Special Relativity: spaceships heading toward each other

In summary, the concept of special relativity illustrates how two spaceships moving toward each other at significant fractions of the speed of light perceive time and distance differently. Observers on each spaceship measure time dilation and length contraction, leading to varying observations of each other's speed and position. This phenomenon emphasizes the relativity of simultaneity, demonstrating that events considered simultaneous in one frame may not be so in another, fundamentally altering our understanding of space and time in high-velocity scenarios.
  • #1
Sidsid
11
2
Homework Statement
So, the problem is this: two spaceships are heading to a bar located exactly between the spaceships, one approaches from the left, the other from the right. They are both moving with a speed of 0.8c. So in the bar's point of view they meet at the bar. Where do they meet in the left ship's view, at the bar , left of the bar or right
?
Relevant Equations
$V_ab= (v_bc+ v_ac)/(1+ (v_bc*v_ac)/c^2) $
In the left point of view the bar is approaching at 0.8c and the other space ship at something very near c (Einsteins velocity addition rule). To reach the left ship the other ship has to bridge double the distance of the bar with less than double the speed of the bar. Therefore they meet right of the bar. But this seems very counterintuitive. The meeting of the spaceships is an event with a time and a place, and I remember something of spacetime events being "immune to such trickery". What is right?
 
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  • #2
If they meet at the bar, is it possible that they also don't meet at the bar? Say they actually collide with and destroy the bar. Which ship(s) would be damaged if they meet at the bar or left or right of the bar?

Have you been taught the Lorentz transforms? If so, start in the rest frame of the bar and write down the coordinates of the ships 1s before they meet and when they meet (hint: make this last event the origin to save yourself some maths). Transform to the rest frame of one of the ships. What do you notice about the time coordinates of the ships' start events?
 
  • #3
The three meet is an event, a point in space time. It is shared with any coordinates as you suspect.

[EDIT]I interpreted that they meet at a point. Bar has length. If OP means the two rockets meet the bar at different points, it is another story.
 
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  • #4
The problem is completely conceptual. No computations are needed and you are given the answer:
Sidsid said:
they meet at the bar
This is an invariant statement as it is a statement about a particular event (the meeting) occurring on the world line of the bar.
 
  • #5
They may meet at the bar, but I betcha their drinks will not arrive simultaneously. :oldsmile:
 
  • #6
Sidsid said:
To reach the left ship the other ship has to bridge double the distance of the bar with less than double the speed of the bar.
Okay.
Sidsid said:
Therefore they meet right of the bar.
I don't see how that follows. In the bar's rest frame each ship is the same distance away at any given time. But those two events will not be simultaneous in the left ship's rest frame!
 
  • #7
Thank you all for your help! I understand now.
 
  • #8
kuruman said:
They may meet at the bar, but I betcha their drinks will not arrive simultaneously. :oldsmile:
Yes, I think I've been to that bar.
 

FAQ: Special Relativity: spaceships heading toward each other

1. What is the basic premise of special relativity in the context of two spaceships heading toward each other?

Special relativity, formulated by Albert Einstein, states that the laws of physics are the same for all observers in uniform motion relative to one another. When two spaceships are heading toward each other at significant fractions of the speed of light, their relative velocities, time dilation, and length contraction must be considered. Observers in each spaceship will perceive time and distances differently due to their high speeds, leading to fascinating implications for how they measure each other's approach.

2. How do time dilation and length contraction affect the perception of time and distance between the two spaceships?

Time dilation refers to the phenomenon where a moving clock ticks slower compared to a stationary clock, as observed by an outside observer. Length contraction means that an object in motion is measured to be shorter along the direction of motion compared to when it is at rest. For the spaceships approaching each other, each spaceship will see the other's clock running slower and will also perceive the distance between them as shorter than it would be in their rest frame. This leads to interesting scenarios regarding how long it takes for them to meet from each ship's perspective.

3. What do the observers on each spaceship see when they look at each other as they approach?

Each observer on the spaceships will see the other ship's clock running slow due to time dilation. Additionally, they will perceive the other ship as being length-contracted. This means that if they were to measure the distance to the other ship, it would appear shorter than it would if they were at rest. Moreover, due to the relativistic Doppler effect, they would also notice a change in the frequency of light emitted from the other ship, which could appear redshifted or blueshifted depending on their relative velocities.

4. How do the concepts of simultaneity change for the observers in the spaceships?

In special relativity, simultaneity is relative; events that are simultaneous in one frame of reference may not be simultaneous in another. For the two spaceships headed toward each other, an event that one observer considers to happen at the same time (like the firing of a signal) may not be perceived as simultaneous by the other observer due to their relative motion. This leads to different conclusions about the order of events, which is a key aspect of relativity and highlights the non-absolute nature of time.

5. What is the significance of the relativistic addition of velocities when calculating their approach speed?

The relativistic addition of velocities is crucial when determining the relative speed of two objects moving toward each other at high speeds. Unlike classical physics, where you simply add their speeds, special relativity requires a specific formula to account for

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