High School Speed of separation of two masses

[bensabriK]

Hello.
Let's say we have two masses, each moving in 90 percentage of light speed in opposite direction.
Then what will be the speed of the one mass according to an observer in the other mass?

 

[PeroK]

Hello.
Let's say we have two masses, each moving in 90 percentage of light speed in opposite direction.
Then what will be the speed of the one mass according to an observer in the other mass?

The velocity transformation formula in this case gives:$$v' = \frac{2v}{1 +\frac{v^2}{c^2}}$$Where $v =0.9c$

 

[topsquark]

Hello.
Let's say we have two masses, each moving in 90 percentage of light speed in opposite direction.
Then what will be the speed of the one mass according to an observer in the other mass?

Do you know the velocity addition formula?

Given a frame O considered to be stationary and where the observer lives, and a frame O' moving at a constant speed v wrt O, and an object moving at a speed u' measured wrt O', the speed of the moving object measured wrt to O will be
$u = \dfrac{u' + v}{1 + \dfrac{u'v}{c^2}}$

Now let v = 0.9c and u' = 0.9c.

-Dan

Addendum: Whoops! Typed too slow!

 

[bensabriK]

Thank you all guys.

So two masses move away from each other with a speed of 99 percent of lightspeed according to the observer in one of them.
It is ok but still i am in confusion. Here we don't add two speed. This formula is for the speed of a walking passenger in a moving train. Here, in train example, we sum up two speed according that formula. But in my question the two moving objects are independent from each other. We cannot use that formula. Am i wrong?

So, let me ask the question in an another way.

You know the universe is expanding. So, let's take a galaxy in one end of universe spreading out in a speed of 0.9c and another galaxy in the orher end in the same speed of 0.9c. Then the separation speed is still 0.99c, instead of 1.8c?

My opinion is the separation speed is 1.8c. But the obseever will not know this. Because the information cannot move faster than light.

What do you thing?

 

[Ibix]

Here we don't add two speed. This formula is for the speed of a walking passenger in a moving train. Here, in train example, we sum up two speed according that formula. But in my question the two moving objects are independent from each other. We cannot use that formula. Am i wrong?

You are wrong. The formula quoted by both replies is the correct formula to add any two speeds in special relativity. Why would you need a different formula for adding two speeds if one object is inside another and one outside?

So, let's take a galaxy in one end of universe spreading out in a speed of 0.9c and another galaxy in the orher end in the same speed of 0.9c. Then the separation speed is still 0.99c, instead of 1.8c?

This requires general relativity, not special relativity. Speed is a much more complicated concept for spatially separated objects in curved spacetime. The recession speed of distant objects can exceed $c$ in this case. The speed of nearby objects cannot, though, which is the case whete SR is applicable.

In other words, you are comparing completely different things by bringing in cosmology.

And, incidentally, "one end of the universe" makes no sense. It has no end.

 

[topsquark]

My opinion is the separation speed is 1.8c. But the obseever will not know this. Because the information cannot move faster than light.

What are you basing this opinion on?

-Dan

 

[Nugatory]

Here, in train example, we sum up two speed according that formula.

Summing the two speeds, even with a person walking inside a train, is never exactly the right formula - the relativistic velocity addition formula topsquark gave in post #3 of this thread is always right. However, when $u’v/c^2$ is very small (as it is for walking and train speeds) the difference is small enough that we naturally use the simpler formula even though it is not exact.

 

[Dale]

This formula is for the speed of a walking passenger in a moving train. Here, in train example, we sum up two speed according that formula. But in my question the two moving objects are independent from each other. We cannot use that formula. Am i wrong?

I am not sure why you think it would be restricted in that way. But if you do think so then you can always directly use the Lorentz transforms.

 

[bensabriK]

What are you basing this opinion on?

-Dan

It's hard to answer it. But, i can say that; if we think the universe like a balloon, then, we don't know the exact diameter of this balloon, we don't know how much the universe wide. Because it expanded with a very high speed in omni direction, not higher than light speed. But the expanding speed may be higher than lightspeed. Therefore we don't know the diameter of universe. It may larger than 13.5 *2 lightyear wide. Therefore i asked that question. The expanding speed of universe may higher than the speed of light.

