Time Dilation & Space Contraction: I'm Confused

[andrepd]

I'm confused. If t=γ*t₀ and L₀=γ*t how does the equation x=v*t hold for x₀=v*t₀, for constant velocity (Let t₀ be the time in the stationary reference frame and t the moving frame, the same for length)? Then v would be equal to γ^2*v... Perhaps I'm missing something here.

 

[ghwellsjr]

I'm confused. If t=γ*to and Lo=γ*t how does the equation x=v*t hold for x0=v*to, for constant velocity (Let to be the time in the stationary reference frame and t the moving frame, the same for length)? Then v would be equal to γ^2*v... Perhaps I'm missing something here.

Would you please spend some time proof reading your post and editing it to remove all typos and grammatical errors? Also, please make sure your equations are really what you want them to be and it would help if you would define all your variables.

 

[Dale]

If t=γ*to and Lo=γ*t ... Perhaps I'm missing something here.

You are missing the full form of the Lorentz transform: https://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction

The time dilation and length contraction formulas you wrote are special cases of the Lorentz transforms, not the general case. You need to use the full form.

 

[andrepd]

Would you please spend some time proof reading your post and editing it to remove all typos and grammatical errors? Also, please make sure your equations are really what you want them to be and it would help if you would define all your variables.

I don't think I did commit grammatical errors in my OP. Maybe you mistaked to (eigentime) with the word to (preposition). I should have used italics, my bad.

You are missing the full form of the Lorentz transform: https://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction

The time dilation and length contraction formulas you wrote are special cases of the Lorentz transforms, not the general case. You need to use the full form.

I see. I have looked deeper into it and I seem to have sorted it out. My initial assumptions were incorrect. Thanks for the help.

 

[sardar]

First of all, it's completely understandable to feel confused about concepts like time dilation and space contraction, as they are not intuitive and go against our everyday understanding of time and space. However, these concepts have been extensively studied and proven in the field of physics, particularly in the theory of relativity.

To address your question, let's break down the equations you mentioned. The equation t=γ*t0 represents time dilation, where t is the time measured in the moving reference frame and t0 is the time measured in the stationary reference frame. This equation shows that time in the moving frame appears to pass slower compared to the stationary frame. This is due to the fact that as an object moves faster, its time appears to slow down from the perspective of an observer in a different frame of reference.

Similarly, the equation L0=γ*L represents space contraction, where L is the length measured in the moving frame and L0 is the length measured in the stationary frame. This equation shows that the length in the moving frame appears to be shorter compared to the stationary frame. This is because as an object moves faster, its length appears to contract from the perspective of an observer in a different frame of reference.

Now, let's look at the equation x=v*t. This equation represents the distance an object travels, where x is the distance, v is the velocity, and t is the time. This equation holds true for both the stationary and moving frames, but the values for v and t will be different in each frame due to time dilation and space contraction.

To better understand this, let's use an example. Let's say we have a spaceship moving at a constant velocity of 0.8c (80% of the speed of light) in the stationary frame. In the spaceship's frame, time appears to pass slower and length appears to be shorter. So, if we measure the time and distance traveled by the spaceship in its own frame, we will get different values compared to the measurements taken in the stationary frame. However, when we use the equation x=v*t, we will get the same value for distance traveled in both frames, as the time and velocity values will adjust accordingly.

In summary, the equations you mentioned may seem contradictory at first glance, but they are actually consistent with the theory of relativity and have been extensively tested and proven by experiments. I hope this explanation helps clear up your confusion. If you have any further questions, please don't hesitate to ask