Question on Michelson Morley experiment and length contraction

[harrylin]

cheers. I understand all that, I just thought that the speed of light was the upper limit, so thought the c+v wouldn't apply because you could only ever measure the speed of light as c, regardless of the relative movement of objects.

This is simply 1+1=2; the basic rules of mathematics always apply, a theory of physics cannot make 1+1=2 wrong; and it is based on the assumption that you measure the speed of light to be c and not 2c.

What you probably did not discern (indeed, many textbooks gloss over it) is that a vector sum (such as the one you asked about and understand) is fundamentally different from a frame transformation. And when we talk about a measurement of the speed of light, we always mean the speed of light relative to a system as measured with respect to that system, so that v-system=0.

In classical mechanics that makes no difference: there a frame transformation may be confounded with a closing speed because the "Galilean" frame transformation uses the same equations as the vector sum. It is different in relativity: there you must use the Lorentz transformation when you switch reference system.

 

[mangaroosh]

It took years of reflection by several people, based on a number of experiments. I doubt that there is a good shortcut for reading up on the history of science...

I'm sure that over that time the cumulative effect of information being passed on will have lead to more concise explanations, and explanations that suit a wider variety of learning types - such as ghwellsjr's animations.

That makes me think of the following which I'll give as illustration:
an other image, of a space shuttle floating in space, with astronauts inside, so the same gravitation effects would be felt by someone in the shuttle. Thus the astronaut feels the gravity?

But would the effect of gravity change depending on what direction your are moving in the shuttle?

 

[mangaroosh]

This is simply 1+1=2; the basic rules of mathematics always apply, a theory of physics cannot make 1+1=2 wrong; and it is based on the assumption that you measure the speed of light to be c and not 2c.

OK, I was thinking of a 1:1 correlation with reality, where c+v wouldn't make sense.

What you probably did not discern (indeed, many textbooks gloss over it) is that a vector sum (such as the one you asked about and understand) is fundamentally different from a frame transformation. And when we talk about a measurement of the speed of light, we always mean the speed of light relative to a system as measured with respect to that system, so that v-system=0.

In classical mechanics that makes no difference: there a frame transformation may be confounded with a closing speed because the "Galilean" frame transformation uses the same equations as the vector sum. It is different in relativity: there you must use the Lorentz transformation when you switch reference system.

cheers. I have absolutely no background in any of that to be honest, and don't really understand what a vector is, or anything like that.

 

[harrylin]

[..]
cheers. I have absolutely no background in any of that to be honest, and don't really understand what a vector is, or anything like that.

OK, I'll try to make it as simple possible.

1. Suppose that the high speed TGV train has a max. speed of 300 km/h (in fact that's in practice the case). And you measure two TGV's pass each other, each at 300 km/h. They have the same speed, but in opposite directions. A vector means simply that you account for both the magnitude and the direction.

Now if we define relative speed (or closing speed) as [change of distance] / [time]; then what is the relative speed of the trains according to your measurements?

2. However, it is altogether a different question what the machinist of a train will measure, if he uses his own, fully independent measurement system. According to classical mechanics he will measure exactly the same relative velocity as you; therefore in classical mechanics we don't care if we stick to one reference system or not. Such a switching of reference systems is mathematically a "frame transformation".

According to relativity however, the machinist will measure a very slightly different speed relative to the other train (although the effect is still negligible at that speed). And if the trains could go at almost the speed of light you would measure their relative speeds to be almost 2c, while each train machinist would measure their relative speeds to be almost c: also according to measurements with his reference frame, a train can not go as fast as the speed of light.

This can be understood by accounting for the combined effects of length contraction, time dilation and relativity of simultaneity (compare with post #29).

 

[harrylin]

[..] But would the effect of gravity change depending on what direction your are moving in the shuttle?

No, you won't notice anything, at least not to very good approximation. It's similar with length contraction etc.: you cannot detect if you are "really" moving (or not).

Now, there is a small imperfection due to gravity getting less at greater distance; and some people have thought that there could be similar imperfections with relativity, for example perhaps wood contracts less than steel and so it would be possible to detect "absolute motion". But all such tests failed to demonstrate any effect of linear motion.

 

[mangaroosh]

That is exactly what Einstein proposed that any inertial (non-accelerating) observer would do in order to define a Frame of Reference in which that observer would be stationary. But this meant that any other observer or objects moving in that FoR will experience length contraction and time dilation in order that they, too, would measure the round-trip speed of light to be the constant value, c. Do you follow that?

