What is the summary of your findings on frame-dragging ?
I think a relationship can be tested between the relativistic speed and the relativistic mass from the experiment , which i suggested earlier .
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Gravity never zero
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What is the summary of your findings on frame-dragging ?
I think a relationship can be tested between the relativistic speed and the relativistic mass from the experiment , which i suggested earlier .
Due to the effect of frame-dragging , space shifts physically . So , I think following events can be considered as some of the effects of frame-dragging .
Bending of lights , precession of Mercury , black-hole creation , expansion of our universe .
Say we took an object of mass M at zero velocity. Next, we add propulsion energy to the Mass, so its velocity increases toward C. Based on SR, we would generate relativistic mass.
Relativistic mass acts analogous to gravitational mass. in that it contains the potential energy intermediate that is needed to alter space-time. The relativistic mass acts in SR in an way that is loosely analogous to the way mass act in GR.
There is a big difference between the two. With mass and GR there is a pressure effect due to gravity which pushes things physically together within the GR space-time reference. This allows things like fusion to occur. It also increases atmospheric pressure so gases condense, etc.
Relativistic mass of SR acts differently than the mass in GR, in that SR is not about inducing pressure and density, but rather relativistic mass acts similar to the unified force altering everything in the reference, so everything can adjust to the needs of the altered space-time while retaining configurational integrity.
Relativistic mass acts analogous to gravitational mass. in that it contains the potential energy intermediate that is needed to alter space-time. The relativistic mass acts in SR in an way that is loosely analogous to the way mass act in GR.
There is a big difference between the two. With mass and GR there is a pressure effect due to gravity which pushes things physically together within the GR space-time reference. This allows things like fusion to occur. It also increases atmospheric pressure so gases condense, etc.
Relativistic mass of SR acts differently than the mass in GR, in that SR is not about inducing pressure and density, but rather relativistic mass acts similar to the unified force altering everything in the reference, so everything can adjust to the needs of the altered space-time while retaining configurational integrity.
Relativistic mass is a fancy way of talking about momentum. It has no gravitational properties beyond those inherent in the object's mass, "rest mass" or proper mass.
While it is true that a gravitationally significant object's linear and angular momentum contributes to its frame-dragging effect, it is not quite the same as gravitation. And while frame-dragging as it relates to angular momentum has been confirmed, the exact mechanisms have not as yet been clearly defined.
The main thing here is to drop the continued reference to "relativistic mass". Consider a bullet that weighs 20 grams, on the table. When fired from a rifle it still weighs only 20 grams, but has much greater momentum than it did when it was just sitting on the table. The mass of an object is not changed by its velocity. It remains the same from all frames of reference.
A bullet has an invariant mass, but a bullet with a high velocity has more energy than a bullet with a low, or no, velocity.OnlyMe said:
So according to Einstein the fast bullet will have a mass greater than its rest mass, because mass and energy are equivalent. That's just a consequence of relativity.
Whar you're referring to is the Newtonian concept of mass.
Who is right? Relativistic mass or not?
But being the Flash, I'm zipping right alongside the bullet, so in my frame of reference, the bullet has no more velocity, and therefore, no more energy that it had before being fired. Therefore, all there is, from my FoR (which since I'm stationary with regards to the bullet, is also the bullets FoR) is the bullet's rest mass. If we were somehow able to invoke E=mc^2 and convert all the bullet's mass into energy, it would take place in the bullet's FoR, and the only mass there is, is rest mass.
That's just a consequence of relativity.
Can you prove that Rest Mass in each FoR is the same. For I understand all scientific experiments performed on the speeding bullet, would not sense it was speeding WRT the first frame.
So if in the second FoR the bullet was re-fired and the whole FoR thing was repeated ad infinitum was there a possibility the bullet could be speed up faster than the Speed of Light WRT to the original FoR?
This is a common misinterpretation, there is more than one historical reference that suggests that Einstein intended the $$m$$ in the equation $$E = mc^2$$, to represent an object's rest mass.
The link below to a paper by Okun, gives a good historical explanation. It is only six pages and does not require any really heavy duty math.
The Concept of Mass
Letter from Albert Einstein to Lincoln Barnett, 19 June 1948. Einstein wrote in German; the letter was typed and sent in English. The highlighted passage in this excerpt says: "It is not good to introduce the concept of the mass M = m / (1 - v^2/c^2) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion." (Reprinted by permission of the Hebrew University of Jerusalem, Israel.)
Letter from Albert Einstein to Lincoln Barnett, 19 June 1948. Einstein wrote in German; the letter was typed and sent in English. The highlighted passage in this excerpt says: "It is not good to introduce the concept of the mass M = m / (1 - v^2/c^2) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion." (Reprinted by permission of the Hebrew University of Jerusalem, Israel.)
And then in the author's own words, a bit later...
$$E = mc^2$$
This is equation 1: Rest mass was one of Einstein's great discoveries.
This is equation 1: Rest mass was one of Einstein's great discoveries.
Not! See my previous post.
$$E=mc^2$$ is only true for a stationary object.
