Comparison of Special Relativity with a Galilean "preferred frame" theory

I didn't say proper time because that isn't what I was referring to. I said the rate of time passage for each other.

You know, Tach, when I saw your first posts on this forum a couple of years ago I announced that you would make a fine contributor once you matured; I'm beginning to doubt this. You manage to troll up every thread you're involved in. What kind of massive insecurities must you be concealing where you have to include derogatory comments in every single post you ever make?

 

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"Rate of time passage" is a fringe term that you invented, pretty much in line with your using "co-moving" to mean "moving with respect to each other".
Look, RJ, I showed that no matter how you twist and turn and try to re-phrase your statements, they still contain basic errors.

What is the mathematical expression for "rate of time passage"? can you write it down, please?

I simply pointed out your gross mistakes <shrug>. You can see them redlined. I can only suggest that you take an introductory class in SR, at least you would be able to learn the proper terms rather than making up your kooky ones.

 

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What? You really can't figure that out? The rate of time passage of a frame under consideration would be expressed in seconds over seconds.

\({S_{frame}}\over{S_{reference}}\)

The reference frame would be your timepiece representing local proper time. You can calculate this rate via fiddling with

\(t = \frac{t_0}{\sqrt{1-v^2/c^2}}\)

I'm sure I don't need to hold your hand on how to derive this, but I figured you would know what a "rate" meant in the first place.

While I highly doubt I'm the inventor of such a profound and radically earth-shattering phrase as "time passage", you are hereby free to use the term without paying me acknowledgement.

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Err, you are comparing the elapsed proper time of one observer with the elapsed coordinate time of another observer, i.e. apples and oranges. In addition, neither of these qualifies as "rate of time". That SR 101 looks more and more necessary for you, RJ. SR is a theory of invariants (so is GR, by the way).

 

As a point of conversation, I have looked at it per time's empirical dynamics and locally (as seen from a reference frame), it is t=x/v.

That is easiest to see in the function of clocks however; an argument can be made in how it is consistent with experiment and our perceptions of time also. One can also make circular arguments saying formally that velocity is function of time, yet observationally one would physically observe a change of position with energy in respect to distance, than measure points in-between as time.

In any event I would call t=x/v, a “rate” of time, and note that for x/v the ratio matters to a value of t.

Maxila

 

It's not apples and oranges, it's the very basis of the concept of time dilation. The rate of time passage of clocks changes with relative velocity.

 

Actually it doesn't, all clocks tick at the same exact rate, of 1s per second. Look, RJ, instead of pretending that you know what you are talking about while all along making up your own terminology, what don't you enroll in a class. At least, this way, you would know what you are talking about. Using "co-moving" to express observers in motion wrt. each other is not the way to convey that you know the subject matter. Calling time dilation "the rate of time passage" is just as bad.

 

Uhh, if all clocks ticked "at the same exact rate" then time dilation would not exist.

 

Baaaad, time for your class.

 

If I sign up for SR101 will you sign up for courses on Maturity, Civility, and Common Sense? (yes, I recognize the irony in that statement)

 

Sign up for the class, learn the subject matter, hopefully this will help you stop passing nonsense as science and I will treat you with respect.

 

They are only seen to tick at the same exact rate in constant motion when an observer can say that he is at rest relative to the clock. They do not tick at the same rate relative to an observer that is not at rest relative to the clock.

You don't know for a fact that the rate of the passage of time is not different. It is still pseudoscience even though it follows a Newtonian common sense method! Taking a course won't help with this when there are some people that teach it this way even though it is not mainstream science. Most books written on the subject claim that they cannot know the passage of time is slower because everything in that frame runs slower, so there is no difference in the rate of anything in order for them to perceive this change, and that is why they don't notice the change in the rate of the passage of time.

 

In which class do they teach about doppler shift in matte rolling wheels?

 

LOL. I get that inside joke, because I've been reading this forum for a long time. In other words, I'm old.

 

Hey Neddy Bate!!! How's it going? Long time no see! How you been?

 

Hey Motor Daddy!! I'm fine thanks, and you? Don't worry, I've been reading your posts too. Not much luck overturning all of physics, eh?

 

Really?

time = distance/(distance/time)?

So t=(x/1)/(x/t)=(x/1)(t/x)=xt/x=t

Or t=t

So your "rate of time" is the time. Wow, what brilliance.

 

I'm gettin' there, thanks to your help!

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Hi Prof.Layman,

That is a pretty nice derivation of basic time dilation of a vertical light clock (traveling horizontally). Do you have a similar derivation for length contraction of a horizontal light clock (traveling horizontally)? If so, then my next question would be whether you can derive the full Lorentz Transformation equations from there.

