- #1
PhDeezNutz
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- 465
- Homework Statement
- Part (C), The book contends ##\gamma## should be in the denominator where as I think it should be in the numerator$$
- Relevant Equations
- The Lorentz Transform (see below)
Check this.PhDeezNutz said:
TSny said:Check this.
TSny said:It should be easy to write down the space and time coordinates for the second event in the primed frame. They are easily expressed in terms of ##l_0## and ##v##. In your first post, you have the correct expression for the time coordinate of this event in the primed frame. But, you mistakenly wrote the space coordinate as ##0##. What is the space coordinate of the tail of the ship in the primed frame (at any time)?
Yes.PhDeezNutz said:##- l_0##? I say minus because in my mind it's to the left of the origin of ##S'##.
TSny said:Yes.
From S' viewpoint, the point A (in S) moves to the left with speed v and the distance A must travel to get from the front to the back of the ship is the length of the ship in S'.PhDeezNutz said:There's still one part I haven't reconciled with intuition. Namely ##t' = \frac{l_0}{v}## when ##B'## crosses ##A## because it almost looks classical; ##v## is the speed of ##B'## in ##S## and ##l_0## is proper length. Don't quite get it.
The theory of relativity states that the laws of physics are the same for all observers in uniform motion. This means that the rocket passing by the space station will experience the same physical laws as the space station, even though they are moving at different speeds.
Time dilation is the phenomenon where time appears to pass slower for objects that are moving at high speeds. In the case of a rocket passing by a space station, time will appear to pass slower for the rocket compared to the space station due to their different velocities.
According to the theory of relativity, the time dilation effect increases as the speed of the rocket increases. This means that the faster the rocket is moving, the slower time will appear to pass for the rocket compared to the space station.
Yes, the time dilation effect has been observed in experiments and is also taken into account in the operation of GPS satellites. The satellites orbiting the Earth at high speeds experience time dilation, which must be corrected for in order for the GPS system to function accurately.
The theory of relativity has revolutionized our understanding of time and space. It has shown that time and space are not absolute, but are relative to the observer's frame of reference. It has also led to the development of important concepts such as time dilation and the curvature of space-time, which have been confirmed through various experiments and observations.