Actual earth measurement contradicts measurement predicted by special relativity

[GregAshmore]

A particular muon lives to the ripe old age of 4.5 microseconds (three half lives). As it sits in its chair, ticking off the picoseconds, it observes the Earth streaking by at 99.99999995% light speed. What will be the elapsed time of the muon's life, as measured on the Earth clock?

As I understand SR, the time measured in the Earth frame should be much less than 4.5 microseconds. Yet the actual measurement of muons in the atmosphere is much more than 4.5 microseconds.

What have I missed?

 

[Doc Al]

As I understand SR, the time measured in the Earth frame should be much less than 4.5 microseconds.

You have it backwards. According to the Earth frame, the muon lives much longer than 4.5 microseconds. (Moving clocks run slow.)

 

[George Jones]

Okay, I'm getting annoyed. Stop (mis)using variants of "contradict" in thread titles.

 

[GregAshmore]

Okay, I'm getting annoyed. Stop (mis)using variants of "contradict" in thread titles.

If the word is appropriate, it should be used.

 

[GregAshmore]

You have it backwards. According to the Earth frame, the muon lives much longer than 4.5 microseconds. (Moving clocks run slow.)

Maybe. I gave myself a headache thinking about this on the way to work.

In every example of special relativity, the reading on the moving clock is less than the reading on the stationary clock. Take the clock on the spaceship in the twin paradox, for example. So why isn't the clock in the lab reading lower than the clock in the muon's chair?

 

[Doc Al]

In every example of special relativity, the reading on the moving clock is less than the reading on the stationary clock.

And this situation is no different. In the Earth frame, the muon acts as a moving clock.

So why isn't the clock in the lab reading lower than the clock in the muon's chair?

If you want to understand what an observer riding along with the muon would say about those clock measurements made on earth, you need to understand the relativity of simultaneity as well as time dilation. (I'd suggest reading Spacetime Physics... but that's not working, is it?)

Time dilation is symmetric. The muon observer will say that Earth clocks are running slowly. But he'd also say that Earth clocks are out of synchronization, which explains how Earth observers can measure a longer time. (Note: The time measurements made on Earth take place at different locations (since the muon moves), but time measurements made in the muon frame all take place at the same location. That makes all the difference.)

 

[George Jones]

If the word is appropriate, it should be used.

And "contradict" is not appropriate if the mistakes and misconceptions are yours. I am not going to continue bandying words. At the top of the Special & General Relativity forum, there two stickies. Read them. Also read the rules to which you agreed when you registered here. From the sticky with title "IMPORTANT! Read before posting"

This forum is meant as a place to discuss the Theory of Relativity and is for the benefit of those who wish to learn about or expand their understanding of said theory. It is not meant as a soapbox for those who wish to argue Relativity's validity, or advertise their own personal theories. All future posts of this nature shall either be deleted or moved by the discretion of the Mentors.

Any further threads that have a misused variant of "contradict" in their titles will be deleted, and will remain deleted until they are appropriately titled.

 

[bcrowell]

If the word is appropriate, it should be used.

But it hasn't been appropriate the last three times you used it. If you're having trouble understanding something, you could just say so and ask for help.

 

[JesseM]

Maybe. I gave myself a headache thinking about this on the way to work.

In every example of special relativity, the reading on the moving clock is less than the reading on the stationary clock. Take the clock on the spaceship in the twin paradox, for example. So why isn't the clock in the lab reading lower than the clock in the muon's chair?

In the lab frame, the muon is moving, so to measure the amount of time between the muon clock reading 0 and the muon clock reading 4.5 microseconds, the lab frame requires two synchronized clocks at different locations to make local readings of the lab time as the muon passes each of these synchronized clocks. If you switch to the muon's frame, each of these lab clocks is running slow, but they are also out-of-sync due to the relativity of simultaneity, with the second clock the muon passes being way ahead of the first clock the muon passes at any given instant in the muon frame. So despite the fact that the two clocks are individually running slow in the muon frame, this explains (from the perspective of the muon frame) why the difference in the readings of each clock at the moment the muon passes it can be much greater than 4.5 microseconds.

 

[GregAshmore]

But it hasn't been appropriate the last three times you used it. If you're having trouble understanding something, you could just say so and ask for help.

I give you my word that in future posts I will avoid the word "contradict", or any form of it.

I will take this opportunity to point out that there is an incontrovertible contradiction in Taylor-Wheeler. Therefore, the word was correctly used in that posting:

1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." ... as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."

In the Train Paradox explanation of the relativity of simultaneity, the observer on the ground makes a judgment of simultaneity based on what he sees by his eye. That is a direct contradiction of what is permitted, according to Taylor-Wheeler.

The observer on the ground then goes on to make a prediction about what will happen in the train frame based on the combination of what he saw with his eyes in the ground frame and the motion of the train relative to him. Your opinion is that this is perfectly consistent with the principle of relativity. I contend that at the very least this procedure assumes the thing that it is trying to prove--a particular space-time relationship between the two frames. Once that assumption is removed, there is no way to determine the time of the strikes in the train frame.

