Instead of reading about it, how about following the actual equations used in Einstein's paper and show us precisely, in the equations, where, what and why you specifically disagree with the conclusions.

__________________
Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Tensor

i recently reopened this thread with a post detailing some simulated experiments.

the reasoning for the experiments was to check the validity of the pythagorean geometry involved in the generation of gamma.

the results showed that the required hypotenuse line cannot be formed in the unit time allowed.

therefore there is no base for the maths to apply to.

This paradox is observed in the Astronomy. A Quasar ejects a jet, This jet emits a light. For us a distant observers seems it like velocity faster then "c".
It is only illusion because a time dilation. There is just one second longer and light can travel a longer distance in the same time.

In a Madman example a photon will reach both mirrors for an inner and outside moving observers because a time dilation and space deformation. The outside observer will see an additionally redshift of the photon. We do not exactly know who is moving - the 2 mirrors or an outside observer. Effect is the same.

Your reasoning was flawed. You said:

What he assumed was that light would travel at the same speed in a frame inertially moving relative to the light clock, which results in the time taken for the light to travel from one mirror to the other to be greater in that moving frame, not the same.

Ah, this old chesnut had me confused for ages and is what initially brought me to bad astronomy. Time dialation is symmetrical all the time both twins are moving apart (or together) intertially -- they both see each others clock running slow [ after taking into account the time taken for the light signals from each other's clock to reach them - this is what is usually meant by "what they see" in these sort of thought experiments ]. This is not paradoxical because they cannot directly compare clocks without coming back together, which would require at least one of them to accelerate.

It is only when one turns around that the symmetry is broken. A sudden turn around causes a sudden forward leap of the other's clock. It is caused by the Lorentz transformation from one intertial frame to the other, the transformation changes what is now over there. And the further away "over there" is, the bigger the leap.

A more realistic turn around over some time causes the other's clock to run fast, according to the turning twin, throughout the turn around. Interestingly, if you integrate over many small Lorentz transformations to work out the effect of accelerating the twin, rather than just suddenly changing his direction of motion, then the effect comes out the same as gravitational time dilation due to a unform g field equivalent to the acceleartion -- the stay-at-home twin is very high up in this pseudo g-field of the turning-around twin and has a subsequently faster running clock (according to the turning-twin) throughout the turn around.

__________________
There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.

worzel (and Tim too)
yes it was wrong of me to use the term "time".

velocity or speed would have been better.

look at the 2nd gif again.

the vertical speed of the light pulse is the same as shown in the first gif (and since it is the unit measurement for light-speed i called it "time" by mistake).

worzel

i can't believe in sudden alterations or "symmetry breaking" concepts as being required for time dilation.


supposedly the basic operation relies upon the strict formation of a right angled triangle.

from which gamma may be derived.

this requires a set unit of velocity for eg: a spaceship.


in the gif examples i posted (taken from and based on many physics websites) the exercise is organised to allow the transmission of the light signal over a physical distance (the hypotenuse) which is always longer than the vertical distance (hence the difference, and supposed acceptable input value for time dilation).

this transmission completes the function by creating the required physical parameter known as "the observer".

without the observer no data is transferred and no result of "time dilation" may be returned.

for example...no one can see the "triangle" or "the zig-zag"....because only the mirror/observer contact points receive data (if the triangle were a polygon..then the observers see only the vertices).

we would not see the light clock "tick-tock" in a meadow near a train because it is not sending that data to us.

if the observer/mirror is kept as part of the exercise then he/it will observe either a tick or a tock...but not both.

Ok, slow down a bit Madman. Start from the beginning.

Do you agree that experiments before the formulation of SR suggested that the speed of light was always the same (against expectations at the time)?

Do you agree that Maxwell's equations imply that the speed of light is always c in a vacuum?

PS I don't understand Maxwell's equations, but I'm happy to accept the word of those that do until such time as I can understand them myself.

__________________
There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.

yes...we are dealing at all times (in these exercises) with light travelling at speed C.

relative motion of frames would be seen as doppler effects.

@czeslaw

************************************************** *******************************
how the extreme value of Gamma is determined by decimal values when velocity is brought asymptotically closer to C.
************************************************** *******************************

first, the formula for Gamma.

