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.Originally Posted by madman
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.Originally Posted by madman
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:Originally Posted by madman
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.Originally Posted by madman
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.and if your version of time dilation requires a change in relative motion only...then how does a body sustain a time dilation effect for any appreciable time?
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.
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.
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
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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.Originally Posted by madman
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.Originally Posted by madman
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.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.
The light clock example demonstrates only time contraction, there is no length in the direction of motion to contract.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.
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?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.
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.
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.
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:Originally Posted by madman
Both depictions describe the same situation, but from different perspectives. Both are equally correct, given their frame of reference.Originally Posted by madman
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.Originally Posted by madman
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.since (according to the gamma formula) the hypotenuse doesn't actually exist (only the 2 sides "C and V").
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.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.
It does in our moving frame, that's called time dilation.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)
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?the completion of the lines C and V require time...the hypotenuse must be completed at the same time as both of these.
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).
Ach, this is getting confusing!
Madman, let's start at the beginning.
You've got a photon gun pointing straight at a receiver. The distance between them is d. The whole apparatus is stationary. The photon gun fires a photon, the photon travels through the intervening space at velocity c for time d/c, and then hits the receiver. Right?
Now, let's say the whole apparatus is moving perpendicular to the gun-receiver line. It's moving at a significant velocity, say 0.6c. The photon gun fires a photon. Some questions:
1) Will the photon still hit the receiver?
2) Will the photon still be traveling at velocity c, and thus by necessity require more time than d/c to make the journey?
3) Is it true that there is no way to differentiate between
a) a stationary observer observing a moving gun-receiver apparatus; and
b) a moving observer observing a stationary gun-receiver apparatus?
If you answered "no" to any of those questions, then your problem is not with Relativity, it's with the experiments that have shown that the correct answer to those questions is "yes."
If you answered "yes" to all three questions, how do you propose to resolve the inherent conflicts?
worzel
look at the blue wave gif.
the movement of the top mirror produces an internal transmission delay.....the light must travel further to reach the mirror and take more time to do it.
the speed of light remains the same and it's delay in reaching the 2nd mirror is basically a doppler shift.
***************************************
these exercises based on 2d are too limited.
imagine a 3d object with light clocks pointed in every direction...give it a vector and you'll find that the internal clocks pointed in one direction are time dilated...and those pointed in the opposite direction are time contracted.
both are caused by doppler shifting due to relative motion.
we can only achieve einsteinian gamma formulations by using a very abstract and limited 2d model.
But, that was my whole point. You claim the line cannot form in the time allowed. SR claims otherwise. Now, we have two mutually exclusive claims (yours and SRs). You should be able to show exactly where SR is wrong. If you can't, I would say it's a fair assumption that you can't because there is nothing wrong and it's your claim is a simple misunderstanding on your part.Originally Posted by madman
I would also point out that SR has predicts several other effects and has been incorporated QM, and is part of all the QM predictions. Observations, for both SR and QM match predictions to a high degree of accuracy. Why, if SR is so wrong, do those predictions match observations so closely.
It might be better to describe this verbally, or at least explain what the various parts of your animated gif represent. In this case, though, it seems clear that an observer at rest with respect to the red mirror sees the light travel in a straight line, while an observer with respect to the blue mirror sees the light travel along a diagonal path. Is this correct?Originally Posted by madman
The only important difference I see between these two is that in the one you just posted, the source is not moving. Are you claiming that makes a difference? You're also emphasizing a different reference frame, but of course either should be equally valid, right?Originally Posted by madman
But mostly, I'm not sure that you've really answered my question. Say there are two parallel mirrors with a light beam bouncing between them, the whole thing in an inertial reference frame that I'm considering to be "at rest", at least for the moment. If I go zipping past these mirrors, perpendicular to the light path, do we agree that I will see the light pulse travelling in a zig-zag pattern?
No, y was the distance between the mirrors, as I said.Originally Posted by madman
What does that mean? It is just the distance between the mirrors, nothing more.it is the maximum value in the operation and is the "time limit" for the completion of the triangle.
