Light Speed
- Thread starter Mcloud
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Hi Mcloud,
The experiment is still to be conducted, but from the theories we have the answer would be: no, the car will never reach the speed of light (in vacuum). It will go faster and faster (assuming there always is some gravitational interaction that pulls the car down the slope), and asymptotically approach the speed of light. However, it would take an infinite amount of time to actually reach the speed of light.
Bye!
Crisp
The experiment is still to be conducted, but from the theories we have the answer would be: no, the car will never reach the speed of light (in vacuum). It will go faster and faster (assuming there always is some gravitational interaction that pulls the car down the slope), and asymptotically approach the speed of light. However, it would take an infinite amount of time to actually reach the speed of light.
Bye!
Crisp
Hang on. No friction, no air resistance, continually shooting down. If we assume into a gravity well, it is continually accelerating. Regardless of what speed you set as your benchmark, it will reach it. It is continually accelerating. The leaps in speed in m/s are continually growing. How could it not reach lightspeed, or any given speed?
Hi all,
Important remark: from a Newtonian point of view, and this is what our "daily intuition" pretty much comes down to, you would expect that the velocity increases towards infinity:
x(t) = x<sub>0</sub> + (1/2)*a*t<sup>2</sup>
Unfortunately, at high speeds, this formula no longer works out that well. At higher speeds you need to correct the reasoning above. I won't go too much into relativistic dynamics (that covers acceleration), simply because I never studied it a lot, but you can see it goes wrong in the following relativistic formulas:
We know the energy of a particle/object is given by:
E = m<sub>0</sub>c<sup>2</sup> / sqrt( 1 - (v/c)<sup>2</sup>)
Solving this for v<sup>2</sup> gives:
v<sup>2</sup> = (1 - m<sub>0</sub><sup>2</sup>c<sup>4</sup> / E<sup>2</sup>)*c<sup>2</sup>
What the gravitational interaction does is increase the energy. There is no upper limit to the energy, so its contineous increase can be seen as the limit E -> infinity. Taking the limit E -> infinity makes the second term between the brackets disappear and we find:
v = c (for E = infinity)
The limiting speed is hence the speed of light in vacuum, but to attain it we need to supply an infinite amount of energy. Since infinity is very (very, VERY) large, we'll need a long time to add that amount of energy... an infinite amount of time actually. So to conclude: the vehicle/object/particle will always increase its velocity towards the speed of light, but it will never actually reach that speed.
I hope this explains things a bit.
Bye!
Crisp
Important remark: from a Newtonian point of view, and this is what our "daily intuition" pretty much comes down to, you would expect that the velocity increases towards infinity:
x(t) = x<sub>0</sub> + (1/2)*a*t<sup>2</sup>
Unfortunately, at high speeds, this formula no longer works out that well. At higher speeds you need to correct the reasoning above. I won't go too much into relativistic dynamics (that covers acceleration), simply because I never studied it a lot, but you can see it goes wrong in the following relativistic formulas:
We know the energy of a particle/object is given by:
E = m<sub>0</sub>c<sup>2</sup> / sqrt( 1 - (v/c)<sup>2</sup>)
Solving this for v<sup>2</sup> gives:
v<sup>2</sup> = (1 - m<sub>0</sub><sup>2</sup>c<sup>4</sup> / E<sup>2</sup>)*c<sup>2</sup>
What the gravitational interaction does is increase the energy. There is no upper limit to the energy, so its contineous increase can be seen as the limit E -> infinity. Taking the limit E -> infinity makes the second term between the brackets disappear and we find:
v = c (for E = infinity)
The limiting speed is hence the speed of light in vacuum, but to attain it we need to supply an infinite amount of energy. Since infinity is very (very, VERY) large, we'll need a long time to add that amount of energy... an infinite amount of time actually. So to conclude: the vehicle/object/particle will always increase its velocity towards the speed of light, but it will never actually reach that speed.
I hope this explains things a bit.
Bye!
Crisp
hmmmm, strange theory here
ok, don't now where, but i recall i've read something like the following:
when you reach speeds near the speed of light, you become much heavier (due to the enormous amount of energy you 'absorb' orso?????).....and then you need more energy to accelerate, you'll get heavier, more energy etc. etc.
this makes it impossible to reach the speed of light...
No I don't remember all of it....but his it about everything I know about it.
Am i totally wrong here or is there really some speed-weight theory??
ok, don't now where, but i recall i've read something like the following:
when you reach speeds near the speed of light, you become much heavier (due to the enormous amount of energy you 'absorb' orso?????).....and then you need more energy to accelerate, you'll get heavier, more energy etc. etc.
this makes it impossible to reach the speed of light...
No I don't remember all of it....but his it about everything I know about it.
Am i totally wrong here or is there really some speed-weight theory??
the answer is no as terminal velocity with gravity is when the force of air resistance pushing up against the skydiver is equal to the force of gravity pushing her downward or roughly 120 miles per hour. Body weight , size ,and how you lay effect that. But if you go to space or a place with no gravity than no force would push you down.
Common sense will tell you that in order to exceed the speed of light you just accelerate two different objects to more than half the speed of light and have them travel towards one another, thus obtaining a relative speed greater than c. If for example an object is moving at 55 MPH in one direction and another object is moving at 55 MPH in the opposite direction, they're combined speeds will equal 110 MPH. But common sense does not prevail here because the universe doesn't work that way. The fabric of space and time is such that no one observer ever sees another object moving at speeds greater than c. Combined velocities of any two objects moving towards one another will always = < c.
