This is a very common misunderstanding of the relativity namely assuming that speed does increase the gravitational mass. Speed does not change gravitational mass of an object. btw different observers see it as moving at different speeds.
what is ment in popular science textbooks by "mass increases with the increase in speed" is that relativistic mass (as calculated by a given observer) increases with increase in their relative speed. Think of relativistic mass as an attempt by a given observer to calculate what a mass of an object should be to safe the ordinary physics picture in observer's eyes :) so that he can apply for example Newton's law F=ma etc.
"If a rocket A is traveling away from me at 0.6c in a Westerly direction, and another B is traveling away from me at 0.6c in an Easterly direction, then the total distance between A and B as seen in my frame of reference is increasing at 1.2c. An apparent relative speed greater than c can be observed by a third person in this way.
However, this is not what is normally meant by relative speeds. The true speed of rocket A relative to rocket B is the speed at which an observer in rocket B observes his distance from A to be increasing. The two speeds must be added using the relativistic formula for addition of velocities. (see Relativity FAQ How do You Add Velocities in Special Relativity?) In this case the relative speed is actually about 0.88c so this is not FTL travel.
"
In this case it feels natural for me to regard the 'true speed' to be 1.2 c and not the speed observed by the person in rocket B.
One thing.Spacetime itself is supposed to be absolute.As far as we do not try to go below Planck time and length,then space and time loses their meanings.
But where does one single region of this fundamental interval begin? Or at what coordinates in any frame of reference can you identify with any certainty that no events take place in adjacent halves of two such regions? What is meant by 'absolute'?
Planck length is 10^-35m and time is 10^43s.
To get to this scale with collider requires energy needed to create black hole and collider would be bigger than Sol system.
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I took definition of absolute spacetime from The Fabric of Cosmos by Brian Green:
"Look at space at any moment from whatever perspective,as on not-changing stage independent of its content."
so one could treat a mass as 4-vector and then say that the m0 is a 4-vector projection on the time axis and mr is full vector length
and (p/c) would be a projection on 3D space plane
however more appropriate would be to speak not about mass vector but about 4-impulse or 4-vector of quantity of motion and then define mass from there.
rest mass is a motion in the direction of time as opposed to p (3D vector) indicating motion in 3D space.
The fact that different observers in relative motions to each other have their own different 3D-planes and time-axis - that causes them to see masses (projections of the same 4-vector) differently as well
[The fact that different observers in relative motions to each other have their own different 3D-planes and time-axis - that causes them to see masses (projections of the same 4-vector) differently as well
Lets assume that they only use change of gravity to decide the mas of an object, say they measure the changed curvature of space close to the object, would they still have different opinion of the mas in that case?
Assume a disc (or a ring) of solid material with a mass so high that it would almost become a black hole.
Now let's assume this disc is rotating (around its normal vector). Will this cause the critical mass to increase (as there's the fictitious centrifugal force) or to decrease (as the rotation energy is mass according to E=mc²)? Or does "frame dragging" prevent this?
Now, assume two discs located in the same place (provided that they can interpenetrate each other) but rotating in opposite directions. Can the additional mass increase due to rotation energy now cause them to become a black hole?
Assume a disc (or a ring) of solid material with a mass so high that it would almost become a black hole.
Now let's assume this disc is rotating (around its normal vector). Will this cause the critical mass to increase (as there's the fictitious centrifugal force) or to decrease (as the rotation energy is mass according to E=mc²)?
In the inertial frame of the rotating ring, no increase in mass is measured.
Quote:
Or does "frame dragging" prevent this?
Don't know enough about what frame dragging means, but if it means the same as these questions, it's a good one for the physics-top-guns :) By frame dragging, do you mean, “can it curve spacetime enough where it was, to make it felt where it is? And if so, would it increase or decrease the measure of mass in the inertial frame of the rotating ring?� My guess is no, since that would be sort of like it was outrunning its own gravity waves...
Quote:
Now, assume two discs located in the same place (provided that they can interpenetrate each other) but rotating in opposite directions. Can the additional mass increase due to rotation energy now cause them to become a black hole?
