Are you even aware of the contradiction contained in these two statements?
SR Issue
- Thread starter chinglu
- Start date
It is rather easy.
Type this into google:
"Time dilation GPS".
Here is the first result which seems fine.
"Modern 'classical physics'"? Oy. Please just stop embarrassing yourself and Google the term.
Please just explain yourself the first time you make a comment so I don't have to ask you to every time. Make a statement.
http://en.wikipedia.org/wiki/Aether_theory
Please educate yourself about "aether theory" and try to understand it is not part of classical physics.
I don't teach by giving answers. I teach by asking questions and encouraging people to think critically about their ideas and think for themselves. I'm sorry if doing either of these is too much work for you.
The answer, of course, is that the time dialation in the GPS networks is a problem of gravity as well as velocity, and so your desire to deal exclusively with special relativity is contradicted by your desire to deal with the problem of time dialation in the GPS network.
Of the list that I gave you, as I recall, the following problems are ones involving special relativity rather than general relativity:
The extended half-lives of muons created by cosmic ray spallation in the earth's atmosphere.
Cherenkov Radiation.
The colour of gold.
Given the understanding of quantum mechanics you have displayed elsewhere, I would recomend steering well clear of the gold problem, which narrows your list down to Cherenkov radiation and Muons, with Muons being the obvious choice if you want to talk about clocks.
Oy. While I'm quite sure by your line of inquiry that you don't understand aether theory either, the term you were floundering over and need to google was "classical physics".
Russ_Watters:
- "Aether theory is classical physics."
Reference?
- "Aether theory is classical physics."
Reference?
I certainly agree with you. No idea how humbleteleskop could explain that without relativity.
You can use classical physics to determine the trajectory of say a cannon ball. Classical physics is still applicable to problems within certain boundries today. The luminiferous aether was an aspect of classical physics which has been discarded.
What is Classical Physics?
Now it is time to explain the extended life of muons using claissical physics!
Back up a post, to what I was responding to.
I could of course provide the info easily enough, but in the spirit of teaching, it is better if you do the work yourself. Besides, based on your attitude I'd just as soon let you flounder around for everyone to see than bend over backwards to help you.
If the (frame-dependent) equations of the line are $$A ( x - x_P ) + B c ( t - t_P ) = C ( y - y_P ) + D c ( t - t_P ) = E ( z - z_P ) + F c ( t - t_P ) = 0$$ then it follows the line is time-like if $$\frac{B^2}{A^2} + \frac{D^2}{C^2} + \frac{F^2}{E^2} \lt 1$$. Thus $$ A \neq 0, \; C \neq 0, \; E \neq 0$$.
So it follows that for any $$\Delta t \neq 0$$ that $$N \equiv \left( x_N = x_P - \frac{B}{A} c \Delta t, \; y_N = y_P - \frac{D}{C} c \Delta t, \; z_N = z_P - \frac{F}{E} c \Delta t, \;t_N = t_P + \Delta t \right)$$ is an event on the time-like line such that $$P \neq N$$.
So the (frame-dependent) equation of the hyper plane which is Minkowski-Orthogonal to the time-like line is given by:
$$\begin{eqnarray} 0 = \left< Q-P , \, N - P\quad \right> & = & c^2 (t_Q - t_P)(t_N - t_P) - (x_Q - x_P)(x_N - x_P) - (y_Q - y_P)(y_N - y_P) - (z_Q - z_P)(z_N - z_P)
\\ & = & c^2 (t_Q - t_P) \Delta t + (x_Q - x_P) \frac{B}{A} c \Delta t + (y_Q - y_P) \frac{D}{C} c \Delta t + (z_Q - z_P) \frac{F}{E} c \Delta t
\\ & = & ( c \Delta t ) \left( c (t_Q - t_P) + \frac{B}{A} (x_Q - x_P) + \frac{D}{C} (y_Q - y_P) + \frac{F}{E} (z_Q - z_P) \right) \end{eqnarray}$$
Giving: $$ A C E c t + B C E x + A D E y + A C F z = A C E c t_P + B C E x_P + A D E y_P + A C F z_P$$ which is the equation for a 3-dimensional hyper-plane in a four-dimensional Cartesian coordinate system.
