what is the minimum speed range range at which classical physics is over thrown and relativistic physics plays

Answer 1

Correct me if I am wrong, but it is my understanding that classical physics is just relativistic physics where in the frame of reference of time and c, you are considered arbitrarily "stationary". I say aribitrarily, since in effect we are all moving and nothing in the universe is actually stationary.

Since the frame of reference is entirely based on where you are looking from, any other frame of reference that is traveling at a fraction of c more than you and thereby the measurement of time is slower than yours, will operate with relativistic physics from your perspective, while if you were actually in the other frame of reference, everything that occurs around you would actually still be operating in classical physics.

Now the question you are asking I think is: at what fraction of C must a studied object be traveling for you to need to use relativistic calculations to determine the position and course of that object. That I believe would depend on the precision of the calculations you require and your ability to detect the differences in the measurement of time between the two frames of reference.

For example if something is traveling at 10% of c, then time passes 10% slower for that object from your perspective. Now if your ability to measure the passage of time has an error of +/- 20% then you using relativistic physics would be overkill.

However if that object is traveling 5% of c and your ability to measure the passage of time has an error of +/- 0.01% and you needed that precision, then you would have to use relativistic physics.

For most real world applications where velocities are closer to 0.0001% of c and our ability to detect differences in time is measured in tenths of milliseconds (0.01% of a second), classical physics is just fine.

(addendum: The 10% of c rule mentioned above is consistent with what can typically be measured with an average stop watch (1 tenth of a second or 10% of a second) )

sorry for the numerous revisions... I am a horrible typist :)

Answer 2

There's not real boundary value. Most of the relativistic equations have a factor:

sqrt( 1-(v/c)^2) ) in them. As you can see, it depends smoothly on the ratio of velocity to the speed of light. Since the speed of light is so big it's only very, very fast moving particles that show relativistic effects. An example would be the particles in accelerators. They go on the order of 98% of c.

Answer 3

Yeah, the 10% c range is commonly cited, but as Skywalker says it depends on the circumstance.

At 10% c (check this out Skywalker), the gamma function is:

sqrt (1 - v^2/c^2) = sqrt (1 - 0.1^2) = 0.995

So an object traveling at 10% c would appear to have clocks moving only slightly slower than your own - about 0.5% slower. Relativistic effects such as length contraction and time dilation are not linear with velocity, but follow with the gamma function.

Answer 4

I have heard that you are pretty safe using classical physics until you reach about 10% the speed of light.