If you mean that the light can't travel along this diagonal path (i.e. in the frame of the moving observer) in the same amount of time that it does the vertical path (i.e. in the frame of the stationary observer) then you're right. It takes longer to traverse the diagonal path, so the time taken for the photon to traverse the distance between the mirrors is longer in the moving frame -- da da -- time dilation.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.
I think you're just having difficulty letting go of your intuitive notion of absolute time. The 1 second tick of the light clock is longer in the moving frame precisely because it can't travel the diagonal path in the same time that it could travel the vertical path if it always travelled at c in all (inertial) frames.i pointed out that regardless of this anomaly the gamma formula operates as if the hypotenuse is formed according to the unit time.
"In a paper published in 1918 Einstein corrected the “relative motion” error of his 1905 paper and he added “forces” and “atomic clocks” to his thought experiments. He changed the reason for the single clock slow-down from “relative motion” to “forces” exerted on the oscillating atoms in the single atomic clock that slowed down, and thus he basically returned to Lorentz’s basic electrodynamics concept of 1895, and Einstein's own 1911 gravitational redshift theory."
So time dilation is a is not reality, but clocks slowing down is.
So there is no such thing as time dilation.
So Sam5 claims.Originally Posted by upriver
That would be incompatible with SR because the amount by which the clocks differ in the twin paradox is related to how far apart the twins are when one turns around. If it was just the acceleration felt that caused the turning twin's clock to slow then it shouldn't matter how far away the other twin is.Originally Posted by upriver
There isn't an absolutely velocity or absolutely time.
The mirrors move relatively to Earth, Earth relatively to Sun and so on. There is only relative velocity.
A faster velocity means a higher relative energy and processes (atom clock) are running slower for distant observer.
If the observers are in different reference frames (velocity, gravity) they observe different reality (time, redshift-blueshift). If they come together everyting comes back too.
According to Lorentz transformation , you see - there is not a Black Hole in a center of a galaxy but if you come to the galaxy center you fall in a Black Hole. It seems to be a paradox but it is a reality in different reference frames.
Some people call it time dilation, may be it is not correct English word.
I think time dilation and length contraction are good terms for these phenomena. It is important to stress to newbies that clocks do run slower and the rods are shorter for a moving observer. It isn't just some sort of illusion. Most books on SR start out with someting like an some imaginary grid of rods with light receptors and clocks at each intersection and a database recording all the events that happen as they happen on the grid and then say that whenever they talking about Bod "seeing" this or that what they mean is that this is what Bob's database would have recorded on his grid of clocks and receptors which is stationary with respect to him.
It’s not quite that simple. There is no “time dilation” caused by “relative motion” alone, so the 1905 SR theory is wrong about that. Get yourself a copy of Einstein’s 1918 paper and see what he says about it.Originally Posted by upriver
However, atomic clocks (and perhaps other atomic processes too) can slow down if, for example, the atoms of the clock are near the surface of a massive planet or star and if their internal harmonic oscillation rates slow down. However, the old fable that you will live longer at sea level and you will age faster on a mountain top (because your atoms are oscillating more rapidly on the mountain top) is wrong. An atomic clock will “tick” more rapidly on a mountain top, but it’s such a slight amount that the atomic oscillation rate change has nothing to do with our aging rates. Our human aging rates are determined more by our body and cell temperatures (which control thermodynamic time) than by any very slight slowdown or speed up in our atomic oscillation rates when we move from sea level to a mountain top.
Also, different types of clocks slow down and speed up at different rates, depending on which laws of physics are governing the tick rates of the clocks. For example, an atomic clock will “tick” faster on a mountain top, while a pendulum clock will tick slower on a mountain top. An atomic clock will “tick” slower at sea level, while a pendulum clock will tick faster at sea level.
Frozen human embryos can be kept from aging for many years, 5, 10, etc, and then they can be thawed out and the embryo will grow into a baby. This is an example of thermodynamic time that is not related to atomic time. You can have two twin frozen embryos, and thaw one out now, and thaw the other out 10 years from now, and you will have one twin being 10 years older than the other. One will be in the 4th grade while the other is still a baby. This is thermodynamic time. It’s actually performed by doctors every day, although they usually thaw out only one embryo of each group they collect.