How Does Time Dilation and Lorentz Contraction Fit Within SR Framework?

[grav-universe]

SR leans more toward direct observation rather than explanation, which is fine, mostly resulting from experiments with aberration and M-M type experiments, but I would like to know more about the how's and why's involved. I have come to some of my own conclusions, but will only ask questions leading toward my particular areas of interest to see what responses the members here will make, which should be very instructive.

Q1) Why is the time dilation between frames for the ticks of a light clock the same as that of mechanical clocks, radioactive decay, vibrations of cesium atoms, etc? How are they related?

Q2) Why do rods in an M-M type experiment in a moving frame contract in such a way that the result will be null? In other words, why is it so important to a body that light be transmitted isotropically that it must contract in order to do so? Why not just stay the same?

 

[GrayGhost]

SR leans more toward direct observation rather than explanation, which is fine, mostly resulting from experiments with aberration and M-M type experiments, but I would like to know more about the how's and why's involved. I have come to some of my own conclusions, but will only ask questions leading toward my particular areas of interest to see what responses the members here will make, which should be very instructive.

While SR is supported by measurement, it was developed in a theoretical way. Einstein said he was totally unaware of the MMX experiment's null result, yet he already knew that Maxwell's theory of electromagnetism predicted invariant light speed, and that's why he believed it. His theory assumed apriori the following 2 principles were true ...

(1) All inertial observers use the same mechanics, and said mechanics hold equally well for each.

(2) Light travels at c in vacu independent of the relative speed of its source.​

So Einstein redesigned the model of space and time, ie the mathematical relation of space and time between 2 observers who move relativel wrt one another, while assuming that these 2 principles were in fact true. Before he did all that, these 2 principles were known to be incompatible, however some in his day believed they should be able to be made compatible, which Einstein succeeded at.

Q1) Why is the time dilation between frames for the ticks of a light clock the same as that of mechanical clocks, radioactive decay, vibrations of cesium atoms, etc? How are they related?

Because TIME DILATION is all about TIME itself. If time slows down, then so too do all (moving) physical processes, including mechanical clocks, radioactive decay, vibrations of cesium atoms, etc. They are all governed by TIME.

Q2) Why do rods in an M-M type experiment in a moving frame contract in such a way that the result will be null? In other words, why is it so important to a body that light be transmitted isotropically that it must contract in order to do so? Why not just stay the same?

It's not that it's important to the body, or anything else. It's only that the symmetry inherent in space and time require light speed to remain invariant. A body never discerns any change in and of itself, ever. Hence the length contraction you note of a moving body, is real only per you. It contracts because you and it are angularly rotated relatively within the spacetime continuum. The relative angular orientation causes the moving length to be angularly rotated wrt you, which takes away from its length ... as rotating a pencil can, while you do not move. This rotation is caused by a different source though ... ie relative velocity, under an invariant light speed context. Space and time are mutually linked (fused) in SR. What many don't realize at first, is that with length contraction comes desynchronisation of the body along it's length axis. That is, per you who move relatively, no 2 points along the contracted interferometer arm exist in the interferometer's own instant of time ... forward points of the contracted arm lie in the past wrt afterward points of said arm. This is true for any "instant" of your time as you view the moving body.

GrayGhost

 

[bcrowell]

The answer to both questions is the same. The Lorentz transformations are interpreted as describing time and space themselves. If different clocks acted differently from one another, or different measuring rods acted differently from one another, then reality would be described by a theory that, unlike SR, would not be interpretable as describing time and space themselves. For instance, you could have some kind of aether theory, in which the effect of aether drag on a metal ruler was different from its effect on a wooden ruler.

 

[bcrowell]

Einstein said he was totally unaware of the MMX experiment's null result, yet he already knew that Maxwell's theory of electromagnetism predicted invariant light speed, and that's why he believed it.

What Einstein later said turns out not to have been accurate: http://arxiv.org/abs/0908.1545

 

[pervect]

Q2) Why do rods in an M-M type experiment in a moving frame contract in such a way that the result will be null? In other words, why is it so important to a body that light be transmitted isotropically that it must contract in order to do so? Why not just stay the same?

That's an odd-looking question. Without getting into more details on how it's odd, let me say this:

Since we're asking "why", we're getting into the realms of philosophy.

And as far as the philosophy goes, my distillation of the essence of relativity is this:

Length intervals, and time intervals are not good candidates for being fundamental. They turn out to depend on the observer, and they turn out to be interdependent. Due to the relativity of simultaneity, an separation in space and time that contains no time component for one observer will contain a time component for another observer.

What's more fundamental than either length or time, and what replaces both of them, is the Lorentz interval.

[add]
The Lorentz interval replaces space and time as far as all measurements with clocks and rulers go. Describing cause and effect in SR need some almost trivial adjustments as well. The future light cone of an event defines what events it might affect, the past light cone determines what events might be causes.

Knowing the value of the Lorentz interval just by itself doesn't define the direction of the future, though one knows that if two events have a timelike interval, one occurs "before" the other.

This is similar to a way a ruler (used to measure events with a spacelike separation) doesn't define "up", it only defines distance.

 

[Passionflower]

What's more fundamental than either length or time, and what replaces both of them, is the Lorentz interval.

True, but oddly enough, at least to me, many insist on considering spacetime having separate dimensions of space and time.

 

[Janus]

SR leans more toward direct observation rather than explanation, which is fine, mostly resulting from experiments with aberration and M-M type experiments, but I would like to know more about the how's and why's involved. I have come to some of my own conclusions, but will only ask questions leading toward my particular areas of interest to see what responses the members here will make, which should be very instructive.

Q1) Why is the time dilation between frames for the ticks of a light clock the same as that of mechanical clocks, radioactive decay, vibrations of cesium atoms, etc? How are they
related?

