Speed of Moving Object: Exploring Length Contraction & Time Dilation

Click For Summary

Discussion Overview

The discussion centers around the concepts of length contraction and time dilation in the context of a moving object, specifically exploring the implications of these factors when expressed in terms of meters per second. Participants are examining the mathematical relationships and units involved in these relativistic effects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions what the factor derived from length contraction and time dilation represents when expressed in meters per second.
  • Another participant seeks clarification on the specific factor being referenced, indicating a lack of understanding.
  • A third participant suggests that the factor in question is related to \(\sqrt{1 - \frac{v^2}{c^2}}\) but expresses confusion about its application in the context of units.
  • A fourth participant explains that the factor \(\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}\) is dimensionless, asserting that transformed lengths and times retain their proper units of meters and seconds.
  • One participant apologizes for an unrelated post due to a personal emergency, indicating a distraction from the discussion.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints and some confusion regarding the interpretation of the factors involved in length contraction and time dilation. No consensus is reached on the specific factor being discussed or its implications.

Contextual Notes

Participants express uncertainty about the application of the factor in relation to units, and there is a lack of clarity regarding the mathematical steps involved in the transformation of lengths and times.

petm1
Messages
397
Reaction score
1
What does the factor that you get when you plug the length contraction and time dilation of a moving object back into the form of meters/second represent?
 
Physics news on Phys.org
I don't understand what factor you're asking about. Can you give a specific example?
 
petm1 said:
What does the factor that you get when you plug the length contraction and time dilation of a moving object back into the form of meters/second represent?
?? I have no idea what you mean. I think the factor you are talking about is [itex]\sqrt{1- \frac{v^2}{c^2}}[/itex] but I don't know what you mean by "plug back into the form of meters/second".
 
I think the OP is asking this. You operate on the lengths and times of the traveling frame with some algebraic factor involving [tex]\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]. And does that factor have units of its own, and if so how do the transformed lengths and times get back to their own proper units? We ssee their transformed values, but their units should still be lengths like meters and times like seconds shouldn't they?

And the answer to that is that if you look at the expression for gamma, the only dimensionful amounts in it are the speeds v and c. And they only occur as their ratio, so their units are divided out. This means that gamma is a pure number, and no algebraic function of it alone can be anything but a pure number, so the transformed lengths and times have the same units that the rest frame amounts do.
 
Sorry, I had a small problem, house fire and when that alarm sounds I have to run, I didn't know that I had posted this instead of just previewing it until I read it the next day. Thanks for the effort and I will be more careful in the future.
 

Similar threads

Undergrad What causes time dilation and length contraction
  • · Replies 10 ·
Replies
10
Views
2K
High School Why does length contraction occur and how does it relate to time dilation?
  • · Replies 63 ·
3
Replies
63
Views
6K
Undergrad Please explain how length contraction and time dilation result in a constant c
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Question about length contraction
  • · Replies 45 ·
2
Replies
45
Views
6K
High School Check my understanding of Time Dilation and Length Contraction
  • · Replies 11 ·
Replies
11
Views
2K
High School Thought Experiment: Behavior of shadow of object moving at speed c
  • · Replies 14 ·
Replies
14
Views
2K
High School On time dilation and length contraction
  • · Replies 34 ·
2
Replies
34
Views
4K
Undergrad Perceive Length Contraction VS Terrell Penrose
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad How time dilation is a permanent change and length contraction not?
  • · Replies 13 ·
Replies
13
Views
2K
High School What does symmetry of time dilation really mean?
  • · Replies 16 ·
Replies
16
Views
2K