- #1
epkid08
- 264
- 1
(1) From the length contraction equation, would [tex](L\sqrt{1-(v/c)^2} )^3[/tex] give the coordinate volume of an object?
Here's the mass equation:
[tex]M=\frac{m_0}{\sqrt{1-(v/c)^2}}[/tex]
My second question is ultimately about the 'speed limit' of the universe.
As seen by an observer, an object's mass will approach infinity as its velocity approaches c. From this we can say that, as seen by an observer, it will take a force equal to infinity to accelerate the object to c, and because it's impossible for anything to apply that force, we say that the speed limit of the universe is c.
For the most part this makes perfect sense. As seen by an observer, an object approaching a velocity of c would experience the fallowing: length approaching zero, time approaching infinity, mass approaching infinity etc. This can be easily visualized, as something approaches c, it escapes more and more light, and in theory, if it reached c, the object would vanish, in turn revealing a zero length, infinite time, and a questionably visualized infinite mass.
But what about the proper variables? They don't change with an increase in velocity. Mass, time, and length, by definition, don't change in the object's inertial frame. The object keeps its own rest mass. This is my main point as the 'speed limit' was initially set because the object's coordinate mass approaches infinity, but now I'm saying that an object's mass doesn't change in its inertial frame. That being said, I think it's obvious that the energy required for an object to accelerate itself to c, is in fact finite. Keep in mind, it's very important that the force be applied from within the object's inertial frame. If the force was applied from outside of the frame, it would take an infinite force for the object to reach c.
The speed limit of c holds very true in special relativity. In theory, an observer will NEVER see an object traveling at or faster than c, for more than one reason. To be honest, I see no proof that the speed limit of c holds true in all cases. Obviously there is no proof that faster than light travel is possible, but even if it was very possible, we still wouldn't be able to observe that.
To conclude, in theory, an object can reach the speed of light or greater with a finite force applied to itself from within its inertial frame.
(2) Why wouldn't this statement be true?
(whether or not we know how to initiate the above bolded phrase, doesn't change the theoretical case)
Here's the mass equation:
[tex]M=\frac{m_0}{\sqrt{1-(v/c)^2}}[/tex]
My second question is ultimately about the 'speed limit' of the universe.
As seen by an observer, an object's mass will approach infinity as its velocity approaches c. From this we can say that, as seen by an observer, it will take a force equal to infinity to accelerate the object to c, and because it's impossible for anything to apply that force, we say that the speed limit of the universe is c.
For the most part this makes perfect sense. As seen by an observer, an object approaching a velocity of c would experience the fallowing: length approaching zero, time approaching infinity, mass approaching infinity etc. This can be easily visualized, as something approaches c, it escapes more and more light, and in theory, if it reached c, the object would vanish, in turn revealing a zero length, infinite time, and a questionably visualized infinite mass.
But what about the proper variables? They don't change with an increase in velocity. Mass, time, and length, by definition, don't change in the object's inertial frame. The object keeps its own rest mass. This is my main point as the 'speed limit' was initially set because the object's coordinate mass approaches infinity, but now I'm saying that an object's mass doesn't change in its inertial frame. That being said, I think it's obvious that the energy required for an object to accelerate itself to c, is in fact finite. Keep in mind, it's very important that the force be applied from within the object's inertial frame. If the force was applied from outside of the frame, it would take an infinite force for the object to reach c.
The speed limit of c holds very true in special relativity. In theory, an observer will NEVER see an object traveling at or faster than c, for more than one reason. To be honest, I see no proof that the speed limit of c holds true in all cases. Obviously there is no proof that faster than light travel is possible, but even if it was very possible, we still wouldn't be able to observe that.
To conclude, in theory, an object can reach the speed of light or greater with a finite force applied to itself from within its inertial frame.
(2) Why wouldn't this statement be true?
(whether or not we know how to initiate the above bolded phrase, doesn't change the theoretical case)