general relativity

[sidharath]

suppose two isolated heavy masses in space move towards each other will the path followed be straig ht line joining the centres of two masses or curved path?

[Didymus]

GR states that all objects traveling through space travel in straight lines. Even the earth orbiting the sun... that's a straight line. Through curved space.

[swansont]

If they don't have a transverse component to their velocity, they will move straight toward each other

[elfmotat]

"Straight lines" are a subtle topic in GR, but essentially the answer is yes.

[mahesh khati]

According to me, Straight line or linearity is very local phenomena for example, I have drawn straight line on black board. Here, my pen motion with relative to observer in class room is in straight line but for observer in space this motion is not linear but curve as my pen moves in curve path with revolving earth. In world nothing is moving in exact straight line or with constant velocity these are very local relative terms. Everything is falling towards something. There is nothing like 100 % inertial or stable or linear in the world. I may say that perfect inertial frame is not present in this universe.

This may be only my view. thanks

[swansont]

According to me, Straight line or linearity is very local phenomena for example, I have drawn straight line on black board. Here, my pen motion with relative to observer in class room is in straight line but for observer in space this motion is not linear but curve as my pen moves in curve path with revolving earth. In world nothing is moving in exact straight line or with constant velocity these are very local relative terms. Everything is falling towards something. There is nothing like 100 % inertial or stable or linear in the world. I may say that perfect inertial frame is not present in this universe.

This may be only my view. thanks

 

Not really relevant to the discussion. Physicists idealize circumstances all the time. The OP speaks of isolated masses, meaning we ignore everything else. It doesn't matter if this can actually be done.

[md65536]

suppose two isolated heavy masses in space move towards each other will the path followed be straig ht line joining the centres of two masses or curved path?

If the masses can be approximated by point masses then I defer to swansont's answer (yes).

 

But suppose m1 is a 1kg point mass and m2 is 2 planets connected with a bar a few AUs apart. I think that if you start with m1 some astronomical distance away, and have m2 oriented so that one of the planets is closer (say with m1 at an angle of 45deg relative to the bar), then m1 will accelerate toward a point very near the center of mass of m2, but as m1 gets very close it will accelerate toward the nearer planet. So the path of m1 will curve.

Edited March 22, 2013 by md65536

[sidharath]

In thought experiment a box with negligible mass isolated in space is subjected to acceleration directed in direction from floor towards ceiling.A box of certain mass when dropped from ceiling will strike the floor with certain impact force.When the experiment is repeated after sometime the ball will strike the floor with more impact force due to acceleration of box the initial velocity of ball as it starts from ceiling will be more as compared to the previous case hence according to special theory of relativity initial mass or energy or momentum of ball will be more which will lead to more impact force . The balls thrown at different time intervals will strike the floor with different impact forces.

If the above experiment is repreatad in box held stationary in uniform gravitational field associated with acceleration g the ball will always strike the floor with same impact force independent of time interval..The above observation leads to conclusion that the the accelerated box or frame and the stationary frame or box placed in uniform gravitational field are not equivalent .The general theory of relativity is based on equivalence principle which here seems to be not correct .Please let me know if my conclusion is correct

[hypervalent_iodine]

!

Moderator Note

I've merged your two topics of the same name and hidden another. Sidharath, please stop doing this! One thread per topic.

[xyzt]

The above observation leads to conclusion that the the accelerated box or frame and the stationary frame or box placed in uniform gravitational field are not equivalent .The general theory of relativity is based on equivalence principle which here seems to be not correct .Please let me know if my conclusion is correct

The above is , of course, incorrect. The error is in your "experiment". Since you are making assertions without doing any computations you will have a hard time figuring out the error. Try putting your assertions in mathematical formalism and you'll find your error (or I 'll point it out to you).

[Spyman]

When the experiment is repeated after sometime the ball will strike the floor with more impact force due to acceleration of box the initial velocity of ball as it starts from ceiling will be more as compared to the previous case...

No, when the ball is attached to the ceiling it must have the same speed as the box.

 

The difference in speed between the ball and the box when it hits the floor will only depend on the acceleration during the time the ball traverses the distance across the box.

 

If the acceleration is equal in two tests then the ball will strike the floor with equal speed in both tests.

[davidivad]

suppose two isolated heavy masses in space move towards each other will the path followed be straig ht line joining the centres of two masses or curved path?

 

if you are only concerned with two or three dimensions in this experiment, then the path will be a straight line in three dimensions. however, considering these objects also have large masses, it is laso important to build a representation of time by plotting the acceleration of the objects up to the point of contact. if you feed your measurements into a graph, you will immediately recognize that the line is curved in the fourth dimension. to clarify my point, the path that the two masses travel also contains an additional aspect which shows a clear curvature in space-time.

[sidharath]

i am sorry that i wrote the title of the new thread as --general relativity . The title of the new thread should have been as - Equivalence Principle and i request you to discuss the new thread as such. i am eagerly waiting for your valuable thoughts so that my doubts could be removed because i approached you after going through some terxts

according to special theory of relativity the ball in the moving frame or box will acquire more and more mass or energy with time because acceleration leads to increase in velocity which leads increase in mass or energy . The impact momentum depends on mass as well as velocity hence impact force increases with time in accelerated frame or box as compared to stationary frame or it can also be said that more and more force is needed to pick the ball from floor as time increases.Moreover the force formula according to special theory of relativity involves velocity in the denominator hence force changes with time actually it increases with increases in velocity because force relation is of such a form

[pzkpfw]

... according to special theory of relativity the ball in the moving frame or box will acquire more and more mass or energy with time because acceleration leads to increase in velocity which leads increase in mass or energy . The impact momentum depends on mass as well as velocity hence impact force increases with time in accelerated frame or box as compared to stationary frame or it can also be said that more and more force is needed to pick the ball from floor as time increases.Moreover the force formula according to special theory of relativity involves velocity in the denominator hence force changes with time actually it increases with increases in velocity because force relation is of such a form

 

Relative to something else, yes, the ball gets more "relative mass". But relative to the box it's in, no. The whole point of the equivalence principle is that in looking at the box and ball we can consider them as at rest. The ball will hit the floor of the box with the same force, regardless of speed (of the box, relative to whatever else), as long as the acceleration at each time is the same.