Of course, you are entitled to your opinion. In fact, you are more entitled to your opinion than I am to mine. Nevertheless, my opinion is based on logic. In scientific endeavor disputes such as this are settled by experiment. The problem in relativity is that it is very difficult to set up the conditions and the instruments to collect the required data.

I have not challenged any of the experimental results. Nor have I challenged the primary conclusions drawn from them: time dilation and mass-energy equivalence. What I have challenged are the details which have not been tested, but which are held with certainty nonetheless. In my opinion, as someone who has been surprised many times at the difference between what I expected to see in a test and what actually happened, it is important to distinguish between what is known from experience and what is inferred.

 

[GregAshmore]

In the lab frame, the muon is moving, so to measure the amount of time between the muon clock reading 0 and the muon clock reading 4.5 microseconds, the lab frame requires two synchronized clocks at different locations to make local readings of the lab time as the muon passes each of these synchronized clocks. If you switch to the muon's frame, each of these lab clocks is running slow, but they are also out-of-sync due to the relativity of simultaneity, with the second clock the muon passes being way ahead of the first clock the muon passes at any given instant in the muon frame. So despite the fact that the two clocks are individually running slow in the muon frame, this explains (from the perspective of the muon frame) why the difference in the readings of each clock at the moment the muon passes it can be much greater than 4.5 microseconds.

This is my problem: The muon isn't passing any clocks. It is at rest in its frame, watching the world go by. That is one of the two fundamental postulates of relativity--the other being that the laws of nature have the same form for every resting observer.

If the problem were posed in the usual manner, as a resting observer measuring the elapsed time as an object moves between two positions, and the task was to calculate the elapsed time in the frame of the moving object, the answer would be smaller than the time measured in the rest frame.

What is the reason that the usual answer is not correct in this case? How is one to distinguish whether the usual answer applies, or not?

I'll look again at what Taylor and Born have to say about the relativity of simultaneity.

 

[JesseM]

I will take this opportunity to point out that there is an incontrovertible contradiction in Taylor-Wheeler. Therefore, the word was correctly used in that posting:

1. The narrative in figure 3-1 contradicts the text in section 2.7 (pg 39): "Location and time of each event is recorded by the clock nearest to that event." ... as stated in 2.7: "We do not permit the observer to report on widely separated events that he himself views by eye. The reason: The travel time of light."

In the Train Paradox explanation of the relativity of simultaneity, the observer on the ground makes a judgment of simultaneity based on what he sees by his eye. That is a direct contradiction of what is permitted, according to Taylor-Wheeler.

No, not if you understand their actual meaning in that quote. What they are saying there is just that an observer cannot judge whether two events are simultaneous simply by looking at whether the light from each event is seen simultaneously. But if the observer also takes into account "the travel time of light" for an event which happened at a known distance, then a calculation based on both when the events are "seen with the eye" and based on the distances of each event can certainly be used to judge whether the events are simultaneous. For example, if I see the light from one explosion 10 light-years away in 2010, and I see the light from another explosion 15 light-years away in 2015, with times and distances measured by my clock and a ruler at rest relative to myself, I can judge that both explosions happened simultaneously in the year 2000 in my rest frame, even though what I "saw with my eye" was that one occurred 5 years after the other. This is certainly not in contradiction with the Taylor-Wheeler quote above, because they are just making the point that it's a mistake to say seeing two events simultaneously is automatically equivalent to saying they happened simultaneously in my frame (and my example actually illustrates this since one is true but not the other!)

 

[JesseM]

This is my problem: The muon isn't passing any clocks. It is at rest in its frame, watching the world go by.

Sure, and the two clocks in the lab frame pass it in succession. I didn't mean "pass it" to suggest anything about which was moving, I just meant that there was a moment the muon clock and the first lab clock passed one another, and then another moment the muon clock and the second lab clock passed one another. Even if you analyze things from the perspective of the muon frame where these two clocks are running slow, if you take into account that they are also out-of-sync in the muon frame, you still end up with the prediction that the difference in readings between the two lab clocks at the moment they pass the muon is greater than 4.5 microseconds.

If the problem were posed in the usual manner, as a resting observer measuring the elapsed time as an object moves between two positions, and the task was to calculate the elapsed time in the frame of the moving object, the answer would be smaller than the time measured in the rest frame.

No, all frames always agree about all local measurements, specifically what any two clocks read at the moment they pass next to one another. If you have a pair of clocks A and B at rest and synchronized in the lab frame and a pair of clocks A' and B' at rest and synchronized in the muon frame, then the two lab clocks can be used to measure the time elapsed in the lab frame on a single muon clock, and likewise the two muon clocks can be used to measure the time elapsed in the muon frame on a single lab clock. All frames will agree on local facts like what times A and A' showed at the moment they passed one another, and the result will be that the lab clock is measured to run slow in the muon frame and the muon clock is measured to run slow in the lab frame.

