lnsanity
I am reading Michio Kaku books and Brian Green Books and I am planing reading Stephen Hawking books and I have a couple of question please give me a link if it already have been answered.

1-If I move at 90% speed of light and trow something at 90% speed of light in the same direction that object should move approximately at 99% speed of light not 180%. Now my question is 2 object or person moving at 90% speed of light toward each other at witch speed will they see each other approaching (99% I think)? Also does an outside observer see them closing each other at 180% the speed of light ?

Also if I am right and the outside observer see them at 180% but they see themselves going at 99% if they hit each other at witch speed would you calculate the impact collision to determine the trajectory and speed of the debris from the impact?

2-I read that mass of the object increase with speed and near speed of light object reach near infinite mass that's why you cant pass the speed of light because it would be infinite that's why it's impossible according to Einstein. But I think the mass increase is relative right ? I mean the person or object does not see itself with a mass increase its just the observer. My question is what happen when you spin on yourself like tennis ball are you heavier too? If the ball rotate in perfect topspin from the point of view of the ball say bottom, top or side of the ball it may appear that you are in perfect no motion state and it is the world that is spinning around the ball so no mass increase from that point of view. But when the ball hit the racket the ball would be heavier say then a flat ball with no spin ? I understand that a tennis ball may not spin fast enough to feel the difference but every tennis player feel topspin ball like if they are much heavier when they hit the racket so I was wondering why ?

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## Answers and Replies

Agent M27
The underlying concept for all of general relativity is that space-time is relative and dependent upon the frame of refrence from which thigns are observed. For your question above no matter which object or person you choose they will see the other approaching them at at what ever velocity they began with provided they aren't accelerating.

For what an outside observer would see consider the following equation:

$$\frac{v+u}{1+\frac{vu}{c^2}}$$

Where v is the speed of of the moving person and u is the speed of a second object projected in the same direction of motion. This is slightly different than your question but it still portrays accurately what happens. If you plug in your figures of .9c for the two objects, you will result in $$1.8c/1.8$$ which gives you c. In other words it would not add to 180% the speed of light and they are not approaching eachother at 180% the speed of light. As for relativistic mass the person would most definitely be able to perceive the increase in mass. Spinning objects follow the same rules no matter which frame is chosen to be stationary. I am pretty sure that the increased resistance of a tennis ball is soley due to the racket trying to change it's direction not due to the increase in relativistic mass, it is not spinning fast enough. I hope this helps.

Joe

As for relativistic mass the person would most definitely be able to perceive the increase in mass.
Joe,
I'm a little confused by this. An object does not detect a change in its own mass based on its state of motion -- its mass is just its rest mass. Right?

yuiop
$$\frac{v+u}{1+\frac{vu}{c^2}}$$

Where v is the speed of of the moving person and u is the speed of a second object projected in the same direction of motion. This is slightly different than your question but it still portrays accurately what happens. If you plug in your figures of .9c for the two objects, you will result in $$1.8c/1.8$$ which gives you c.

Small correction: It is 1.8c/1.81 which is less than c.

Let us say that A is moving relative to you at 0.9c and B is moving relative -0.9c also relative to you (in the opposite direction and towards A) then A will see B coming towards him at 1.8c/1.81 = aprox 0.99447c and B will see A coming towards him at aprox 0.99447c. No one actually measures any object moving at greater than c relative to the inertial reference frame they are at rest in.

As for mass, the modern opinion is that mass never changes and it is just that the equations of relativity are different to the equations of Newton. Just because in relativity, momentum is equal to y(mv) rather than the just mv in Newtonian mechanics does not mean the mass has increased by a factor of y. What it does tell us is that infinite energy is required to accelerate a particle with non zero rest mass to the speed of light. Now a ball with top spin has more energy than a non spinning ball with the same linear velocity as is obvious from the fact that additional energy is required to get the ball spinning and the additional momentum is a reflection of the additional energy that was put in the first place, but there is no actual change in the mass of the spinning ball.

Now if you are spinning on the spot with your arms outstretched, your hands will feel heavier than what you would predict using Newtonian equations for centrifugal force, but that is because the equations for force are different in relativity and the Newtonian equations are only an aproximation to reality.

I understand that a tennis ball may not spin fast enough to feel the difference but every tennis player feel topspin ball like if they are much heavier when they hit the racket so I was wondering why ?

Certainly, relativistic effects would be almost impossible to detect at the speeds involved in tennis. I magine when a ball with top spin hits a racket it is not only trying to move the racket backwards and stretch the strings, but is also effectively pushing the racket and the hand downwards as the spin momentum is absorbed. This would probably feel noticeably different from the strike of a non spinning tennis ball.

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Joe,
I'm a little confused by this. An object does not detect a change in its own mass based on its state of motion -- its mass is just its rest mass. Right?
Sometimes people make use of a concept called relativistic mass which is distinct from rest mass (although they are equal in the object's own rest frame), though most physicists prefer to avoid this concept now for pedagogical reasons. Probably Joe was just saying that an object's relativistic mass could be measured by a separate observer who saw the object moving relative to himself, not that an object would measure its own relativistic mass to be different from its rest mass.

Sometimes people make use of a concept called relativistic mass which is distinct from rest mass (although they are equal in the object's own rest frame), though most physicists prefer to avoid this concept now for pedagogical reasons. Probably Joe was just saying that an object's relativistic mass could be measured by a separate observer who saw the object moving relative to himself, not that an object would measure its own relativistic mass to be different from its rest mass.
Right. OK, thanks!

lnsanity
The underlying concept for all of general relativity is that space-time is relative and dependent upon the frame of refrence from which thigns are observed. For your question above no matter which object or person you choose they will see the other approaching them at at what ever velocity they began with provided they aren't accelerating.