The author of the website has an explanation for that, which doesn't involve length contraction. He claims to have carried out an experiment which shows that a "beam of light" would be displaced by something like 2mm for a path length of 20m, which would then be amplified by "bouncing" the beam back and forth in an interferometer, which, he says, would account for the null result of the MMX; something he says isn't accounted for.

I'll have to have another read of the website just to get a better understanding, before I can discuss it. Like I say, I'm not in a position to scrutinise it to any reasonable degree, hence why I'm trying to fumble my way around to getting a better understanding of the MMX

 

[mangaroosh]

hey guys,

have another [what might seem like a basic] question; it's with regard to the idea that two observers moving relative to each other, who see a flash of light, will both remain at the centre of the expanding sphere; I'm just wondering how this has been tested experimentally?

 

[harrylin]

hey guys,

have another [what might seem like a basic] question; it's with regard to the idea that two observers moving relative to each other, who see a flash of light, will both remain at the centre of the expanding sphere; I'm just wondering how this has been tested experimentally?

First of all, that idea as you reproduce it can easily be misunderstood. According to each measurement system, the observer in rest will remain at the centre of the expanding sphere while the other will not.
That effect follows directly and with necessity from the relativistic effects (length contraction, time dilation and relativity of clock synchronization), which were derived in order to explain how such observations can be possible. Thus, only those effects need to be tested experimentally. And the only thing that could not been tested "directly" so far (because of technical limits) is length contraction.

Indirectly it has been tested by positive time dilation experiments in combination with a variant of the Michelson-Morley experiment that demonstrated that if time dilation is real, then also length contraction must be real (its original purpose was just the opposite).
See: http://en.wikipedia.org/wiki/Kennedy–Thorndike_experiment

 

[mangaroosh]

First of all, that idea as you reproduce it can easily be misunderstood. According to each measurement system, the observer in rest will remain at the centre of the expanding sphere while the other will not

but both observers will think that it is they that is at rest won't they?

 

[ghwellsjr]

but both observers will think that it is they that is at rest won't they?

It doesn't matter what they think, it only matters what they measure, and they both will measure that they are in the center of the expanding sphere of light, even if one (or both) of them are moving with respect to the source and to each other. Obviously, they cannot both be at rest with respect to each other and yet their measurements are identical.

The idea of representing the essential characteristic of the principle of relativity (part of Einstein's first postulate--that every inertial observer will measure the round-trip speed of light to be the same constant value in all directions) is this thought experiment of an expanding sphere of light because it makes it very obvious what that principle is saying. There is an abundance of evidence that every inertial observer measures the speed of light to be the same. My animations are intended to help people understand how length contraction explains this evidence.

 

[harrylin]

but both observers will think that it is they that is at rest won't they?

Only if they choose their reference systems accordingly. That is an obvious choice but it's not always the most convenient. For example, astronauts (and even the space centre on the Earth) typically think that they are moving.

 

[mangaroosh]

It doesn't matter what they think, it only matters what they measure, and they both will measure that they are in the center of the expanding sphere of light, even if one (or both) of them are moving with respect to the source and to each other. Obviously, they cannot both be at rest with respect to each other and yet their measurements are identical.

The idea of representing the essential characteristic of the principle of relativity (part of Einstein's first postulate--that every inertial observer will measure the round-trip speed of light to be the same constant value in all directions) is this thought experiment of an expanding sphere of light because it makes it very obvious what that principle is saying. There is an abundance of evidence that every inertial observer measures the speed of light to be the same. My animations are intended to help people understand how length contraction explains this evidence.

again, thanks for taking the time to go through the explanations, and the animations are very helpful for explaining how length contraction explains the evidence. I suppose the position I'm in is that I am new to most of this, and am trying to develop an understanding of it. That means that things which are experimentally supported appear as assumptions to me, until I understand how the evidence supports the assumption; whereas others, like yourself, who understand the evidence see them not as assumptions but evidentially supported postulates.

At present, I'm just trying to wade through the evidence.

 

[mangaroosh]

another basic question here guys, but how is time measured in the time dilation experiments? I'm presuming it is some form of a clock; I'm just wondering what kind of clocks they are?