Let's pick an example with easier-to-deal with numbers. Say we have a pair of clocks A' and B' on a rocket which is moving at 0.8c relative to the lab frame, and the clocks are 20 light-seconds apart in the rocket rest frame, meaning they are 12 light-seconds apart in the lab frame due to length contraction. Also these two clocks are synchronized in the rocket's own frame, which means the rear clock is running ahead of the front clock by 0.8*20 = 16 seconds in the lab frame (relativity of simultaneity). Meanwhile we also have two clocks A and B at rest in the lab frame, and 20 light-seconds apart in the lab frame, and synchronized in the lab frame. Suppose before any of them pass one another, they are arranged like the "diagram" below, with B' to the left of A' and A' to the left of A and A to the left of B, and with B' and A' traveling to the right:

B'...A'---> A...B

So, first A' will pass A, and let's suppose A reads t=0 and A' reads t'=0 at that moment. So at t=0 in the lab frame, B' is 12 light-seconds away from A and it reads t'=16 seconds. Moving at 0.8c, it takes 12/0.8 = 15 seconds in the lab frame to reach A, so A reads t=15 when B' passes it, but B' has only elapsed 0.6*15 = 9 seconds in that time, so since it started reading t'=16 it will read t'=16+9=25 at the moment it passes A.

So, so far we have these local facts:

*When A and A' pass, A reads t=0 and A' reads t'=0
*When A and B' pass, A reads t=15 and B' reads t'=25

Now since A and B are 20 light-seconds apart in the lab frame, and A' passed A at t=0 and is moving at 0.8c, A' will pass B at t=20/0.8=25 seconds in the lab frame. At this moment B reads t=25 and since A' read t'=0 when it passed A and is running slow by a factor of 0.6, when A' passes B, A' reads t'=25*0.6=15 seconds.

Likewise since B' passed A at t=15 in the lab frame, B' will pass B 25 seconds later in the lab frame, when B reads t=15+25=40 seconds. B' will tick forward by 25*0.6=15 seconds in this time, but since B' already read t'=25 seconds at the moment it passed A, that means B' will read t'=25+15=40 seconds when it passes B.

So, we have the following local facts:
*When B and A' pass, B reads t=25 and A' reads t'=15
*When B and B' pass, B reads t=40 and B' reads t'=40

So, the full listing of local facts about all 4 passing events is:

1. When A and A' pass, A reads t=0 and A' reads t'=0
2. When A and B' pass, A reads t=15 and B' reads t'=25
3. When B and A' pass, B reads t=25 and A' reads t'=15
4. When B and B' pass, B reads t=40 and B' reads t'=40

Both frames agree about these local facts (that's a basic principle of relativity, there is always complete agreement about local facts like this). But notice that if either frame uses a pair of their own clocks to measure the time elapsed on one of the other frame's clocks, they conclude the other frame's clock is running slow! For example, in the lab frame, if we look at local events 1 and 3, we find that the rocket clock A' elapsed 15 seconds in the time between passing lab clock A and passing lab clock B, while A read t=0 as A' passed it and B read t=25 as A' passed it, meaning that in the lab frame it took 25 seconds for A' to tick forward by 15 seconds. But in the rocket frame, if we look at local events 1 and 2, we find that the lab clock A elapsed 15 seconds in the time between passing rocket clock A' and passing rocket clock B', while A' read t'=0 as A passed it and B' read t'=25 as A passed it, meaning that in the rocket frame it took 25 seconds for A to tick forward by 15 seconds. The situation is entirely symmetrical, as you can see by the numbers in the four local passing events!

For a more visual illustration of the symmetry between frames, you might follow the suggestion I made on your other thread:

You might find it helpful to take a look at the illustrations I did for this thread showing two rulers moving at relativistic speeds relative to one another, each with clocks placed at each ruler-marking that are synchronized in the ruler's rest frame. You can see from the diagrams how length contraction, time dilation and the relativity of simultaneity all work together to make it possible for the situation to be completely symmetrical, with each frame saying that the other ruler is contracted and that the clocks on it are slowed-down and out-of-sync, without there being any contradictions in their predictions about local events like what times a given pair of clocks will read at the moment they pass next to one another.

 

[GregAshmore]

I'm working on it.

 

[yuiop]

A particular muon lives to the ripe old age of 4.5 microseconds (three half lives). As it sits in its chair, ticking off the picoseconds, it observes the Earth streaking by at 99.99999995% light speed. What will be the elapsed time of the muon's life, as measured on the Earth clock?

As I understand SR, the time measured in the Earth frame should be much less than 4.5 microseconds. Yet the actual measurement of muons in the atmosphere is much more than 4.5 microseconds.

What have I missed?

