Time Dilation & Space Contraction: I'm Confused

In summary, the conversation discusses the confusion around the equations x=v*t and x0=v*to in the context of the Lorentz transformation. The speaker realizes they were using special cases instead of the full form and thanks the other person for their help in understanding the concept. The importance of proofreading and defining variables is also mentioned.
  • #1
andrepd
10
0
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.
 
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  • #2
andrepd said:
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.
 
  • #4
ghwellsjr said:
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.

DaleSpam said:
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.
 
  • #5


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
 

FAQ: Time Dilation & Space Contraction: I'm Confused

What is time dilation?

Time dilation is a phenomenon in which time appears to pass at different rates for different observers or in different reference frames. This is due to the distortion of space-time by objects with high gravity or velocity.

How does time dilation occur?

Time dilation occurs because of the theory of relativity, which states that the laws of physics are the same for all observers in uniform motion. This means that the perception of time passing will be different for observers moving at different speeds or in different gravitational fields.

What is space contraction?

Space contraction, also known as length contraction, is a phenomenon in which the length of an object appears to shorten when viewed from a different reference frame. This is also due to the distortion of space-time by high gravity or velocity.

How does space contraction relate to time dilation?

Space contraction and time dilation are both consequences of the theory of relativity. As one occurs, the other must also occur to maintain the consistency of the laws of physics. This means that as an object experiences time dilation, it will also experience space contraction.

Can time dilation and space contraction be observed in everyday life?

Yes, time dilation and space contraction can be observed in everyday life, but the effects are extremely small and can only be detected in extreme conditions. For example, GPS satellites must take into account the effects of time dilation in order to accurately measure time and provide accurate location information.

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