 

[Ibix]

i can say that; if we think the universe like a balloon, then, we don't know the exact diameter of this balloon, we don't know how much the universe wide. Because it expanded with a very high speed in omni direction, not higher than light speed. But the expanding speed may be higher than lightspeed. Therefore we don't know the diameter of universe. It may larger than 13.5 *2 lightyear wide.

I'm afraid this is a mishmash of misunderstandings about the expanding universe model.

The universe is much larger than 2×13.5 light years wide. Even assuming you just forgot the billion and mis-stated 13.8bn. The observable universe is modeled to be currently around 90bn light years across. The universe itself is probably infinite in size.

Recession rates are not limited to $c$, but as already stated this does not mean that in special relativity two speeds can add to more than $c$. Velocities in curved spacetime are complicated concepts for objects that are not close to one another, and there is no universally applicable velocity addition law there.

 

[PeroK]

It's hard to answer it. But, i can say that; if we think the universe like a balloon, then, we don't know the exact diameter of this balloon, we don't know how much the universe wide. Because it expanded with a very high speed in omni direction, not higher than light speed. But the expanding speed may be higher than lightspeed. Therefore we don't know the diameter of universe. It may larger than 13.5 *2 lightyear wide. Therefore i asked that question. The expanding speed of universe may higher than the speed of light.

The expansion of the universe is not a speed. It's a speed per unit distance. About $70 km/s$ per megaparsec.

As others have pointed out, the expanding universe is outside the scope of special relativity. Special Relativity applies locally, on a small scale. On the cosmological scale, you need General Relativity, which is a different ball game.

 

[Vanadium 50]

I'm not sure what kind of answer you are looking for. You asked what the relativistic calculation shows. You got the answer. Now you say you don't like it. Fair enough, but it doesn't change the answer.

 

[bensabriK]

Thank you.

 

[David Lewis]

So, let's take a galaxy in one end of universe spreading out in a speed of 0.9c and another galaxy in the other end in the same speed of 0.9c. Then the separation speed is still 0.99c, instead of 1.8c?

If you have two masses, each moving at 0.9c in opposite direction, the separation speed would be 1.8c. However, your question asked about the speed measured from one of the masses.

 

[Ibix]

If you have two masses, each moving at 0.9c in opposite direction, the separation speed would be 1.8c.

I usually use "separation rate" rather than "separation speed", just to keep the language that little bit more distinct.

 

[Sagittarius A-Star]

This formula is for the speed of a walking passenger in a moving train. Here, in train example, we sum up two speed according that formula. But in my question the two moving objects are independent from each other. We cannot use that formula. Am i wrong?

As others said, you are wrong with regard to this.

It is misleading to speak of "sum up two speed according that formula".

It is better to say "transform one velocity from one reference frame to another". Examples:

• Transform the passenger's velocity from the rest frame of the train to the rest frame of the track.
• Transform the velocity of mass B from the frame, in which both masses are moving in opposite directions, each with 0.9c, to the rest frame of mass A.

 

[Herman Trivilino]

Let's say we have two masses, each moving in 90 percentage of light speed in opposite direction.

Relative to what? Are they moving at speed 0.9 $c$ relative to each other?

Then what will be the speed of the one mass according to an observer in the other mass?

0.9 $c$. On the other hand, if you have an observer in between the two objects (masses are not objects, mass is a property of objects) and the objects move in opposite directions at speed 0.9 $c$ relative to the observer, then an observer at rest on one of the objects will move at a speed of about 0.99 $c$ relative to the other object.

Here we don't add two speed.

No, we don't. When the speeds are small compared to $c$ we can get away with adding them as a very good approximation, but adding is not the correct way to combine the speeds.

What do you thing?

That scientists, engineers, and technicians working at thousands of places around the world every day use this as a fact of life.

It's hard to answer it. But, i can say that; if we think the universe like a balloon,

Yeah, don't think of the universe as a balloon. It's not anything like a balloon.