Let us imagine we have a clock hovering just above the Earth atmosphere that is sychronised with another clock at ground level in the Earth frame. (Ignore any difference in clock rates due to gravitational time dilation as this will be negligable in this example). When both these clocks are showing zero a muon is created near the top clock and speeds towards the ground. The velocity of the muon means it takes (say) 9 microseconds of Earth frame time to reach the ground. The Earth frame sees the muon's clock as ticking slowly and only 4.5 microseconds elapse on the muon clock by the time it reaches the ground so it is still "alive" and is detected at ground level. The muon sees itself as statioary and sees the the Earth clocks whizzing past it. It observes that the Earth clocks are ticking slowly relative to its own clock and as far as it is concerned only (say) 2.25 microseconds elapse on the Earth clocks between the top clock and ground clock passing it. So how does the muon see 2.25 seconds elapse on the Earth clocks when the Earth observer says 9 microseconds elapses on the Earth clocks, during the muon's atmospheric transition? The answer is in the differences of simultaneity. As far as the muon is concerned, when the top clock read zero, the ground clock already had 6.75 seconds elapsed on it. By the time the ground clock arrived at the muon, the ground clock's display advanced from 6.75 to 9 microseconds meaning that only 2.25 seconds elapsed on the Earth clock as far as the muon is concerned.

 

[GregAshmore]

Let us imagine we have a clock hovering just above the Earth atmosphere that is sychronised with another clock at ground level in the Earth frame. (Ignore any difference in clock rates due to gravitational time dilation as this will be negligable in this example). When both these clocks are showing zero a muon is created near the top clock and speeds towards the ground. The velocity of the muon means it takes (say) 9 microseconds of Earth frame time to reach the ground. The Earth frame sees the muon's clock as ticking slowly and only 4.5 microseconds elapse on the muon clock by the time it reaches the ground so it is still "alive" and is detected at ground level. The muon sees itself as statioary and sees the the Earth clocks whizzing past it. It observes that the Earth clocks are ticking slowly relative to its own clock and as far as it is concerned only (say) 2.25 microseconds elapse on the Earth clocks between the top clock and ground clock passing it. So how does the muon see 2.25 seconds elapse on the Earth clocks when the Earth observer says 9 microseconds elapses on the Earth clocks, during the muon's atmospheric transition? The answer is in the differences of simultaneity. As far as the muon is concerned, when the top clock read zero, the ground clock already had 6.75 seconds elapsed on it. By the time the ground clock arrived at the muon, the ground clock's display advanced from 6.75 to 9 microseconds meaning that only 2.25 seconds elapsed on the Earth clock as far as the muon is concerned.

If one accepts the "pre-charge" of 6.75 seconds on the ground clock, everything adds up very nicely. I need to do my homework on this to make sure I have it, but the math isn't difficult.

For me, there is still an unresolved conceptual problem.

According to Einstein, Born, and Taylor-Wheeler, the aging process (as T-W put it) in the moving object is slower than the aging process in the resting object. (This is inferred from the fact that the clock in the moving object ticks at a slower rate.) Each object has the right to claim that it is moving. Therefore the aging process for each object is slower than it is for the other.

This, of course, is the Twin Paradox, but without the distraction of the turn-around.

I do not know how to resolve this difficulty. The obvious approach is to declare, as Born does regarding the absolute ether and absolute simultaneity, that a unique state which can be claimed with equal right by multiple entities can have no physical meaning: There is no such thing as slowed aging.

But that declaration causes other problems. And it is too late this evening to think about them.

 

[yogi]

For me, there is still an unresolved conceptual problem.

According to Einstein, Born, and Taylor-Wheeler, the aging process (as T-W put it) in the moving object is slower than the aging process in the resting object. (This is inferred from the fact that the clock in the moving object ticks at a slower rate.) Each object has the right to claim that it is moving. Therefore the aging process for each object is slower than it is for the other.

This, of course, is the Twin Paradox, but without the distraction of the turn-around.

I do not know how to resolve this difficulty. But that declaration causes other problems. And it is too late this evening to think about them.

them.[/QUOTE]

The muon experiments are a perfect example of the one way experiment Einstein described in the first few lines of Part IV of his 1905 paper - This involves two clocks initially synchronized while at rest in the same frame - the accelerated clock will have logged less time when it reaches the distant non-accelerated clock - the reciprocal experiment is never performed - it is assumed that Relativety is correct and that neither clock has a right to a preferred frame - but what happens if a clock is already in motion and it passes a point on the Earth - and we read it as it passes then use some signaling to start a distant clock allowing for the light travel time - the question becomes whether the two clocks will measure different times when they pass - we never perform this experiment - there is no acceleration - and there is no way to distinguish which clock is moving - so can you have a meaningful actual time difference when they meet. SR is independent of accelerations - but in every experiment where actual objective age difference is measured, there is acceleration somewhere (either at start up or turn around). In other words, in a totally symmetrical situation involving a pion already in motion at the time we take its measure by a lab clock, will the result correspond to the case where the clocks were initally synced while at rest in the same frame. If yes - then it seems that you would have a way of detecting absolute motion - but if the clocks read the same when the meet - the initial changing of frames due to acceleration becomes the real factor that contributes to the age difference.