**********************************
gamma = 1/sqrt(1-(v*v)/(c*c))
**********************************

and a few examples of deriving Gamma for various velocities...


velocity = 0.9C

gamma = 1/sqrt(1-(90*90)/(100*100))
gamma = 1/sqrt(1-(8100/10000))
gamma = 1/sqrt(1-0.81)
gamma = 1/sqrt(0.19)
gamma = 1/0.4359
gamma = 2.2941
*********************************

velocity = 0.99C

gamma = 1/sqrt(1-(99*99)/(100*100))
gamma = 1/sqrt(1-(9801/10000))
gamma = 1/sqrt(1-0.9801)
gamma = 1/sqrt(0.0199)
gamma = 1/0.1411
gamma = 7.0872
*********************************

velocity = 0.999C

gamma = 1/sqrt(1-(999*999)/(1000*1000))
gamma = 1/sqrt(1-(998001/1000000))
gamma = 1/sqrt(1-0.998001)
gamma = 1/sqrt(0.001999)
gamma = 1/0.0447
gamma = 22.3714
*********************************

note the 3rd last lines in each block of calculations (above)...which i've listed below.

gamma = 1/sqrt(0.19)
gamma = 1/sqrt(0.0199)
gamma = 1/sqrt(0.001999)


to get those values...a subtraction is performed.

gamma = 1/sqrt(1-0.81)
gamma = 1/sqrt(1-0.9801)
gamma = 1/sqrt(1-0.998001)


if the square and square root conversions are stripped out?...then we are left with the core operation.

C - velocity = time dilation (seed value)

*****************************************

the speed of light (C) is given the value 1.
velocity ranges from 0 to 1 (a fraction of light speed C).

velocity is subtracted from C (and the remainder becomes a seed value for Gamma).


so basically (in this slimmed-down exercise) we are dealing with the operational range of 1 - 0 up to 1 - 1.

ie(roughly):

1 - 0 = 1 (no time dilation)
1 - 0.1 = 0.9
1 - 0.2 = 0.8
1 - 0.3 = 0.7
1 - 0.4 = 0.6
1 - 0.5 = 0.5
1 - 0.6 = 0.4
1 - 0.7 = 0.3
1 - 0.8 = 0.2
1 - 0.9 = 0.1
1 - 1 = 0 (time stops?)

************************************************** ****

so what happens when velocity is brought asymptotically closer (nearer and nearer) to C....ie: >0.9C?


******************************************
C - velocity = time dilation seed value
******************************************

1 - 0.9 = 0.1
1 - 0.99 = 0.01
1 - 0.999 = 0.001
1 - 0.9999 = 0.0001
1 - 0.99999 = 0.00001
1 - 0.999999 = 0.000001
1 - 0.9999999 = 0.0000001
1 - 0.99999999 = 0.00000001

*****************************************

as the velocity increases towards 1, the product of "C - velocity" will become a smaller fraction.

accordingly with each decimal increase in velocity, the gamma seed value will be pushed a decimal place smaller as a fraction.

this is solely a product of the mathematical model chosen...it in no way relates to any supposed "special" qualities of "relativistic" speed.

but instead shows the real reason why Gamma attains "significant" values at speeds "very close to C".

**************************************************

here's another version

http://www.fourmilab.ch/cship/timedial.html


and a slightly tidied up copy of the proper results (from that page) to show the numerical progression.

************************************************** **
velocity.................................days..... .....years
************************************************** **
0.9.........................................2.2... .......0.006
0.99.......................................7...... .......0.019
0.999....................................22....... ......0.061
0.9999..................................70........ ......0.19
0.99999...............................220......... .....0.61
0.999999.............................700.......... ....1.9
0.9999999..........................2200........... ...6.1
0.99999999........................7000............ .19
0.999999999.....................22000............. 61
0.9999999999...................70000 ...........190
0.99999999999 ...............220000............610
0.999999999999..............700000...........1900
0.9999999999999...........2200000...........6100
0.99999999999999.........7000000..........19000
0.999999999999999......22000000..........61000
************************************************** **
*************************************************

I'm arguing that you're saying Einstein was wrong in assuming the light could travel along the diagonal in unit time, but since Einstein never said that, he can't have been wrong about it.

Grey

my impression is that the light is supposed to travel the length of the hypotenuse in the unit time.

this is supposed to create the quandary that einstein resolves by formulating the following.

light speed must not alter...instead distance and time must be adjusted.

and this is to explain how the light could travel the larger distance of the hypotenuse in the same amount of time as if it had travelled along the eg: vertical distance.

the light travels a longer distance than it should be able to...therefore the distance must contract.

it does it in less time than it should be able...therefore time is contracted too.

otherwise, how do your muons supposedly get to earth?

Then your impression is incorrect.