For a fast bullet, the correct equation is:
$$E=\sqrt{(mc^2)^2+(pc)^2}$$
Which as you can see for a stationary object (p=0) boils down to:
$$E=mc^2$$
And for a photon boils down to:
$$E=pc$$
The first point is the important one to note - if you are co-moving with the fast bullet, you observe its momentum to be zero, therefore you observe only its rest mass.
Correct.
No, there is no possibility that the bullet could be sped up faster than the speed of light, because an observer co-moving with the bullet observe the guns to be being accelerated, and the motion of the guns as seen in the bullets frame obeys relativity just as much as the bullet does in each guns reference frame.So if in the second FoR the bullet was re-fired and the whole FoR thing was repeated ad infinitum was there a possibility the bullet could be speed up faster than the Speed of Light WRT to the original FoR?
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When Einstein said "it is better" that to me is not quite going as far as to saying it doesn't exist. It is better not to mention the bear down the back, doesn't mean there is no bear in the backyard. No it just best not to mention it!
So that reference has not convinced me yet, sorry.
No it isn't a "common misinterpretation". A bullet with a high velocity will appear to have a higher "mass energy" than a bullet with a low, or no, velocity. With the exception that a frame of reference comoving with said bullet will not see a greater energy.OnlyMe said:
Note I stated "mass and energy are equivalent"; this is true for any mass according to Einstein, hence his stipulation: "It is not good to introduce the concept of the mass $$ M = m / (1 - v^2/c^2) $$ of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m."
So $$E=mc^2$$ is only true when m is a rest mass, i.e. when it corresponds to an object with zero relative momentum.
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$$E=mc^2$$ applies for all objects in all frames of reference, it just does not account for any kinetic energy, derived from an object's velocity.
See, the above... The discussion has fallen into a confusion of the energy associated with mass and the kinetic energy of an object that is associated with momentum.
There is only one "mass", which could be described as an object's "proper mass" or "rest mass".
Make note of the following part of Trippy's post,
$$
In both cases momentum is now being described, not just the energy associated with an object's mass. In the case of a photon there is no rest mass. For massive particles and objects, composed of matter, the mass never changes while the total energy does.
Another point, $$E=mc^2$$ does not boil down to mass and energy being interchangeable. What it is really saying is that mass can be described as a specialized form of energy. That is a long way from saying that all energy is mass.$$
I've gotten used to thinking of the 'E' as being total energy (or something along those lines) the point I was driving at is that $$E=mc^2$$ only accounts for the rest energy, and the only time that's equivalent to the total energy is if the object is at rest.
Yes, it applies to all objects, but it only describes the total energy of a stationary object (stricly speaking though, wouldn't that be a stationary object with a temperature of 0k?)
I read that too. Hot objects weigh more than same body when cold. So if heat energy adds to the mass of an object, one would think kinetic energy does too, but with the difficulty of weighing something in motion.
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I'm not sure if you're paraphrasing someone in that last sentence. But are you saying there is only one "energy", which could be described as an object's "proper energy", or "rest energy"?OnlyMe said:
Because clearly that is not true unless the only energy (in the universe) is potential energy, and there is kinetic energy as well. I really can't see what the "confusion" is.
I think the Wikipedia section on "Mass–energy equivalence" and the links from that article go a long way to explaining it.
Trippy, your earlier post was right on and IF you always assume that E is total energy you are also correct. The problem lies in that the equation, $$E = mc^2$$ is describing the energy associated with a particle's or object's frame invariant mass.
When one adds a component of momentum or kinetic energy into the mix, the equation is no longer describing, only the mass energy relationship. It becomes a description of momentum.
The confusion comes in that long ago and still in popular publications and sources, that momentum is often called relativistic mass, which becomes confusing.
An object's gravitational field does not increase with velocity. It remains the same without reguard to an object's velocity.., at rest or in motion. And is associated with its frame invariant mass.
At the risk of adding some additional confusion... The velocity or acceleration of a gravitationally significant mass, can affect the shape of a gravitational field but not its potential. But that gets into frame-dragging and even propagation velocities.
Most of the time what I post is what I am thinking right then. If I add reference, it is generally something I remember having on my digital bookshelf. If I quote or paraphrase, I try to make sure that is set apart from my own words in some way. So, no those were my own words. (But they may be similar to something Okun said in the link I gave earlier.)
Note: I never used the terms, "proper energy" or "rest energy". Those are yours. And I was not not intending to suggest that there is only one energy.
I was talking about mass and then defined that as, "proper mass" or "rest mass", to associate it with frame invariant mass. Mass is mass, it does not change if an object is in motion or at rest. But it can only easily be measured from an object's rest frame of reference.
When an object is in motion (has some velocity or acceleration), it has a mass which is the same as if it were not in motion.., and momentum, which is the product of its mass and velocity.
The idea of relativistic mass, once again, is just a fancy and confusing way to describe momentum. (Likely further confused by its association with the Lorentz factor and speed of light limitation, for velocities.)
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