1 = v^2 + t^2? and look at spacetime as velocity as x axis, time as y axis.

In summary, the conversation discussed the equation sqrt( 1 - v^2/c^2 ) for time dilation, and how it can be thought of as 1 = v^2 + t^2 if v is a fraction of c and t is the amount a clock will be dilated. It was also mentioned that this equation can be used to understand the twin paradox. Additionally, the concept of the 4-dimensional law of pythagoras, using space and time, was brought up.
  • #1
darkhorror
140
1
I am not so sure how to explain this. But when looking at sqrt( 1 - v^2/c^2 ) for time dilation. It seems to follow that you may be able to think about it as 1 = v^2 + t^2 if look at v as fraction of c, and t as the amount a clock will be dilated.

Then you could think about it in your frame of reference that all objects are moving at 1 through spacetime. If the velocity of an object gets larger then that just means that the t gets smaller.
 
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  • #3
I think it's more like sqrt(x^2 + y^2 + z^2 + t^2) = 1
4 dimensional law of pythagoras, using space and time.

next step is using this to understand / work out a twin paradox :)
 
  • #5
HotBuffet said:
I think it's more like sqrt(x^2 + y^2 + z^2 + t^2) = 1
4 dimensional law of pythagoras, using space and time.

next step is using this to understand / work out a twin paradox :)

Do you mean s2=-t2+x2+y2+z2 ? The OP wasn't talking about the interval. He was talking about the relationship between time dilation and velocity.
 

1. What does the equation 1 = v^2 + t^2 represent in terms of spacetime?

The equation 1 = v^2 + t^2 represents the relationship between velocity (v) and time (t) in the context of spacetime. It shows that the sum of the square of an object's velocity and the square of its elapsed time is always equal to 1 in a two-dimensional spacetime diagram with velocity as the x-axis and time as the y-axis.

2. How is this equation derived and what does it tell us about the nature of spacetime?

This equation is derived from the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In the context of spacetime, it tells us that time and velocity are related in a way that is similar to the relationship between the sides of a right triangle, highlighting the interconnectedness of space and time in our universe.

3. How does this equation relate to Einstein's theory of relativity?

The equation 1 = v^2 + t^2 is a fundamental concept in Einstein's theory of relativity. It shows that time is relative and can be affected by an object's velocity, demonstrating the concept of time dilation. This equation is also used to derive the famous equation E=mc^2, which describes the relationship between energy, mass, and the speed of light.

4. Can this equation be applied to objects with different velocities?

Yes, this equation can be applied to objects with any velocity, including those traveling at the speed of light. In fact, when an object is traveling at the speed of light, the equation becomes 1 = c^2 + t^2, where c is the speed of light. This highlights the significance of this equation in understanding the nature of spacetime and the behavior of objects at high velocities.

5. What are some real-world applications of this equation?

This equation has many real-world applications, particularly in the field of physics. It is used to calculate the trajectory of objects in space, understand the behavior of particles at high speeds, and even in the development of technologies like GPS. It also plays a crucial role in the study of black holes and other phenomena that involve extreme velocities and the bending of spacetime.

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