 

[ghwellsjr]

Take three very stable atomic clocks, leave one on the ground, fly one around the world in an easterly direction, fly the other one around the world in a westerly direction, compare their elapsed times when they come back together.

Or the original famous muon half-life experiment which showed that even though they have a relatively short life time, they survive much longer when traveling at very high speeds.

 

[mangaroosh]

Take three very stable atomic clocks, leave one on the ground, fly one around the world in an easterly direction, fly the other one around the world in a westerly direction, compare their elapsed times when they come back together.

Or the original famous muon half-life experiment which showed that even though they have a relatively short life time, they survive much longer when traveling at very high speeds.

I know this is a very crude explanation, but am I anywhere near right in the understanding that the, let's say, "tick" of an atomic clock is measured from the detection of microwave emissions of changing electrons, or something along those lines? Is it the emissions as they change energy, or how does it work?

Is it an atomic clock that is used in the muon half-life experiment as well, to measure the decay time?

 

[harrylin]

I know this is a very crude explanation, but am I anywhere near right in the understanding that the, let's say, "tick" of an atomic clock is measured from the detection of microwave emissions of changing electrons, or something along those lines? Is it the emissions as they change energy, or how does it work?

Quite so.

Is it an atomic clock that is used in the muon half-life experiment as well, to measure the decay time?

No, it's the fraction of muons that arrive on Earth that is measured. That together with their speed (nearly c) tells us that they "live" longer.

The first experiments to measure time dilation were done by means of the Doppler effect. See:
http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

 

[mangaroosh]

Quite so.

No, it's the fraction of muons that arrive on Earth that is measured. That together with their speed (nearly c) tells us that they "live" longer.

The first experiments to measure time dilation were done by means of the Doppler effect. See:
http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

cheers.

 

[mangaroosh]

I have another pretty basic question.

How does a clock measure the property known as time?

I see time more as a system of measurement as opposed to a property to be measured.

 

[ghwellsjr]

I have another pretty basic question.

How does a clock measure the property known as time?

Any device that operates with a repetitive process and provides a mechanism to count those repetitions can be used as a clock.

A metronome is a device that operates with a repetitive process but it lacks a counter mechanism so it is not a clock. Old mechanical clocks had a similar repetitive process but added a counter consisting of gears and dials to keep track of the repetitions. Normally, an actual clock hides the repetitive process and just displays the result of the counter in some convenient manner. A stopwatch provides a mechanism to display elapsed repetitions between two events. A timer is similar in that it counts backwards from a preset number of repetitions and provides an alert when the count reaches zero. A watch provides a mechanism to set it to some arbitrarily established convention for keeping track of absolute time.

When discussing relativity, we often imagine an ideal clock that keeps perfect time such as a light clock where an imagined packet of light energy bounces back and forth between two rigidly fixed mirrors but this is really a metronome because it lacks a counter. It also lacks a mechanism for the light to continue forever so we really need a mechanism to regenerate the light at the location of one mirror. But we imagine that somehow these devicits are taking care of and we don't worry about it.

I see time more as a system of measurement as opposed to a property to be measured.

If you couldn't measure the property of time with some system, then it wouldn't be a characteristic qualifying to be dealt with by science.

 

[mangaroosh]

Any device that operates with a repetitive process and provides a mechanism to count those repetitions can be used as a clock.

A metronome is a device that operates with a repetitive process but it lacks a counter mechanism so it is not a clock. Old mechanical clocks had a similar repetitive process but added a counter consisting of gears and dials to keep track of the repetitions. Normally, an actual clock hides the repetitive process and just displays the result of the counter in some convenient manner. A stopwatch provides a mechanism to display elapsed repetitions between two events. A timer is similar in that it counts backwards from a preset number of repetitions and provides an alert when the count reaches zero. A watch provides a mechanism to set it to some arbitrarily established convention for keeping track of absolute time.

When discussing relativity, we often imagine an ideal clock that keeps perfect time such as a light clock where an imagined packet of light energy bounces back and forth between two rigidly fixed mirrors but this is really a metronome because it lacks a counter. It also lacks a mechanism for the light to continue forever so we really need a mechanism to regenerate the light at the location of one mirror. But we imagine that somehow these devicits are taking care of and we don't worry about it.

I understand that a "device that operates with a repetitive process and provides a mechanism to count those repetitions can be used as a clock", but I don't see how that repetitive process measures the propery called time; that is, I don't see how a clock measures the property called time.