If I am standing next to a light clock that have the mirrors 149896229 meters apart, I will measure 1 sec for a light pulse to make the round trip. It doesn't really matter how I measure the second except that some methods will be less prone to error. (I can use an atomic clock, a stopwatch, a cheap wristwatch or say to myself, "One thousand, one".)

Now consider someone traveling at 0.866c relative to me in a direction perpendicular to the path of my light pulse. He has his own light clock, identical to mine, and he also measures how long it takes for his light pulse to make the round trip. Since we both measure the speed of light to be the same relative to ourselves, he also measures 1 sec per tick of his clock.

He is also watching my clock. From his perspective the my light pulse has to travel a diagonal path to travel between the mirrors. Since my pulse has to travel at the same speed as his, it will take a longer time to make the round trip from mirror to mirror.(twice as long in fact.) Which means I have to say "one thousand, one" twice before his clock completes one tick. He however said it once for the same tick. I have to agree that he said it once for each tick of his clock, otherwise we would have a physical contradiction on our hands.

So the answer is that the reason the light clock, cesium clock, mechanical clock in the same frame all agree is that they are all measuring the same time interval, it is just that a frame moving relative to that frame will measure the interval (by its devices) differently

Q2) Why do rods in an M-M type experiment in a moving frame contract in such a way that the result will be null? In other words, why is it so important to a body that light be transmitted isotropically that it must contract in order to do so? Why not just stay the same?

The fact that light is measured to have a constant speed in all frames, quite frankly just seems to be the way that universe is put together. Every experiment to date has verified this.

We can go back to the light clock again. Only this time, we have a second clock aligned at a right angle to the first. A person stationary to these clock will see pulses emitted from them take the same time to make the round trip.

If we look at this from the perspective of someone traveling along the line joining the light clocks, he must also agree that both of them tick( per round trip) at the same rate. In his case each leg of the round trip for the clock parallel to the relative motion will take different times (relativity of simultaneity). If he adds up the legs of the trip, given that the speed of light is constant for both legs, he determines that this clock must be shorter than the other clock. Like this:

[URL]http://home.earthlink.net/~parvey/sitebuildercontent/sitebuilderpictures/length_con2.gif[/URL]

So we have the different frames measuring the distance between the mirrors differently.

It's kind of like two people facing in different directions. They are each asked how far to the left one point is from the other. Since each defines "left" according the direction they are facing, they will give a different answer. This is more or less how Relativity deals with time and space. The measurements of time and space are frame dependent just the way left and right are dependent on the way you face.

 

[grav-universe]

Thanks for the replies so far, guys.

So as viewed from the stationary frame, are contraction and time dilation just coordinate effects of space and time due to observing and measuring from a different frame from that of the moving body, or are they physical effects that actually occur to the body upon accelerating to the moving frame even though in the frame of the body everything appears the same?

 

[bobc2]

What Einstein later said turns out not to have been accurate: http://arxiv.org/abs/0908.1545

Thanks a lot for that great reference, Ben.

 

[bobc2]

Thanks for the replies so far, guys.

So as viewed from the stationary frame, are contraction and time dilation just coordinate effects of space and time due to observing and measuring from a different frame from that of the moving body, ...

Yes. It helps to visualize the object as a 4-dimensional object with different observers having different 3-D cross-section views of the object (including the 4-D clock object).

...or are they physical effects that actually occur to the body upon accelerating to the moving frame even though in the frame of the body everything appears the same?

No.

 

[grav-universe]

Yes. It helps to visualize the object as a 4-dimensional object with different observers having different 3-D cross-section views of the object (including the 4-D clock object).

No.

I am interested in the real physical changes that the body undergoes according to the stationary frame. Couldn't we stay solely in the frame of the stationary observer and describe the physical aspects of what is taking place according to what the stationary observer would directly observe of the body upon accelerating to another frame, how that process would physically be described by the stationary observer?

 

[bobc2]

I am interested in the real physical changes that the body undergoes according to the stationary frame. Couldn't we stay solely in the frame of the stationary observer and describe the physical aspects of what is taking place according to what the stationary observer would directly observe of the body upon accelerating to another frame, how that process would physically be described by the stationary observer?

You should take another look at GrayGhost's earlier post. Reflect on the comment GrayGhost made about the analogy between length contraction as a consequence of a different angular view of a 4-dimensional object as compared to the quite common experience of seeing a projected length of a pencil change as you rotate it in 3-D.

So, think about rotating a pencil and ask yourself if you are seeing a "real physical change" in the pencil. Of course you will answer that the changing angular view gives the appearance of the pencil changing length, and you know exactly what is going on in this instance--the 3-D pencil retains its inherent dimension measurements. Thus, you conclude there is no "real physical change" with the pencil.

The same thing is going on with a fixed 4-D object. As GrayGhost pointed out, different observers moving at different relativistic velocities have different angular views. So, it would not seem fruitful to look for the "real physical change."

 

[GrayGhost]

What Einstein later said turns out not to have been accurate: http://arxiv.org/abs/0908.1545

Interesting, thanx. I had not seen that reference before.

Einstein was only age 9 when the MMX experiment was run. At age 16, he began his first contemplation of riding a beam of light, 7 years after the MMX experiment. He was age 26 in 1905 when he published OEMB, 18 years after the MMX experiment. It seems odd that the MMX null result would not have been discussed at all at university where Einstein attended. I suppose when you consider all this in collective, it's difficult to imagine that Einstein would not have known of the MMX result. Given the theory he developed, I cannot imagine not being very interested in that null result. Yet as the web reference stated, he may well have never given the MMX experiment much thought because he was already convinced by Maxwell's theory. Interesting historical summary though, thanx.

GrayGhost