[xyzt]

i am sorry that i wrote the title of the new thread as --general relativity . The title of the new thread should have been as - Equivalence Principle and i request you to discuss the new thread as such. i am eagerly waiting for your valuable thoughts so that my doubts could be removed because i approached you after going through some terxts

according to special theory of relativity the ball in the moving frame or box will acquire more and more mass or energy with time because acceleration leads to increase in velocity which leads increase in mass or energy . The impact momentum depends on mass as well as velocity hence impact force increases with time in accelerated frame or box as compared to stationary frame or it can also be said that more and more force is needed to pick the ball from floor as time increases.Moreover the force formula according to special theory of relativity involves velocity in the denominator hence force changes with time actually it increases with increases in velocity because force relation is of such a form

Spyman (and pzkpfw) explained to you why you are wrong. Put his words into math and , hopefully, if you do the math right, you will realize why, despite your insistence, you are wrong. I asked you to do that before.

In thought experiment a box with negligible mass isolated in space is subjected to acceleration directed in direction from floor towards ceiling.A box of certain mass when dropped from ceiling will strike the floor with certain impact force.When the experiment is repeated after sometime the ball will strike the floor with more impact force due to acceleration of box the initial velocity of ball as it starts from ceiling will be more as compared to the previous case hence according to special theory of relativity initial mass or energy or momentum of ball will be more which will lead to more impact force . The balls thrown at different time intervals will strike the floor with different impact forces.

 

 

In the frame of the box, your statement is false.

 

 

 

If the above experiment is repreatad in box held stationary in uniform gravitational field associated with acceleration g the ball will always strike the floor with same impact force independent of time interval..The above observation leads to conclusion that the the accelerated box or frame and the stationary frame or box placed in uniform gravitational field are not equivalent .The general theory of relativity is based on equivalence principle which here seems to be not correct .Please let me know if my conclusion is correct

In any frame in motion wrt. the box, your statement is false. You made two false statements, taken together, they do not make a correct statement.

Edited March 6, 2014 by xyzt

[sidharath]

i have applied theory of relativity to arrive at the conclusion that if the ball is placed at floor of the accelerated box the mass o r energy or momentum of the ball goes on increasing due ti increase in velocity hence with time due to increase in mass greater force is needed with time to pick it up from floor (mg).I shall be thankful to you if you let me know why theory of relativity is not applicable . If there is no increase in mass , where does the energy which is associated with increase in velocity goes?

Please devote some time to convey your opinion related to another thought similar to the first . Suppose electron and proton are annihilated in accelerated box and box at rest , will the energy of photons emitted from accelerated box and box or frame at rest be same .?

[Strange]

i have applied theory of relativity to arrive at the conclusion that if the ball is placed at floor of the accelerated box the mass o r energy or momentum of the ball goes on increasing due ti increase in velocity hence with time due to increase in mass greater force is needed with time to pick it up from floor (mg).I shall be thankful to you if you let me know why theory of relativity is not applicable .

 

As has been explained: it is the theory of relativity. The ball and you always have the same relative velocity as the box accelerates and so you will not see it increase in mass. To assume it does, assumes you think that the velocity is relative to some absolute frame of reference.

 

 

If there is no increase in mass , where does the energy which is associated with increase in velocity goes?

 

Relative to you, in the box, there is no change in velocity.

 

 

Please devote some time to convey your opinion related to another thought similar to the first . Suppose electron and proton are annihilated in accelerated box and box at rest , will the energy of photons emitted from accelerated box and box or frame at rest be same .?

 

(I assume you mean electron and positron.)

 

This is very ambiguous. If, as in the first question, you are in the box then there is no relative velocity between you and the particle-antiparticle and the energy of the photons will be 511keV.

 

But if the box is moving relative to you, then the energy of the photons (as measured by you) will be greater.

[pzkpfw]

i have applied theory of relativity to arrive at the conclusion that if the ball is placed at floor of the accelerated box the mass o r energy or momentum of the ball goes on increasing due ti increase in velocity hence with time due to increase in mass greater force is needed with time to pick it up from floor (mg).I shall be thankful to you if you let me know why theory of relativity is not applicable . If there is no increase in mass , where does the energy which is associated with increase in velocity goes?

Please devote some time to convey your opinion related to another thought similar to the first . Suppose electron and proton are annihilated in accelerated box and box at rest , will the energy of photons emitted from accelerated box and box or frame at rest be same .?

 

Say you are standing on scales, on the "floor" of the accelerated box. It shows your weight, as a result of your mass and the acceleration of the box.

 

If the box is accelerating at 9.8 m/s/s, it will show the same weight as if you were at home in your bathroom.

 

If it continues to accelerate at the same rate, and you measure yourself after some time - when your speed (relative to something left behind where you started from) is hugely greater - you'd still see the same weight on the scales. In the frame of the box, nothing's changed, in that constant acceleration.

 

Your relativistic mass is in relation to something else. Accelerate at 9.8 m/s/s for one minute then smack into something (that's at rest relative to where you started from), or accelerate at 9.8 m/s/s for one day then smack into that same thing - then you'll see the difference.