As an object approaches the speed of light, its relativistic mass increases. That is not to say that the actual mass of the object (rest mass) begins to increase, or gets 'heavier' but instead certain properties of the mass increase. Those properties include the relativistic momentum and relativistic kinetic energy. The amount of energy required to accelerate mass to attain light speed reaches infinity. And the only known source of energy that is considered infinite enough is the energy contained in a 'Big Bang.'
The Einstein velocity addition expressions are used to show that the relative velocity of any two objects never exceeds the velocity of light. One would apply the Lorentz transformation to the different velocities to express the relative velocities as seen by the different observers. However, in most applications, Newtonian physics can be used to calculate velocities to about 85-90% the speed of light. Once the velocities or combined velocities exceed 90% the speed of light, the velocity addition expressions should be used. It is within this window of near speed of light velocities that most drastic changes occur; ie. time dilation, length contraction, relativistic mass increases and relative velocities.
As an object approaches the speed of light, its relativistic mass increases. That is not to say that the actual mass of the object (rest mass) begins to increase, or gets 'heavier' but instead certain properties of the mass increase. Those properties include the relativistic momentum and relativistic kinetic energy. The amount of energy required to accelerate mass to attain light speed reaches infinity. And the only known source of energy that is considered infinite enough is the energy contained in a 'Big Bang.'
The Einstein velocity addition expressions are used to show that the relative velocity of any two objects never exceeds the velocity of light. One would apply the Lorentz transformation to the different velocities to express the relative velocities as seen by the different observers. However, in most applications, Newtonian physics can be used to calculate velocities to about 85-90% the speed of light. Once the velocities or combined velocities exceed 90% the speed of light, the velocity addition expressions should be used. It is within this window of near speed of light velocities that most drastic changes occur; ie. time dilation, length contraction, relativistic mass increases and relative velocities.
I want to see c....
ok Q, you're raising some questions now:
when we can calculate up to 85% of light-speed, why can't the observer see someone relatively going faster than c? As long as they both travel at 1/2 c, I can't of any phusic-law to 'forbid' it.
another note about the big-bang thing...I don't think you are right there, as long as e=mc^2 is valid....an infinite amount of energy at the big-bang will give us an infinite amount of energy in space, combined with an infinte amount of mass....that's impossible as far as I know:
an infinite amount of energy at the start will give the expansion of space an infinite acceleration, space will be infinite, with infinite mass....which will be impossible because of the acceleration....
phew, I know, I am making some mistakes here, but the main point is true: There is no such thing as an infinite amount of energy.
space ya!
ok Q, you're raising some questions now:
when we can calculate up to 85% of light-speed, why can't the observer see someone relatively going faster than c? As long as they both travel at 1/2 c, I can't of any phusic-law to 'forbid' it.
another note about the big-bang thing...I don't think you are right there, as long as e=mc^2 is valid....an infinite amount of energy at the big-bang will give us an infinite amount of energy in space, combined with an infinte amount of mass....that's impossible as far as I know:
an infinite amount of energy at the start will give the expansion of space an infinite acceleration, space will be infinite, with infinite mass....which will be impossible because of the acceleration....
phew, I know, I am making some mistakes here, but the main point is true: There is no such thing as an infinite amount of energy.
space ya!
why can't the observer see someone relatively going faster than c?
The speed of light is the ultimate speed limit in the universe. Neither of the observers can travel faster than c, in fact they can only approach c, at best.
As observer (A) approaches c, he sees observer's (B) clock slowing down and practically stopping. Observer (A) also sees the distance between himself and observer (B) in his direction of motion become infinitesimally small. From his (A) point of view he is able to get to observer (B) in practically no time. In pother words, if observer (A) were to hypothetically reach the speed of light, he would, from his point of view, get to observer (B) instantaneously. These are relativistic effects caused by length contraction and time dilation and are why observer (A) cannot see (B) moving faster than c.
All of the above effects are the same for observer (B) from his own point of view.
The speed of light is the ultimate speed limit in the universe. Neither of the observers can travel faster than c, in fact they can only approach c, at best.
As observer (A) approaches c, he sees observer's (B) clock slowing down and practically stopping. Observer (A) also sees the distance between himself and observer (B) in his direction of motion become infinitesimally small. From his (A) point of view he is able to get to observer (B) in practically no time. In pother words, if observer (A) were to hypothetically reach the speed of light, he would, from his point of view, get to observer (B) instantaneously. These are relativistic effects caused by length contraction and time dilation and are why observer (A) cannot see (B) moving faster than c.
All of the above effects are the same for observer (B) from his own point of view.
another note about the big-bang thing...I don't think you are right there
Probably not, that was more or less a tongue-in-cheek comment to help visualize the magnitude of energy required. In my opinion, the only infinite source of energy imaginable is that contained in a Big Bang.
It could arguably be infinitely finite.
Probably not, that was more or less a tongue-in-cheek comment to help visualize the magnitude of energy required. In my opinion, the only infinite source of energy imaginable is that contained in a Big Bang.
It could arguably be infinitely finite.