 

[ghwellsjr]

The obvious approach is to declare, as Born does regarding the absolute ether and absolute simultaneity, that a unique state which can be claimed with equal right by multiple entities can have no physical meaning: There is no such thing as slowed aging.

But that declaration causes other problems.

Yes, like it isn't true. Who is Born and where does he make this declaration?

 

[yuiop]

If one accepts the "pre-charge" of 6.75 seconds on the ground clock, everything adds up very nicely. I need to do my homework on this to make sure I have it, but the math isn't difficult.

For me, there is still an unresolved conceptual problem.

First I should mention that I took the liberty of using 0.866c rather than 0.9999c for the velocity of the muon relative to the Earth because the gamma factor for 0.866c is 2 which makes the maths simpler (and the principles involved are more important than the actual numbers). However, it might be useful for you to see how the the "pre-charge" is calculated using a numeric example. The "pre charge" is actually the difference in simultaneity and a useful term to look up is the "relativity of simultaneity" which is at the root of 90 percent of the confusion present in all relativity paradoxes. The formula for the "simultaneity difference" is \Delta t = L_0 v/c^2 where L_0 is the proper distance.

Now in the example I gave earlier, the time for the muon to traverse the atmosphere was given as 9 microseconds as measured in the Earth frame. (Whether this is accurate is not relevant). In 9 microseconds at 0.866c the muon would travel 9 * 10^(-6) * 0.866 * 299792458 = 2336.65 metres (where 299792458 m/s is the speed of light c). The "simultaneity offset" of the two Earth clocks according to the muon is then:

\Delta t = L_0 v/c^2 = \frac{2336.65 * 0.866}{299792458} = 6.75 \textrm{microseconds}

Of course the atmosphere is greater than 2336.65 meters and the velocity of the muon is probably greater than 0.866c in real life. You might like to try repeating the calculations with more realistic numbers.

The nice thing about this calculation is that I obtained exactly the same result in the previous post by simply assuming:

1) The elapsed time on the muon clock is half the elapsed time on the Earth clocks from the point of view of the Earth frame.

2) The elapsed time of the ground clock is half the elapsed time on the muon clock from the point of view of the muon frame.

 

[chronon]

I went out for a walk the other day, in a straight line. A colleague also went out for a walk, at an angle of 45 degrees to me. So naturally I made forward progress quicker than he, after I had gone forward a mile, he had only gone forward 1/\sqrt 2 of a mile. But when we met up afterwards the blaggard disagreed - he claimed he made the quicker progress forward, and that I lagged behind. I hit him over the head with a copy of Euclid's Elements, but he stuck to his story. Clearly geometry is wrong and needs to replaced

 

[GregAshmore]

I went out for a walk the other day, in a straight line. A colleague also went out for a walk, at an angle of 45 degrees to me. So naturally I made forward progress quicker than he, after I had gone forward a mile, he had only gone forward 1/\sqrt 2 of a mile. But when we met up afterwards the blaggard disagreed - he claimed he made the quicker progress forward, and that I lagged behind. I hit him over the head with a copy of Euclid's Elements, but he stuck to his story. Clearly geometry is wrong and needs to replaced

Thanks, I needed a good chuckle. (And the point behind the humor is well taken.) Actually, I had another chuckle this morning--at myself--as I thought about my recent posts. It happens that I read Greek--mostly New Testament. I'm self-taught, and well aware of my limitations. Still, after ten years I am able to do reasonably well. So I find it interesting when I hear a message in which the speaker makes a comment on the Greek (which I have open in front of me), a comment which was obviously pulled out of a book by someone who does not read Greek himself, and is clearly off base. No doubt I have been doing much the same thing these past few days--or worse.

 

[GregAshmore]

Yes, like it isn't true. Who is Born and where does he make this declaration?

You have misunderstood me. Born says that there is aging of a moving object--or so I understood it when I read it. My [non]declaration was based on logic laid out by Borne in another context.

Max Born was a contemporary of Einstein, and Nobel Laureate in 1955.

 

[Dale]

As I understand SR, the time measured in the Earth frame should be much less than 4.5 microseconds. Yet the actual measurement of muons in the atmosphere is much more than 4.5 microseconds.

What have I missed?

Hi GregAshmore,

There is, to date, no repeatable measurement which contradicts SR. I recommend that you read the sticky on the experimental basis of SR.

However, your confusion here is illustrative of a problem that many students of relativity have. The general formula which governs SR is the Lorentz transform. The formulas for time dilation and length contraction are simplificatons of the Lorentz transform equations that are only valid in very specific circumstances. When you attempt to use them in situations where they do not apply then you get nonsense results and confusion.

I recommend that you never use the length contraction and time dilation formulas. I never use them myself. Simply use the Lorentz transform equations always. When appropriate they will automatically simplify, and you will avoid this type of confusion.

