Help Me Understand Relative Speeds

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In summary: I'm not sure anyone knows how to do this in a way that's comprehensible.I don't really understand how these interactions play out. can someone help me?
  • #1
some bloke
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the laws of physics dictate that nothing can exceed C, but if 2 ships travel away from one another at 0.6C, they would perceive each other as travelling faster than C (1.2C).
at what point does something class as travelling this fast?
This came to me in a blur of confusion whilst reading another thread about a giant wheel spinning, and it's made me confused. I'm hoping that this is something which someone can explain to me in a way I'll understand.

Summary of my knowledge:
1: the speed of light is the same in all directions, no matter how fast you are travelling, as discovered in the "Ethereal Wind" experiment.
2: no physical object can reach the speed of light

But what I'm confused about is what speed of light?

For example:
2 rockets leaving the earth, in opposite directions. The rockets accelerate to travel at 0.6C, relative to the earth.
Rocket 1 looks at rocket 2 and sees it moving away at 1.2C, and sees itself as stationary. Rocket 2 observes the same about rocket 1.

The same experiment works if Rocket 1 and Rocket 2 are passing each other at 0.6C, they will see themselves as stationary and the other as flying past at 1.2C.

Now imagine they are orbiting a point, 180° offset from one another, in the same direction (so they are always traveling in opposite linear directions from one another). This imitates a wheel, with the point as a hub and the ships as the outer edge. They travel at 0.6C, see one another as traveling at 1.2C but also at 0, as they are not moving compared to one another.

I don't really understand how these interactions play out. can someone help me?
 
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  • #2
By definition, the speed of rocket 1 relative to rocket 2 is the speed of rocket 1 as measured in the restframe (SIC!) of rocket 2.
 
  • #3
some bloke said:
Summary: the laws of physics dictate that nothing can exceed C, but if 2 ships travel away from one another at 0.6C, they would perceive each other as traveling faster than C (1.2C).
at what point does something class as traveling this fast?

This came to me in a blur of confusion whilst reading another thread about a giant wheel spinning, and it's made me confused. I'm hoping that this is something which someone can explain to me in a way I'll understand.

Summary of my knowledge:
1: the speed of light is the same in all directions, no matter how fast you are travelling, as discovered in the "Ethereal Wind" experiment.
2: no physical object can reach the speed of light

But what I'm confused about is what speed of light?

For example:
2 rockets leaving the earth, in opposite directions. The rockets accelerate to travel at 0.6C, relative to the earth.
Rocket 1 looks at rocket 2 and sees it moving away at 1.2C, and sees itself as stationary. Rocket 2 observes the same about rocket 1.

The same experiment works if Rocket 1 and Rocket 2 are passing each other at 0.6C, they will see themselves as stationary and the other as flying past at 1.2C.

Now imagine they are orbiting a point, 180° offset from one another, in the same direction (so they are always traveling in opposite linear directions from one another). This imitates a wheel, with the point as a hub and the ships as the outer edge. They travel at 0.6C, see one another as traveling at 1.2C but also at 0, as they are not moving compared to one another.

I don't really understand how these interactions play out. can someone help me?

Velocities do not simply add in the way that you imagine. In the case of two rockets moving in opposite directions relative to the Earth, say, the speed of one rocket (as measured in the reference frame of the other is):

##\frac{0.6 + 0.6}{1 + (0.6)^2}c \approx 0.88c ##

This is called "relativistic velocity addition". You can read about it here:

https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity
 
  • #4
some bloke said:
2 rockets leaving the earth, in opposite directions. The rockets accelerate to travel at 0.6C, relative to the earth.
Rocket 1 looks at rocket 2 and sees it moving away at 1.2C, and sees itself as stationary. Rocket 2 observes the same about rocket 1.
As @PeroK says, velocities don't add linearly. A velocity of ##u## and a velocity of ##v## combine to make a velocity of ##(u+v)/(1+uv/c^2)##. Note that this is almost indistinguishable from ##u+v## if both ##u## and ##v## are very much less than ##c##, which is why you don't notice this at every day speeds.
some bloke said:
Now imagine they are orbiting a point, 180° offset from one another, in the same direction (so they are always traveling in opposite linear directions from one another). This imitates a wheel, with the point as a hub and the ships as the outer edge. They travel at 0.6C, see one another as traveling at 1.2C but also at 0, as they are not moving compared to one another.
If you have switched to a frame of reference where the two ships are not moving, this is a rotating frame of reference. This involves a fairly major change in what you mean by "velocity", and the speed of light is neither constant nor isotropic, nor is ##c## a maximum speed limit in such a frame. This doesn't mean anything particularly exotic - simply that the definitions of "velocity" one has to use in a rotating frame are complicated.

My advice is not to worry too much about rotating reference frames until you have a good understanding of inertial frames.
 
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  • #5
some bloke said:
Summary: the laws of physics dictate that nothing can exceed C, but if 2 ships travel away from one another at 0.6C, they would perceive each other as traveling faster than C (1.2C).
at what point does something class as traveling this fast?

I don't really understand how these interactions play out. can someone help me?

Some may see the scenario outlined in this post as over-complicated, but it helped me understand the concepts a bit better:

https://www.physicsforums.com/threa...moving-frame-of-reference.972860/post-6190127
 
  • #6
some bloke said:
… 2 rockets leaving the earth, in opposite directions. The rockets accelerate to travel at 0.6C, relative to the earth.
For you on Earth, with each second that passes, the distance between the rockets increases by 1.2 light-seconds.
 
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  • #7
David Lewis said:
For you on Earth, with each second that passes, the distance between the rockets increases by 1.2 light-seconds.
Indeed. Some things are still just that simple.

Of course this is not the "relative velocity" of anyone thing in the rest frame of another. Instead is it a "closing velocity". Further, it is expressed as a ratio of so much Earth-relative distance in so much Earth-relative time.

When translated to the rest frame of either rocket we need to transform coordinates so that we are talking in terms of rocket-relative distances and rocket-relative times to obtain a rocket-relative velocity. Time dilation, length contraction and the relativity of simultaneity all have roles to play in the transformation. The result will be the velocity of one physical thing in the rest frame of another and will have a magnitude less than c.
 

1. What is relative speed?

Relative speed is the speed of an object in relation to another object. It is the difference in speed between the two objects, taking into account their direction of motion.

2. How is relative speed calculated?

Relative speed is calculated by finding the difference between the speeds of the two objects and taking into account their direction of motion. If the objects are moving in the same direction, their speeds are subtracted. If they are moving in opposite directions, their speeds are added.

3. How is relative speed different from absolute speed?

Absolute speed is the speed of an object measured in relation to a fixed point, such as the ground. Relative speed, on the other hand, is the speed of an object in relation to another object. It takes into account the motion of both objects and their direction of movement.

4. How does relative speed affect collisions?

Relative speed plays a crucial role in determining the outcome of collisions between objects. The greater the relative speed between two objects, the greater the force of impact and the more damage that can occur.

5. How can relative speed be used in everyday life?

Relative speed is used in a variety of ways in everyday life, such as in driving and navigation. It is also important in sports, as athletes must take into account the relative speed of their opponents to anticipate their movements. In addition, relative speed is used in air travel to calculate flight times and fuel consumption.

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