About c being constant and interaction at c.

[A Dhingra]

Hi..
I was reading about the special theory of relativity, and was thinking about interactions and speed of source retained by the body getting ejected from the body.
As per the classical idea, imagine an airplane dropping something on the ground, then the dropped object acquires the speed of the airplane, that is due to the interaction between the object and the plane. Now consider if the object starts moving inside the plane with respect to the airplane, then gets ejected we say it has acquired a velocity of itself and also due to the source(depending upon the direction of motion). But as per special relativity there is a bit change in the formula if the speed is comparable to that of light. This suggests that the interaction gets affected by the speed of the body,i.e. reduces with increase in speed; and when the speed approaches c it tends to zero. Well, this can truly explain why light is same speed from every frame because it doesn't acquire the velocity of the source. Further suggesting that the maximum speed with which interactions occur.

I was trying to convince myself if this is how the idea of interaction speed limit =c be explained. Please tell me if this is so or not.

thanks in advance..

 

[ghwellsjr]

Hi..
I was reading about the special theory of relativity, and was thinking about interactions and speed of source retained by the body getting ejected from the body.
As per the classical idea, imagine an airplane dropping something on the ground, then the dropped object acquires the speed of the airplane, that is due to the interaction between the object and the plane. Now consider if the object starts moving inside the plane with respect to the airplane, then gets ejected we say it has acquired a velocity of itself and also due to the source(depending upon the direction of motion). But as per special relativity there is a bit change in the formula if the speed is comparable to that of light. This suggests that the interaction gets affected by the speed of the body,i.e. reduces with increase in speed; and when the speed approaches c it tends to zero. Well, this can truly explain why light is same speed from every frame because it doesn't acquire the velocity of the source. Further suggesting that the maximum speed with which interactions occur.

I was trying to convince myself if this is how the idea of interaction speed limit =c be explained. Please tell me if this is so or not.

thanks in advance..

You are trying to explain Einstein's second postulate. Since it's a postulate, it doesn't need an explanation. We only need to determine if it is consistent with reality and it is.

 

[A Dhingra]

To an extent, yes, i am trying to explain the second postulate (to myself) to feel satisfied that i have understood it somewhat.
is the argument logical?

 

[Nugatory]

This suggests that the interaction gets affected by the speed of the body,i.e. reduces with increase in speed; and when the speed approaches c it tends to zero. Well, this can truly explain why light is same speed from every frame...

If thinking about it this way helps satisfy you as to the intuitive reasonableness of the second postulate, then go ahead and think about it that way.... But you may find that it becomes problematic when you introduce a third observer who is in motion relative to both the airplane and the earth as the one interaction has to make things come out right for both observers.

 

[ghwellsjr]

To an extent, yes, i am trying to explain the second postulate (to myself) to feel satisfied that i have understood it somewhat.
is the argument logical?

Arguments don't apply to postulates. You need to understand that.

 

[A Dhingra]

But you may find that it becomes problematic when you introduce a third observer who is in motion relative to both the airplane and the earth as the one interaction has to make things come out right for both observers.

this came to my mind while i was writing the post and i just neglected it......
true this creates problem.

 

[ghwellsjr]

I think the best way to "feel good" about the second postulate is to draw a spacetime diagram with radar and/or light signals traveling at c and use the Lorentz Transformation process to make another spacetime diagram for the same scenario and note that all observers continue to see exactly the same things and make exactly the same observations even though the radar and/or light signals are also traveling at c for different distances in this new spacetime diagram.

 

[harrylin]

Hi..
I was reading about the special theory of relativity, and was thinking about interactions and speed of source retained by the body getting ejected from the body.

I don't understand the last part... but next you seem to agree that the speed of the source has no effect on the speed of light, and also very little effect on the speed of particles that are emitted at almost the speed of light.

As per the classical idea, imagine an airplane dropping something on the ground, then the dropped object acquires the speed of the airplane, that is due to the interaction between the object and the plane. Now consider if the object starts moving inside the plane with respect to the airplane, then gets ejected we say it has acquired a velocity of itself and also due to the source(depending upon the direction of motion). But as per special relativity there is a bit change in the formula if the speed is comparable to that of light. This suggests that the interaction gets affected by the speed of the body,i.e. reduces with increase in speed; and when the speed approaches c it tends to zero. Well, this can truly explain why light is same speed from every frame because it doesn't acquire the velocity of the source. Further suggesting that the maximum speed with which interactions occur.

I was trying to convince myself if this is how the idea of interaction speed limit =c be explained. Please tell me if this is so or not. [..]

If with "reduced interaction" you imply that an emitted particle from an object going at almost the speed of light acquires nearly no additional momentum and energy, then definitely no, that's wrong.

There have been hypotheses according to which the speed of light is a limit speed because at that speed there is zero force to accelerate a particle. That was debunked by demonstrations such as the Bartozzi experiment.
https://en.wikipedia.org/wiki/Bertozzi_experiment#Bertozzi_experiment
It confirmed that the kinetic energy of accelerated electrons continues to increase as expected, even with little increase in velocity. Although the acceleration method differs from yours, the effect can hardly be any different: as far as we know (and based on uncountable observations) kinetic energy does not depend on the acceleration history.

 

[amos carine]

This isn't about sr exactly, and I don't mean to divert attention away from the sound and important posts above, but I've been struggling with the idea of the postulate of consistency of light in vacum being done away with in gr as mentioned in the popular book authored by Einstein called simply Relativity. I think the argument for dropping the postulate was that because light bent in gravity fields globally or on a large (at least planetary) scale of view, that the principle could no longer be maintianed. Yet when reading the about local regoins in the gr section in On the Meaning of Relativity, I see that they discuss the exact value of the speed of light beinging maintained mathematically in local, regions of spacetime even with gravity, if my read was correct. So is it that c as the speed of light as constant and very important number is not maintained as that exact number in all situations, but is in the regions or special cases when gr is reduced to sr? In my reading of the book Relativty, my impression was that while the rule that in curved spacetime, nothing exceeds the speed of light, not even information, but, yet that what this number is as a numerical value changes ever so slightly because of non Euclidean geometry.
Also, I think in general that while a postulate doesn't need explaining, that looking for new ways to give a reason for known facts is very useful in theoretical pursuits and the development of new ideas.

 

[harrylin]

This isn't about sr exactly, and I don't mean to divert attention away from the sound and important posts above, but I've been struggling with the idea of the postulate of consistency of light in vacum being done away with in gr as mentioned in the popular book authored by Einstein called simply Relativity. I think the argument for dropping the postulate was that because light bent in gravity fields globally or on a large (at least planetary) scale of view, that the principle could no longer be maintianed. Yet when reading the about local regoins in the gr section in On the Meaning of Relativity, I see that they discuss the exact value of the speed of light beinging maintained mathematically in local, regions of spacetime even with gravity, if my read was correct. So is it that c as the speed of light as constant and very important number is not maintained as that exact number in all situations, but is in the regions or special cases when gr is reduced to sr? [..] .

With local measurements the speed of light is still c. However, what Einstein hinted at is that a light wave can only bend due to a speed gradient. See http://en.wikipedia.org/wiki/Huygens–Fresnel_principle. As a matter of fact, Einstein used the Huygens principle for his prediction of light bending around the Sun. No doubt he had that in mind when he wrote the passage that you read. If you need more explanation, please start it as a separate topic.