 

[GregAshmore]

Hi GregAshmore,

There is, to date, no repeatable measurement which contradicts SR. I recommend that you read the sticky on the experimental basis of SR.

However, your confusion here is illustrative of a problem that many students of relativity have. The general formula which governs SR is the Lorentz transform. The formulas for time dilation and length contraction are simplificatons of the Lorentz transform equations that are only valid in very specific circumstances. When you attempt to use them in situations where they do not apply then you get nonsense results and confusion.

I recommend that you never use the length contraction and time dilation formulas. I never use them myself. Simply use the Lorentz transform equations always. When appropriate they will automatically simplify, and you will avoid this type of confusion.

This is probably the answer to thehttps://www.physicsforums.com/showthread.php?t=452553" I just created, which restates my problem in a non-confrontational manner, and supplies the numbers which caused my angst.

 

[GregAshmore]

Hi GregAshmore,

There is, to date, no repeatable measurement which contradicts SR. I recommend that you read the sticky on the experimental basis of SR.

However, your confusion here is illustrative of a problem that many students of relativity have. The general formula which governs SR is the Lorentz transform. The formulas for time dilation and length contraction are simplificatons of the Lorentz transform equations that are only valid in very specific circumstances. When you attempt to use them in situations where they do not apply then you get nonsense results and confusion.

I recommend that you never use the length contraction and time dilation formulas. I never use them myself. Simply use the Lorentz transform equations always. When appropriate they will automatically simplify, and you will avoid this type of confusion.

I will read the full text of the article about experimental evidence for SR. For the moment, this caught my eye:

At this time there are no direct tests of length contraction, as measuring the length of a moving object to the precision required has not been feasible. There is, however, a demonstration that it occurs: [the summary of the experiment follows, but is not relevant to my question of the moment]

Does the author mean that the length of a moving object physically contracts? Born and T-W seem to be emphatic that it does not.

 

[Dale]

Does the author mean that the length of a moving object physically contracts?

What do you mean operationally by "physically contracts"? I.e. What experiment could you do to determine if something "physically contracts" or not?

 

[GregAshmore]

What do you mean operationally by "physically contracts"? I.e. What experiment could you do to determine if something "physically contracts" or not?

T-W and Born make a distinction between the intrinsic structure and operation of material objects and the measurement of their structure and operation. T-W: "We conclude that free-float motion does not affect the structure of operation of clocks or rods." This even though it is presumed that free-float motion does affect the measurement of clocks and rods.

I'm trying to understand whether the author is assuming that motion affects the intrinsic structure of material.

The distinction between the intrinsic structure and operation of nature and the measurement of nature is important as we evaluate the possibilities open to us as we operate within nature. Example: In chapter 4 of T-W, the argument in favor of going anywhere in the cosmos in as little time as we please is based entirely on the invariance of the spacetime interval. The spacetime interval is derived from quantities which are measured in a single frame. What cannot be measured (so far as I know) is the "pre-charge" on the clocks in another frame due to the relativity of simultaneity. The tacit assumption is that the trip will not be affected operationally by the swing in the reading of the Earth clocks at the turnaround. I'm not convinced that this is true. I note that when the relativity of simultaneity is taken into account, the tally of time is the same in both frames, even though the measured clock rates are different.

I need to think about this more, and be more precise in my thinking...that will take time, and experience solving problems.

 

[Dale]

Sorry, but if you answered my question I missed it. What experiment could you do to determine if something "physically contracts" or not?

The reason I ask this question is in order to answer your earlier question. "Physically contracts" is not a term of art, but if you can explain what you mean in terms of an experiment then I can simply use the Lorentz transform to figure out the answer.

 

[ghwellsjr]

What experiment could you do to determine if something "physically contracts" or not?

Are you suggesting that length contraction is not physical in the same way that time dilation is physical?

 

[JesseM]

Are you suggesting that length contraction is not physical in the same way that time dilation is physical?

Do you distinguish between "time dilation" and "differential aging"? There is no frame-independent sense in which we can say the rate a clock is ticking at a single moment is slower or faster than that of another clock, but if the two clocks start at a single location, move apart, and then come back together and compare times again at a single location, there is a frame-independent sense in which one clock has aged less in total between meetings than the other (i.e. one clock has elapsed less proper time between the events of the two meetings). I would say that "length contraction" is more analogous to "time dilation" in the first sense, it's an inherently frame-dependent notion. Whether you think frame-dependent quantities can be "physical" depends on how you choose to define the word "physical", as DaleSpam noted the word doesn't really have any "official" definition.

 

[ghwellsjr]

Would you say that a traveling clock physically has aged less than the stationary clock after they reunite?

 

[Dale]

Would you say that a traveling clock physically has aged less than the stationary clock after they reunite?

No, I wouldn't say that because "physically" is an ambiguous word.

I am not suggesting or implying anything, please don't read anything into it. I am simply trying to get GregAshmore to clarify his ambiguous question.

 

[ghwellsjr]

No, I wouldn't say that because "physically" is an ambiguous word.