I can see that the repetitive process can be used as a unit of comparison, but can't see how it is a unit of the property called time.

If you couldn't measure the property of time with some system, then it wouldn't be a characteristic qualifying to be dealt with by science.

That's what I was thinking.

 

[ghwellsjr]

I can see that the repetitive process can be used as a unit of comparison, but can't see how it is a unit of the property called time.

If there is a property called time and if it affected all repetitive processes equally, do you agree that any of these repetitive processes could be used as the basis for a valid instrument to measure time?

 

[mangaroosh]

If there is a property called time and if it affected all repetitive processes equally, do you agree that any of these repetitive processes could be used as the basis for a valid instrument to measure time?

that's assuming the conclusion though. how do we know that there actually is a property called time which affects all repetitive processes equally?

 

[harrylin]

[..] I can see that the repetitive process can be used as a unit of comparison, but can't see how it is a unit of the property called time.
[..]
that's assuming the conclusion though. how do we know that there actually is a property called time which affects all repetitive processes equally?

You may think that we have it the wrong way round, but it's easy to show that it's not so. Just consider how the concept of time must have arisen: from the daily sequence of sunrise and sundown, as well as the seasons. Thus, man's concept of "time" was formed by the observation of natural clocks. Man-made clocks came much later, and expensive ones often incorporated models of the sun and moon.

Anyway, for physics we cannot do otherwise than work with measurable standards for all such things as "time" and "temperature" that we may want to describe and predict.

 

[ghwellsjr]

that's assuming the conclusion though. how do we know that there actually is a property called time which affects all repetitive processes equally?

Should we suspend all scientific endeavors until we find a counter example, at which point, we would just be locked into a different conundrum?

 

[mangaroosh]

You may think that we have it the wrong way round, but it's easy to show that it's not so. Just consider how the concept of time must have arisen: from the daily sequence of sunrise and sundown, as well as the seasons. Thus, man's concept of "time" was formed by the observation of natural clocks. Man-made clocks came much later, and expensive ones often incorporated models of the sun and moon.

Anyway, for physics we cannot do otherwise than work with measurable standards for all such things as "time" and "temperature" that we may want to describe and predict.

the same problem applies to those natural clocks; how do they measure the property called time?

 

[mangaroosh]

Should we suspend all scientific endeavors until we find a counter example, at which point, we would just be locked into a different conundrum?

not at all; all that should happen is that science should do what science does best*, challenge our assumptions about the nature of the universe; otherwise any theory which includes time as a property and measures that property using a clock is arguably guilty of circular reasoning.

*forgive the personification of science

 

[harrylin]

the same problem applies to those natural clocks; how do they measure the property called time?

Again, it's the inverse: the concept "time" arose from observing the natural cycles. Naturally people decided to divide the year in (moon-) months and (solar) days. That's how people started to use the natural clocks that they observed, as measurement instruments for the progress of natural processes (such as aging, growing to harvest, etc); and this concept that evolved with the use of those clocks they called "time".

 

[mangaroosh]

Again, it's the inverse: the concept "time" arose from observing the natural cycles. Naturally people decided to divide the year in (moon-) months and (solar) days. That's how people started to use the natural clocks that they observed, as measurement instruments for the progress of natural processes (such as aging, growing to harvest, etc); and this concept that evolved with the use of those clocks they called "time".

I would agree that the concept of time arose from observing such natural cycles, coupled with man's innate capacity for memory; but that is all time is, a concept.

EDIT: regardless of how the concept arose though, it doesn't support the contention that time is a property of the universe which can be measured; or that any kind of clock, natural or manmade, actually measures a property called time.

 

[mangaroosh]

It might also be worth pointing out that the concept of a geocentric universe also arose from observing such natural cycles, until the assumption was challenged.

 

[ghwellsjr]

Should we suspend all scientific endeavors until we find a counter example, at which point, we would just be locked into a different conundrum?

not at all; all that should happen is that science should do what science does best*, challenge our assumptions about the nature of the universe; otherwise any theory which includes time as a property and measures that property using a clock is arguably guilty of circular reasoning.

*forgive the personification of science

Even if this were true or even if it were false but you believed it to be true, it won't hamper you from learning relativity which is what this forum is for. I'm only interested in helping those people who want to learn about Special Relativity. Are you one of those people?