For what an outside observer would see consider the following equation:

$$\frac{v+u}{1+\frac{vu}{c^2}}$$

Where v is the speed of of the moving person and u is the speed of a second object projected in the same direction of motion. This is slightly different than your question but it still portrays accurately what happens. If you plug in your figures of .9c for the two objects, you will result in $$1.8c/1.8$$ which gives you c. In other words it would not add to 180% the speed of light and they are not approaching eachother at 180% the speed of light. As for relativistic mass the person would most definitely be able to perceive the increase in mass. Spinning objects follow the same rules no matter which frame is chosen to be stationary. I am pretty sure that the increased resistance of a tennis ball is soley due to the racket trying to change it's direction not due to the increase in relativistic mass, it is not spinning fast enough. I hope this helps.

Joe

For the tennis ball is it the same effect as a gyroscopic effect ? Once I had a bicycle wheel full of lead in my hands in a science expo and as far as I remember it was there to show the effect of gyroscope when i sniped the wheel it was really hard to change its direction left and right.

This equation is for object moving toward each other or for the object i am throwing while moving or both ?

For the outside observer I find it really strange that 2 object moving at .9 c appear to move at c toward each other, I thought it would only be the case for the observer moving toward each other...

I don't get C as answer from your equation...

v+u = 1.8
vu = 0.81
c2 = 1

So 1.8 / (1+0.81/1) = 0.994475c = not c ??

or

v+u = 540 000 KM/s
vu = 72 900 000 000 KM/s
c2 = 90 000 000 000 Km/s

So 540 000/ (1+(72 900 000 000/90 000 000 000)=298342 Km/s

I don't get C as answer from your equation...

v+u = 1.8
vu = 0.81
c2 = 1

So 1.8 / (1+0.81/1) = 0.994475c = not c ??
You're right, see kev's post...an object which has a v lower than c in one frame must have a velocity lower than c in any other frame too. However, if the velocity v of the moving object in the first frame is exactly c, in that case the velocity of the object in the second frame (the one that sees the first frame moving at velocity u relative to itself) would be exactly c too...for example, if v=1c and u=0.9c, then (v + u)/(1 + vu/c^2) = (1.9c)/(1 + 0.9) = 1c.

lnsanity
I just thought about something I was saying then when a ball spin then it could be argue that from the point of you of the ball its the world witch is spinning around but now I think this is not true because if you spin you feel the force centrifuge but if the world spin around you you don't feel that force. There is no symmetry or covariance I think ?

I just thought about something I was saying then when a ball spin then it could be argue that from the point of you of the ball its the world witch is spinning around but now I think this is not true because if you spin you feel the force centrifuge but if the world spin around you you don't feel that force. There is no symmetry or covariance I think ?
This is the famous Newton's bucket thought experiment, and what motivated Mach's principle. You should research these ideas and see what you think of Mach's answer!

lnsanity
This is the famous Newton's bucket thought experiment, and what motivated Mach's principle. You should research these ideas and see what you think of Mach's answer!

I will do so eventually if I don't forget because I have at least 8 other book to read in my near listing of to read. It would be great if you could point me out to books internet article link or video (YouTube or torrent) I will do a few Google research myself...

lnsanity
This is the famous Newton's bucket thought experiment, and what motivated Mach's principle. You should research these ideas and see what you think of Mach's answer!

I just read Mach's principle if I understand correctly if the universe was empty there would not be any centrifuge force ?

I just read Mach's principle if I understand correctly if the universe was empty there would not be any centrifuge force ?
That's what Mach's principle claims, though it doesn't seem to be true in general relativity (but Julian Barbour has some interesting speculations about how GR might be tweaked to produce a truly Machian theory)

lnsanity
That's what Mach's principle claims, though it doesn't seem to be true in general relativity (but Julian Barbour has some interesting speculations about how GR might be tweaked to produce a truly Machian theory)

So you say its not true in general relativity than what is true in general relativity ? What is the interpretation or prediction of general relativity about this ?

So you say its not true in general relativity than what is true in general relativity ? What is the interpretation or prediction of general relativity about this ?
In GR you can have distinct solutions for a bucket in an otherwise empty ('asymptotically flat') universe...in one solution the bucket is not rotating as evidenced by the fact that the surface of the water remains flat and accelerometers at various positions on the bucket would register no G-forces, in another solution the bucket is rotating as evidenced by the fact that G-forces would be registered by accelerometers and the surface of the water becomes concave (the water pushed up along the sides by the apparent centrifugal force). For example, Brian Greene discusses this on p. 74 of his book Fabric of the Cosmos which can be viewed here on google books.

lnsanity
In GR you can have distinct solutions for a bucket in an otherwise empty ('asymptotically flat') universe...in one solution the bucket is not rotating as evidenced by the fact that the surface of the water remains flat and accelerometers at various positions on the bucket would register no G-forces, in another solution the bucket is rotating as evidenced by the fact that G-forces would be registered by accelerometers and the surface of the water becomes concave (the water pushed up along the sides by the apparent centrifugal force). For example, Brian Greene discusses this on p. 74 of his book Fabric of the Cosmos which can be viewed here on google books.

Ya I have that book I am finishing the elegant universe right now and was wondering witch book to read next between M.K. Parallel Worlds and B.G. The Fabric Of The Cosmos since I posses both does a particular logical order is better than another ?

Ok edit I just read p74 so according to G.R. you would still feel Centrifugal force in empty Universe but not all physicist Agree and as far as I understand there is no possible experiment to test this so I will need to read all of Julian Barbour works and book to get my own idea I guess...

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