\\ & = & c^2 (t_Q - t_P) \Delta t + (x_Q - x_P) \frac{B}{A} c \Delta t + (y_Q - y_P) \frac{D}{C} c \Delta t + (z_Q - z_P) \frac{F}{E} c \Delta t
\\ & = & ( c \Delta t ) \left( c (t_Q - t_P) + \frac{B}{A} (x_Q - x_P) + \frac{D}{C} (y_Q - y_P) + \frac{F}{E} (z_Q - z_P) \right) \end{eqnarray}$$
Giving: $$ A C E c t + B C E x + A D E y + A C F z = A C E c t_P + B C E x_P + A D E y_P + A C F z_P$$ which is the equation for a 3-dimensional hyper-plane in a four-dimensional Cartesian coordinate system.
Now if we set $$A = 1, \; D = F = 0, \; y_P = z_P = y_Q = z_Q = 0 $$ then we restrict ourselves to the x-t plane. The equation of the time-like line is : $$x + B c t = x_P + B c t_P$$, the condition of being time-like is $$B^2 \lt 1$$, the hyper-plane is now a line: $$B x + c t = B x_P + c t_P$$.
But this line, is a reflection of the time-like line in either of the light-like lines: $$x \pm c t = x_P \pm c t_P$$. So the geometrical meaning of Minkowski-Orthogonal intersecting lines is that bisectors of either of their intersection angles is light-like. This is clearly the case for lines f and j from post #2. Likewise, it is true for lines h and k.
OK, you have a job! [or anyone else attuned with the gold problem]
I understand the muon and Cherenkov radiation illustrations, but am unaware of this "Gold problem"
Can someone fill me in?
OK, don't bother and thanks for raising this "gold problem" re SR of which I was ignorant of.
https://www.fourmilab.ch/documents/golden_glow/
http://www.reddit.com/r/todayilearned/comments/1sgmrn/til_that_gold_gets_its_color_from_special/
Nice to learn something else supporting Einstein's SR....
Why is everyone still referring to Hafele & Keating from 1971, has no one repeated that experiment ever since?
Because repeating an experiment that gives the theoretically expected result is so boring that it is usually referred to as a demonstration. As it happens, many have repeated this experiment including for inclusion on British science television shows.
Classical physics is conducted in the classical domain of applicability. Quantum physics is conducted in a quantum domain of applicability. Research that and you should be able make comments about this subject which are informed.
Aether theory is a topic from 19th century physics, and therefore consists of pre-quantum and pre-relativity (and thus strictly classical) models purporting to describe phenomena for which we have experimental evidence since 1859 don't obey predictions of Newtonian absolute space and absolute time.
Currently, a few child molesters have attempted to re-purpose the term to describe quantum excitations of a relativistic quantum field, but that physics already has a perfectly reasonable name of quantum field theory and doesn't need a old-and-misleading one.
If you link to a specific source, I will tell you if it is child-molesting or physics, and why.
Currently, the simplest physical theories that agree with experiments are Lorentz-covariant and are far simpler than classical models or wildly at odds with 150 years of experimental results.
Currently, a few child molesters have attempted to re-purpose the term to describe quantum excitations of a relativistic quantum field, but that physics already has a perfectly reasonable name of quantum field theory and doesn't need a old-and-misleading one.
If you link to a specific source, I will tell you if it is child-molesting or physics, and why.
Currently, the simplest physical theories that agree with experiments are Lorentz-covariant and are far simpler than classical models or wildly at odds with 150 years of experimental results.
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Neddy Bate
Valued Senior Member
After you apply the LT you get a different location for the light, but you also get a different time, (as rpenner has already explained in his response to this post). Using my example where v=0.500c and d'=1.000 the following results:
According to the Σ frame, the co-location of C' and M event has a time coordinate of t=0.866, and because c=1.000 that means the light flash must be located at x=ct=0.866 at that time. The event described by the light flash being located at (x,t)=(0.866,0.866) can be Lorentz transformed to the Σ' frame and found to have a time coordinate of t'=0.500, so that event is not simultaneous with the co-location event which had a time of t'=1.000.
According to the Σ' frame, the co-location of C' and M event has a time coordinate of t'=1.000, and because c=1.000 that means the light flash must be located at x'=ct'=1.000 at that time. The event described by the light flash being located at (x',t')=(1.000,1.000) can be Lorentz transformed to the Σ frame and found to have a time coordinate of t=1.732, so that event is not simultaneous with the co-location event which has a time of t=0.866.
You did not answer.
What is the distance of the lightning from C' and M in M' frame coordinates when calculated by the M frame.
What is the distance of the lightning from C' and M in M' frame coordinates when calculated by the M' frame.
Why are they different and how can lightning be 2 different distances in M' frame coordinates from C' and M when the are co-located?