Then what unambigous word do you prefer instead?

 

[JesseM]

Then what unambigous word do you prefer instead?

How about "frame-independent"? Then in answer to your previous question, it is a frame-independent fact that one clock has aged less than the other when they reunite, since the proper time between two events on a worldline has a frame-independent value. On the other hand there is no frame-independent truth about which of two inertial clocks has a slower rate of ticking, and likewise no frame-independent about which of two inertial rulers (with the same length in their respective rest frames) has a shorter length.

 

[Janus]

Thanks, I needed a good chuckle. (And the point behind the humor is well taken.) Actually, I had another chuckle this morning--at myself--as I thought about my recent posts. It happens that I read Greek--mostly New Testament. I'm self-taught, and well aware of my limitations. Still, after ten years I am able to do reasonably well. So I find it interesting when I hear a message in which the speaker makes a comment on the Greek (which I have open in front of me), a comment which was obviously pulled out of a book by someone who does not read Greek himself, and is clearly off base. No doubt I have been doing much the same thing these past few days--or worse.

Humor aside, chronon's post does offer a good way of thinking about time dilation. Just like Chronon and his friend disagree as to who is making better progress, clocks in relative motion will disagree as to which one is runner slower.

We can even apply this analogy to the twin paradox. Let's assume that while Chronon kept walking in a straight line, his friend, at some point makes a 90 degree turn that has him heading towards chronon's path. Upon intersecting chronon's path, he then turns again to walk in the sam direction as chronon. Would not he and chronon agree that he is now behind chronon? ( even though on the second leg of his trip he would still maintain that he was making better progress than chronon)

Is this not similar to the way that someone can travel away from the Earth at some high fraction of speed and then return to find that he has aged less than everyone on Earth, even though while going out and coming back he determined that time on Earth went slower than it did for him?

 

[ghwellsjr]

So, then it would be unambiguous to say "it is a frame-independent fact that one clock has physically aged less than the other when they reunite"?

 

[JesseM]

So, then it would be unambiguous to say "it is a frame-independent fact that one clock has physically aged less than the other when they reunite"?

I would say it's unambiguous, yes.

 

[Dale]

So, then it would be unambiguous to say "it is a frame-independent fact that one clock has physically aged less than the other when they reunite"?

I would get rid of the word "physically" here also. It doesn't add anything other than confusion.

 

[JesseM]

Humor aside, chronon's post does offer a good way of thinking about time dilation. Just like Chronon and his friend disagree as to who is making better progress, clocks in relative motion will disagree as to which one is runner slower.

We can even apply this analogy to the twin paradox. Let's assume that while Chronon kept walking in a straight line, his friend, at some point makes a 90 degree turn that has him heading towards chronon's path. Upon intersecting chronon's path, he then turns again to walk in the sam direction as chronon. Would not he and chronon agree that he is now behind chronon? ( even though on the second leg of his trip he would still maintain that he was making better progress than chronon)

Is this not similar to the way that someone can travel away from the Earth at some high fraction of speed and then return to find that he has aged less than everyone on Earth, even though while going out and coming back he determined that time on Earth went slower than it did for him?

I also expanded on this type of geometric analogy in [post=2972720]this post[/post], there are even more parallels with relativity than the ones that have been mentioned so far.

 

[ghwellsjr]

Dalespam, what unconfusing, unambiguous word would you use in place of physically?

 

[JesseM]

Dalespam, what unconfusing, unambiguous word would you use in place of physically?

Why does any word need to be in its place? Do you think there is some alternate frame-dependent notion of "aging" other than proper time, so that the statement "it is a frame-independent fact that one clock has aged less than the other when they reunite" would be too ambiguous?

 

[Dale]

Dalespam, what unconfusing, unambiguous word would you use in place of physically?

What do you mean by "physically"?

If you can answer that then use those words, if you cannot answer that (as I cannot in any useful way) then why would you say it at all?

EDIT: JesseM beat me to it! But his post is along the lines of what I was thinking. The statement was clear and unambiguous without the word "physically". It seems to be just an unnecessary and useless filler word in that statement.

 

[ghwellsjr]

There are plenty of people on this forum that think the idea of clocks running at different rates just because there is a relative speed between them is an illusion, an artifact, a measurement error, or otherwise not real. What do you tell them?

 

[JesseM]

There are plenty of people on this forum that think the idea of clocks running at different rates just because there is a relative speed between them is an illusion, an artifact, a measurement error, or otherwise not real. What do you tell them?

Can you define "illusion" and like terms? The rate at which any clock is running at is not frame-independent like the total elapsed time on a clock between two events on its worldline. Would you say that a frame-dependent quantity is "an illusion, an artifact, a measurement error, or otherwise not real"?

 

[yuiop]

There are plenty of people on this forum that think the idea of clocks running at different rates just because there is a relative speed between them is an illusion, an artifact, a measurement error, or otherwise not real. What do you tell them?