No, "light speed must not alter" was the starting point, the quandary if you like. That time and space are interwoven in a 4d lorentzian geometry rather than a 3d Euclidean space and 1d absolute time was the resolution to that quandary. The problem is we're all hard-wired to think in Newtonianesque absolute space and time so the first hurdle to understanding relativity is to realize that this is just an assumption that happens to be very accurate on the scale of relative motions that we're used to, but can't be correct if light speed is constant for all intertial observers. I'm not sure, but I think you may still be stuck at the first hurdle.

The light clock example demonstrates only time contraction, there is no length in the direction of motion to contract.

Right, stop there. Forget about doppler effects for now. Just focus on this. If a photon travels between two points at c relative to me, and the very same photon travels at c relative to you as well, even though you are moving relative to me at 0.5c then what's going on?

This implies that if I shoot a laser at your rapidly retreating back, but miss, the laser beam will leave me at c relative to me and then overtake you at c relative to you, even if you are running away from me and the gun at 0.99999c. Think about that, it is very strange.

__________________
There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.

A.You say this 2 mirrors are moving and a distant observer stay at rest.
B.I say this 2 mirrors stay at rest but the distant observer is moving.
We both are right and the photons reach both mirrors in A and B.
Speed of light is always "c" - time dilation explains it.

worzel

in effect the light pulse travels the length of the hypotenuse in the unit time.

since (according to the gamma formula) the hypotenuse doesn't actually exist (only the 2 sides "C and V").

the pythagorean relationship that would be afforded by the hypotenuse is used in the maths to generate gamma...but the discrete time that would be associated with it's generation is not.

otherwise if we waited for the light pulse to complete it's journey along the hypotenuse it would take a time longer than 1 (aka: C)


gamma = 1/sqrt(1-(v*v)/(1.?c*1.?c))


this cannot occur if we are to form a triangle with sides C and V.



in other words...


the completion of the lines C and V require time...the hypotenuse must be completed at the same time as both of these.

What is the problem, really?
If the observer is at rest wrt the mirrors, the pulse reaches the other mirror in one time unit.
If another observer is moving wrt the mirrors, the pulse takes longer, gamma times the time unit.
This is implicitly understood to mean that both observers have also taken into consideration the time it took for them to "see" the events and calculated backwards to get the actual time between events.

According to the second observer, time passes slower for the mirrors. The first one would disagree. Both are correct, but since they have no way of comparing measurements directly, there isn't a problem.

__________________
"We do not require reality to conform to the expectations of the ignorant"

Madman, suppose there is a light beam clock sitting next to me. I see the beam of light bouncing back and forth, right? Now, suppose that I go driving past the stationary light clock at high speed. What path do I see the light beam take?

I'll clarify. This is the situation as seen by the first observer.
These two describe the situation as seen by the second:

Both depictions describe the same situation, but from different perspectives. Both are equally correct, given their frame of reference.

__________________
"We do not require reality to conform to the expectations of the ignorant"

Grey

when the experiment is arranged in the following way, i can accept that everything works out right.




but not as arranged and shown in the last 2 gifs (re-posted by AstroSmurf).

No it doesn't. It completes the journey from one mirror to the other in the unit time when we are at rest relative to the light clock. If we move relative to the light clock then the path traced by the photon in our moving frame is longer and hence the time taken to complete the journey from one to the other is greater than one. You can use pythagorus' theorem to figure out by how much, gamma.

If we move distance x relative to the light clock while a photon moves distance y between the two mirrors, and x and y are at right angles then they form the two right sides of a right angled triangle and the hypotenuse is the path travelled by the photon in our frame of reference. I don't understand what your problem is with that.

What discrete time? The path between the mirrors is longer in our moving frame so the photon must take more time because it always goes at the same speed.

It does in our moving frame, that's called time dilation.

I don't understand. y is the distance between the mirrors, x is the distance we move while the photon travels from on mirror to the other. So the photon travels along this hypotenuse of x and y in our moving frame. Where's the problem?

__________________
There are 10 types of people in the world. Those who understand ternary, those who don't, and those waiting for a bus.
If logic doesn't work, then surely it does.

worzel

using your configuration...y is time.

it is the maximum value in the operation and is the "time limit" for the completion of the triangle.

if the hypotenuse is not formed in that time...the triangle is not formed with side C.

i posted the last gif to illustrate a format in which the completion of the hypotenuse occurs with the correct time and coordinates.

in the 2 gifs reposted by AstroSmurf it does not.


i pointed out that regardless of this anomaly the gamma formula operates as if the hypotenuse is formed according to the unit time.

there is no anomaly when just using the formula, because it does not rely on the hypotenuse as an input....it only uses the y and x (C and V).