 

Word salad. "Empirical dynamics" implies you have examples of experiments that change time in some physical sense. Special Relativity, on the other hand, is about how two different inertial observers make equivalent choices of describing the same space-time and therefore do not change anything.

Word salad. "Locally" cannot be the word you want here.

This is true only of objects whose motion is constant and which at time t=0 are at the coordinate origin, x=0.

The general expression for average velocity (which is of course just velocity if the object's motion is constant) is \( v_{1 \to 2} = \frac{x_2 - x_1}{t_2 - t_1}\). Or generically, written in differences of coordinates: \(v_{A \to B} = \frac{\Delta x}{\Delta t}\) where \(\Delta\) refers to a difference in coordinate values between two related points in space-time.

The general expression for velocity when it is not constant was the reason why calculus was created and in modern notation we can write: \(v = \frac{dx}{dt}\) with an obvious parallel with the expression above. In fact, the expressions are related: \(\lim_{B \to A} v_{A \to B} = \lim_{A \to B} \frac{\Delta x}{\Delta t} = \left. \frac{dx}{dt} \right| _{A} = v(A)\).

What moves in muon decay? Muons have no known moving parts and yet muons which are co-moving with a clock have a fixed rate of proportional decay per nanosecond. This is best explained with proper time being more real than coordinate time and there is never any motion associated with proper time since \(\Delta x_{\tiny \textrm{proper}} = 0\).

For an object moving slower than light, it traces out a curve \(f\) in space-time. This curve can be parametrized equally well in in an infinite number of ways, including by elapsed proper time and elapsed coordinate time for any inertial coordinate system. Even so, we can pick points on the curve, \(A,B \in f\) and talk about their components in any inertial coordinate system. \(\exists \tau_A, t_A, t'_A, t''_A, \dots \left[ A = \left( { A_t \\ A_x \\ A_y \\ A_z } \right) = f(\tau_A) = f(t_A)= f(t'_A)= f(t''_A) \dots \right]\). The coordinate system and parametrization choice are both the imaginary works of man, that doesn't change that the curve \(f\) goes through the space-time point A, no matter what its coordinates might be considered to be. Similarly the curve \(f\) goes through B. So in a given choice of inertial coordinate system the average velocity exists:
\(\vec{v}_{A \to B} = \frac{\Delta \vec{x}}{\Delta t} = \begin{pmatrix} \frac{\Delta x}{\Delta t} \\ \frac{\Delta y}{\Delta t} \\ \frac{\Delta z}{\Delta t} \end{pmatrix} = \begin{pmatrix} \frac{B_x - A_x}{B_t - A_t} \\ \frac{B_y - A_y}{B_t - A_t} \\ \frac{B_z - A_z}{B_t - A_t} \end{pmatrix}\)
But not all inertial coordinate systems agree on the value or direction of this velocity, because coordinate systems are imaginary.
What isn't imaginary is the invariant interval \(c^2( \Delta t)^2-( \Delta x)^2-( \Delta y)^2-( \Delta z)^2 = c^2(B_t - A_t)^2 - (B_x - A_x)^2 - (B_y - A_y)^2 - (B_z - A_z)^2\) as all inertial coordinate systems agree on this value.
Further, \(\Delta \tau = \int_A^B d \tau = \int_{t_A}^{t_B} \sqrt{1 - \frac{v^2}{c^2}} dt = \int_{t_A}^{t_B} \sqrt{1 - \frac{(d f_x)^2+(d f_y)^2+(d f_z)^2}{c^2 (d f_t)^2}} dt\) gives a value that all inertial systems agree on: the proper time for a particle as it moves along space-time path \(f\) from A to B. In Special Relativity two different paths between A and B may have different proper times, which is the origin of the so-called twin paradox.
Thus time experienced by a body is a function of the path the object takes through space-time, or equivalently a function of the history of its velocity.

What observations are you referring to. Please be specific.

Word salad. Nothing here parses as a communicable idea.

This is not physics.

These equations describe the Special Relativistic physics of a free particle:
\(E \vec{v} = c^2 \vec{p} \\ E^2 = c^4 m^2 + c^2 \vec{p}^2 \)

Making \(\vec{v}\) the independent variable and assuming \(m\neq 0\), we have:
\(E = \frac{mc^2}{\sqrt{1 - \frac{\vec{v}^2}{c^2}}} \\ \vec{p} = \frac{m \vec{v}}{\sqrt{1 - \frac{\vec{v}^2}{c^2}}}\)