I agree with this sentiment because you often see people asking if the differential clock readings in the twins paradox would actually cause differential biological ageing, which of course it does (when you have a frame independent differential in elapsed proper times).

As a side question, would it reasonable to assume there always some ambiguity in the differential ageing of two clocks unless the initial and final measurements are made only when the clocks are right alongside each other?

For example, if the traveling twin (Bob) is 3/4 of the way home, the stay at home twin (Alice) might decide to take a trip and follow a path through spacetime such that when they eventually reunite, Alice could conceivably be the younger twin.

 

[Dale]

There are plenty of people on this forum that think the idea of clocks running at different rates just because there is a relative speed between them is an illusion, an artifact, a measurement error, or otherwise not real. What do you tell them?

I tell them that it is a measurable, frame-dependent effect. I try to let them decide how to categorize such things as illusion, or real, etc. since I don't feel comfortable with any such terms.

 

[ghwellsjr]

There are plenty of people on this forum that think the idea of clocks running at different rates just because there is a relative speed between them is an illusion, an artifact, a measurement error, or otherwise not real. What do you tell them?

Can you define "illusion" and like terms? The rate at which any clock is running at is not frame-independent like the total elapsed time on a clock between two events on its worldline. Would you say that a frame-dependent quantity is "an illusion, an artifact, a measurement error, or otherwise not real"?

I didn't say "the rate at which any clock is running at", which I agree is not frame-independent. I said "clocks running at different rates [with] a relative speed between them", which is frame independent (except in special cases), but more generally, I say, whenever a clock accelerates, its tick rate changes, which is a frame-independent truth, just like the clocks having different times on them when they re-unite. And so I say this is not an illusion, it is a frame-independent physical truth.

 

[Dale]

And so I say this is not an illusion, it is a frame-independent physical truth.

Then why not just say "frame-independent" instead of words like "illusion", "real", and "physical"? It is not only what you mean, but it is unambiguous.

 

[JesseM]

I didn't say "the rate at which any clock is running at", which I agree is not frame-independent. I said "clocks running at different rates [with] a relative speed between them", which is frame independent

I don't think it's a normal use of the terminology to say a verbal proposition is "frame independent", I've only ever seen physicists refer to frame-independent quantities like the elapsed proper time between two events on a given worldline. And even if you want to define "frame independent" more broadly, I'd say that for some fact to be frame-independent it must be true in all coordinate systems, not just inertial ones. You could construct a non-inertial coordinate system where two clocks have different coordinate velocities but are both ticking at the same rate relative to coordinate time.

but more generally, I say, whenever a clock accelerates, its tick rate changes, which is a frame-independent truth

Both criticisms above apply to this too.

just like the clocks having different times on them when they re-unite.

This example is unlike the first two in the sense that it's not vulnerable to either of my criticisms above. If you want to avoid my first criticism you can just talk about the amount of proper time that elapses on each clock's worldline between the two local meetings, and of course the second criticism doesn't apply either since even non-inertial coordinate systems agree about the proper time between two events on any given worldline.

 

[GregAshmore]

No, I wouldn't say that because "physically" is an ambiguous word.

I am not suggesting or implying anything, please don't read anything into it. I am simply trying to get GregAshmore to clarify his ambiguous question.

My question is indeed ambiguous. Some of that ambiguity will probably be cleared up by experience. However, in my opinion a good deal of the ambiguity is tightly bound to the nature of light.

The fundamental question is whether there is a difference between perception (measurement) and reality. In the case of length contraction, does a measured reduction in length imply an actual reduction in length?

It is easy enough to say that we don't know how to define reality apart from measurement. I appreciate that point of view, but cannot be satisfied with it philosophically. My dissatisfaction would become a very practical matter if you were to ask me to travel with you on a round trip to Canopus.

In ch. 4 of Taylor-Wheeler, discussing a trip to Canopus:

Dr. Bright sits back in his chair with a smile, obviously believing that he has disposed of all objections single-handedly. "Yes," we conclude, "about the reality of the effect there is no question."

This without a single experiment involving round trip high-speed travel. And with a number of unanswered questions even closer to home.

Take the muon experiments, for example. As impressive as the data are, we are still missing key bits of information. It is one thing to speculate about the readings on clocks in the muon frame; to have actual measurements is another. I understand that the numbers all work out on paper, and I have a deep sense (due to my own sluggishness, if nothing else) of the genius of Einstein in developing the theory. But without more data, I don't see that we can rule out the possibility of other explanations for our measurements.

Born spends over eleven pages discussing appearance and reality in SR. With regard to length contraction he says, "We do not mean to say that a body which is moving in a straight line with respect to an inertial system S "undergoes a change", although it actually changes its situation with respect to S." A few paragraphs later he concludes, "It is only the strip as a manifold of world points (events) which has physical reality, and not the cross section. Thus the contraction [the body seen in cross section] is only a consequence of our way of regarding things and is not a change of a physical reality."

Born's language is very clear, yet I doubt that he has escaped the ambiguity inherent in the subject.