Like counter-rotating concentric spheres? Like something magnetohydrodynamic inside a neutron star? That's even better than the frame dragging question! Gonna have to guess a definite maybe on that one :)
While the geodetic effect has been confirmed, there are not yet solid results for frame dragging, much more difficult to observe. See this: Gravity probe B
Tullio
This is a very common
)
This is a very common misunderstanding of the relativity namely assuming that speed does increase the gravitational mass. Speed does not change gravitational mass of an object. btw different observers see it as moving at different speeds.
what is ment in popular science textbooks by "mass increases with the increase in speed" is that relativistic mass (as calculated by a given observer) increases with increase in their relative speed. Think of relativistic mass as an attempt by a given observer to calculate what a mass of an object should be to safe the ordinary physics picture in observer's eyes :) so that he can apply for example Newton's law F=ma etc.
Thank you for your
)
Thank you for your clarifications. After reading your explanation and the information found here http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html and here http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html I understand that most of the time I have difficulties to understand the theory of relativity it is because I have a different meaning of certain words than a scientist have, as in this case...
"If a rocket A is traveling away from me at 0.6c in a Westerly direction, and another B is traveling away from me at 0.6c in an Easterly direction, then the total distance between A and B as seen in my frame of reference is increasing at 1.2c. An apparent relative speed greater than c can be observed by a third person in this way.
However, this is not what is normally meant by relative speeds. The true speed of rocket A relative to rocket B is the speed at which an observer in rocket B observes his distance from A to be increasing. The two speeds must be added using the relativistic formula for addition of velocities. (see Relativity FAQ How do You Add Velocities in Special Relativity?) In this case the relative speed is actually about 0.88c so this is not FTL travel.
"
In this case it feels natural for me to regard the 'true speed' to be 1.2 c and not the speed observed by the person in rocket B.
RE: Klimax
)
Planck length is 10^-35m and time is 10^43s.
To get to this scale with collider requires energy needed to create black hole and collider would be bigger than Sol system.
-
I took definition of absolute spacetime from The Fabric of Cosmos by Brian Green:
"Look at space at any moment from whatever perspective,as on not-changing stage independent of its content."
RE: Thank you for your
)
well if you look more carefully at the formulae
mr = E/c^2
m0 = sqrt(E^2/c^4 - p^2/c^2)
you can almost see the pithagor triangle here.
m0^2 + (p/c)^2 = mr^2
so one could treat a mass as 4-vector and then say that the m0 is a 4-vector projection on the time axis and mr is full vector length
and (p/c) would be a projection on 3D space plane
however more appropriate would be to speak not about mass vector but about 4-impulse or 4-vector of quantity of motion and then define mass from there.
rest mass is a motion in the direction of time as opposed to p (3D vector) indicating motion in 3D space.
The fact that different observers in relative motions to each other have their own different 3D-planes and time-axis - that causes them to see masses (projections of the same 4-vector) differently as well
RE: [The fact that
)
Lets assume that they only use change of gravity to decide the mas of an object, say they measure the changed curvature of space close to the object, would they still have different opinion of the mas in that case?
Assume a disc (or a ring) of
)
Assume a disc (or a ring) of solid material with a mass so high that it would almost become a black hole.
Now let's assume this disc is rotating (around its normal vector). Will this cause the critical mass to increase (as there's the fictitious centrifugal force) or to decrease (as the rotation energy is mass according to E=mc²)? Or does "frame dragging" prevent this?
Now, assume two discs located in the same place (provided that they can interpenetrate each other) but rotating in opposite directions. Can the additional mass increase due to rotation energy now cause them to become a black hole?
RE: Assume a disc (or a
)
In the inertial frame of the rotating ring, no increase in mass is measured.
Don't know enough about what frame dragging means, but if it means the same as these questions, it's a good one for the physics-top-guns :) By frame dragging, do you mean, “can it curve spacetime enough where it was, to make it felt where it is? And if so, would it increase or decrease the measure of mass in the inertial frame of the rotating ring?� My guess is no, since that would be sort of like it was outrunning its own gravity waves...
Like counter-rotating concentric spheres? Like something magnetohydrodynamic inside a neutron star? That's even better than the frame dragging question! Gonna have to guess a definite maybe on that one :)
RE: Don't know enough about
)
I mean the effect seen around a rotating black hole. IMHO it should also appear (to a lesser extend) around rotating massive objects, too.
Yes.
RE: RE: Don't know enough
)
This effect was examinated by Gravity probe B.
While the geodetic effect has
)
While the geodetic effect has been confirmed, there are not yet solid results for frame dragging, much more difficult to observe. See this:
Gravity probe B
Tullio