unit of time relative
to the coordiante system you defined. You can also
"break" it up into velocity along each axis you define.
Acceleration is the change in velocity per unit of time.
So, if relative to your system I were moving along the
X axis my location would be my distance from the
center of your system (presumably - you), my velocity
would be the extra feet I move per second (for example),
and my acceleration would discribe by how much my velocity
changes from one second to the next.

BTW, that face looks awfully green, maybe you should cure it.

Live long and prosper.
 
  • #3


Originally posted by drag
Greetings Jimmy !

Acceleration is not a dimension, and velocity is
not a dimension either...

Live long and prosper.

I understand what you are saying but I didn't suggest that velocity or acceleration were dimensions. I was asking if acceleration required another physical dimension along with the three dimensions of space. I was considering the fact that given three dimensions, we have certain degrees of freedom with regard to motion. I was curious if a fourth dimension was required to allow us the added degree of freedom, ie. acceleration.

Thanks for your reply. :smile:
 
Last edited:
  • #4
i suppose that "fourth dimension" would be time as there is no motion without time

just a thought ;)
 
  • #5
drag: BTW, that face looks awfully green, maybe you should cure it.

Live long and prosper.

Yeah, good old Mr. Yuck. Lots of poison control centers in the US give out stickers of Mr. Yuck for parents to put on anything dangerous. I remember when I was younger, I saw lots of public service announcements from the West Virgina Poison control center which featured Mr. Yuck and warned children not to touch anything that had his face on it.

If I chose a better avatar, I might get more responses.
 
Last edited:
  • #6
Originally posted by Ace Nova
i suppose that "fourth dimension" would be time as there is no motion without time

just a thought ;)

That's the general consensus. What I'm asking is, is a fourth, 'Physical' dimension necessary to accommodate all the degrees of freedom that we experience.
 

1. What are dimensions in the context of science?

Dimensions refer to the measurable aspects or parameters that describe an object or system. In science, dimensions can include physical properties such as length, width, height, and mass, as well as more abstract concepts like time and temperature.

2. What is the difference between dimensions and degrees of freedom?

Dimensions and degrees of freedom are closely related but not interchangeable terms. Dimensions refer to the number of independent parameters needed to fully describe an object or system, while degrees of freedom refer to the number of ways that object or system can move or change without violating any constraints.

3. How do dimensions and degrees of freedom impact scientific research?

Dimensions and degrees of freedom play a crucial role in scientific research as they determine the complexity and behavior of a system. They also allow scientists to accurately model and predict the behavior of a system, and identify any constraints or limitations that may affect their experiments or observations.

4. Can dimensions and degrees of freedom change over time?

Yes, dimensions and degrees of freedom can change depending on the conditions and environment of the system. For example, the dimensions of a material can change when exposed to different temperatures, and the degrees of freedom of a molecule can change when it undergoes a chemical reaction.

5. How are dimensions and degrees of freedom related to the concept of space-time?

Dimensions and degrees of freedom are essential components in the concept of space-time, which is the mathematical model used to describe the physical universe. The three spatial dimensions (length, width, and height) and the one temporal dimension (time) make up the four dimensions of space-time, while the degrees of freedom allow for the movement and interaction of objects within this framework.

Similar threads

  • Other Physics Topics
Replies
20
Views
3K
Replies
2
Views
262
  • General Math
Replies
22
Views
1K
  • Other Physics Topics
2
Replies
54
Views
3K
  • Special and General Relativity
Replies
12
Views
1K
  • Linear and Abstract Algebra
Replies
4
Views
766
Replies
2
Views
177
  • Special and General Relativity
Replies
22
Views
1K
  • Beyond the Standard Models
Replies
2
Views
2K
  • Linear and Abstract Algebra
Replies
6
Views
2K
Back
Top