Below is a quote in the OP from the thread “Comparison of Special Relativity with a Galilean "preferred frame" theory” by poster James R, which brought up an issue I wanted to discuss. I thought this was sufficiently off that topic to warrant a new thread:
As I’ve looked at SR, the constant speed of light postulate has become more intriguing because it appears implicit in SR that c, in a way, can be considered a constant, yet a frame dependent constant? I know there are posters that are substantially more advanced in physics than I am, so perhaps if I outline how I interpret it they can help me understand where I may have erred?
As far I know the constant for c is the ratio of distance per time or x/t (i.e. 299,793,458 per second or 299,793,458/1). Using this, and information on the Muon Experiment from http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html I will explain why it appears implicit to me that x/t of c is “observed” constant (or invariant) from every frame, yet it is also relative constant value to a frame?
Note, as per the site I referenced, t is stated in microseconds, muon speed observed from the ground is .98c, gamma is 5, and I will round c to .3 kilometers/1µs (microsecond), unless otherwise noted.
Essentially I can convert the ground frame’s x and t to the muon frame simply by multiplying them by the inverse of the gamma factor 5 (1/5). Where the ground clock measures the muon traveling for 34 microseconds the muon clock records 34*1/5 or 6.8, the ground observes a distance of 10km the muon observes 10*1/5 or 2km.
Where I see this invariant, yet frame relative c, is that for each frame they must see c as .3km/1 µs (x/t), yet we also know that x/t as seen from the muon frame is (x/t)/5 as compared to the ground frame, implying a ground value of c = .3km/1 µs, when the muon value is c = (.3km/1 µs)/5 for the muon?
This does makes sense how c is invariant as seen from a frame, yet also a frame specific value, because where the ground will see light travel 1okm from the muon in 33.333us, the muon will see that light travel 2km in 6.666 µs. In other words the muon observes 1/5, the inverse of the gamma factor, for the light distance and time (x/t); implying that for the muon in order for that frame to observe c as .3km/1us relative to its x/t, that value must also be 1/5 of the grounds c?
My use of (?) is to indicate I know my reasoning may be flawed, yet the math is simple, I am certain it is correct, and the deductions seem sound and logical. There are a few other things that also seem implicit in the math also.
I. That the muon must see x in any direction (x. y, z) as x/5 relative to the ground frame
II. Space (x, y, z,) in the muon frame must be contracted by x/5 relative to the space of the ground in order for both of them to observe a constant and invariant value of c relative to each frames value for x and t to c = x/t.
It would be most helpful if any responders referred directly to this example when discussing any errors or flaws I may have made in my reasoning.
Maxila
As I’ve looked at SR, the constant speed of light postulate has become more intriguing because it appears implicit in SR that c, in a way, can be considered a constant, yet a frame dependent constant? I know there are posters that are substantially more advanced in physics than I am, so perhaps if I outline how I interpret it they can help me understand where I may have erred?
As far I know the constant for c is the ratio of distance per time or x/t (i.e. 299,793,458 per second or 299,793,458/1). Using this, and information on the Muon Experiment from http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html I will explain why it appears implicit to me that x/t of c is “observed” constant (or invariant) from every frame, yet it is also relative constant value to a frame?
Note, as per the site I referenced, t is stated in microseconds, muon speed observed from the ground is .98c, gamma is 5, and I will round c to .3 kilometers/1µs (microsecond), unless otherwise noted.
Essentially I can convert the ground frame’s x and t to the muon frame simply by multiplying them by the inverse of the gamma factor 5 (1/5). Where the ground clock measures the muon traveling for 34 microseconds the muon clock records 34*1/5 or 6.8, the ground observes a distance of 10km the muon observes 10*1/5 or 2km.
Where I see this invariant, yet frame relative c, is that for each frame they must see c as .3km/1 µs (x/t), yet we also know that x/t as seen from the muon frame is (x/t)/5 as compared to the ground frame, implying a ground value of c = .3km/1 µs, when the muon value is c = (.3km/1 µs)/5 for the muon?
This does makes sense how c is invariant as seen from a frame, yet also a frame specific value, because where the ground will see light travel 1okm from the muon in 33.333us, the muon will see that light travel 2km in 6.666 µs. In other words the muon observes 1/5, the inverse of the gamma factor, for the light distance and time (x/t); implying that for the muon in order for that frame to observe c as .3km/1us relative to its x/t, that value must also be 1/5 of the grounds c?
My use of (?) is to indicate I know my reasoning may be flawed, yet the math is simple, I am certain it is correct, and the deductions seem sound and logical. There are a few other things that also seem implicit in the math also.
I. That the muon must see x in any direction (x. y, z) as x/5 relative to the ground frame
II. Space (x, y, z,) in the muon frame must be contracted by x/5 relative to the space of the ground in order for both of them to observe a constant and invariant value of c relative to each frames value for x and t to c = x/t.
It would be most helpful if any responders referred directly to this example when discussing any errors or flaws I may have made in my reasoning.
Maxila
