An Experiment With Clocks.

[sigurdV]

We have two stopwatches and we begin by starting them.

We put one on the table and the other in a centrifuge made of glass so we can observe both clocks simultaneously.

Now observe the clocks throughout the experiment. And now stop centrifuging the clock. Stop both clocks.

 

My first simple question is: For how long time have we been observing BOTH clocks?

(Suppose the stationary clock says for one hour and the spinning clock says fiftynine minutes.

1 Is it then so that we have observed BOTH clocks for both one hour and for fiftynine minutes? Is 60=59?

(The experiment seems to me to be the twin paradox with a difference:

The clocks can be observed simultaneously all the time...whether that makes any difference is one of my further questions.)

2 What speed and radius of the centrifuge will give the 59/60 result?

3 Why and how is rotation shortening the rate of time of the rotating clock, where is "the missing minute"?

[JMJones0424]

Your questions are not as simple to answer as they may seem to appear. I think the fact that the clock in the centrifuge is undergoing constant acceleration as it spins, it is therefore not in an inertial frame of reference. As such, I don't know how to answer your question, but I don't doubt that others here could.

 

Were the moving clock in an inertial frame of reference, then my go to source, GSU's HyperPhysics provides a convenient calculator to determine the relative velocity difference required to elicit a measure time difference of 60/59 here. 60/59 is roughly 1.01695, therefore the moving clock must be moving relative to the stationary clock at 0.181816 c. Ignoring the problem of inertial acceleration, the rate of spin would therefore be dependent on the radius of the centrifuge.

 

The "missing minute" only exists in your mind.

 

EDIT: corrected typo "60/59 is roughly 1.01659"

Edited April 13, 2013 by JMJones0424

[sigurdV]

Your questions are not as simple to answer as they may seem to appear. I think the fact that the clock in the centrifuge is undergoing constant acceleration as it spins, it is therefore not in an inertial frame of reference. As such, I don't know how to answer your question, but I don't doubt that others here could.

 

Were the moving clock in an inertial frame of reference, then my go to source, GSU's HyperPhysics provides a convenient calculator to determine the relative velocity difference required to elicit a measure time difference of 60/59 here. 60/59 is roughly 1.01659, therefore the moving clock must be moving relative to the stationary clock at 0.181816 c. Ignoring the problem of inertial acceleration, the rate of spin would therefore be dependent on the radius of the centrifuge.

 

The "missing minute" only exists in your mind.

Hi! As to the second question I also got stuck on the complications.

 

... But as to the third?

 

Well I can think of other explanations...and Id like to see your proof that its really there in my mind ;)

 

It could be so that the speed mysteriously subtracts a 1/60 of a minute from each of the 60 minutes the rotating clock is within the laboratory, "stealing" one minute and leaving the remaining 59 minutes to the clock to experience.

But if so, where then is this stolen minute hidden? And wont the minutes now be discontinuous minutes? And how is this actually done by "speed"?

This surely is only "the last chance" if all other explanations fail?

 

I hesitate to be the first to give a non-ridiculous solution...I think somebody else should be first.

So tell me what speed actually does in making time shorter: What IS the actual mechanism? And what makes it work?

That explanation is roughly what I obviously(?) meant by the expression the "missing minute"!

[Rade]

Concerning what you observed, I would say you do not observed BOTH clocks for BOTH of two number measures of time (60 & 59). Time is the number of motion and also of rest of an entity, time is the number of motion that is intermediate between moments. In your experiment the moments are the start and stop events of watch. What you observed between those two moments are two watches each in some state of motion at some (x,y,z) location on flat table and each has independent moments associated with them (e.g., it takes two hands to start two watches). The watch on table has motion = 0 units of measure between the two moments of start and stop. The watch spinning in centrifuge some motion > 0. Motion that can be measured by time does not have to be linear, such as from location A to B where there is a change in (x,y,z) coordinates. Rotation or spinning in place, where (x,y,z) space locations do not change, also is a type of motion that time can measure. What you observe are independent watches that record independent records of time between two moments (start and stop of watches) of two entities with different motion.

 

As said above, there is no missing minute, what is missing is the ability of human eye to observe how space-time is modified for a watch sitting on a table compared to a second one next to it on same table spinning like a top between two moments (start and stop events). The rest motion of watch #1 and the non-rest motion of watch #2 informs space-time how to behave independently for each watch, while simultaneously, the space-time informs each watch how to move. For me, this is the beauty found in the GR equation of Einstein, the word simultaneously.

 

There is no TIME if there are not SIMULTANEOUS events that are the limits of TIME as moments.

 

This is how I understand your experiment. If I error please inform.

[Doctordick]

My first simple question is: For how long time have we been observing BOTH clocks?

(Suppose the stationary clock says for one hour and the spinning clock says fiftynine minutes.

1 Is it then so that we have observed BOTH clocks for both one hour and for fiftynine minutes? Is 60=59?

(The experiment seems to me to be the twin paradox with a difference:

The clocks can be observed simultaneously all the time...whether that makes any difference is one of my further questions.)

Thank you sigurdV for pointing out something I noticed sixty five years ago (when I read a book my dad had bought). The book was George Gamow's book “One Two Three ... Infinity”. The central theme of the book (or at least the part I found interesting) was his explanation of Einstein's relativity which no one I knew seemed to understand. Being but a child I had no idea of the mathematical constructs of Minkowski's geometry and misinterpreted much of what Gamow said. When he said time was an “imaginary” coordinate, I thought he meant “make believe”. I connected that fourth “imaginary” coordinate with Plato's shadows on the wall comment on what we think we know. That is, the three dimensional world we see is projected out of that imaginary four dimensional geometry of Einstein's picture. With regard to the measurements on the moving train (Gamow's example) my reaction was, “Oh, clocks don't measure time!” (time is make believe). But their measure is proportional to how far we move!

 

I came up with an interpretation which made perfect sense to me. Things moved in that four dimensional universe just as we perceive of them moving in our three dimensional universe except that the fourth dimension was being projected out. If we are standing still, we are actually moving to the future in that "make believe" direction. Since I thought imaginary meant make believe, it never dawned on me that the fourth axis was any different from the other three axes. If we move, we are, in addition, moving in the three dimensions we perceive. Since we cannot tell we are actually moving (i.e., the central thesis of relativity), motion through space must also move us into the future.

 

The net effect? If we go a light year as fast as possible (essentially instantaneously) we will have moved into the future (in spite of the fact that our clock reads zero: i.e., we moved instantaneously) a distance exactly one year (that is the definition of a light year).

 

Work out the mechanics of the thing and you will get exactly the same results for any experiment which are given by special relativity. As a child, I thought I understood relativity. I didn't discover I had “made a mistake” until I got into college and discovered that wasn't at all what Einstein had in mind. On the other hand, my mental construct gave exactly the same answers as his did so, when it came to calculating answers to specific questions I generally used whichever picture was quicker. Sometimes mine was and sometimes his was.

 

I was never able to find a circumstance where the answers ever differed. None the less, one thing bothered me about my picture. I could never come up with any reason for that fourth dimension to be projected out.

 

When I was in graduate school (the first time I ever heard of quantum mechanics) it dawned on me that quantized momentum in that fourth dimension was a perfect mechanism for projecting out that dimension. It was my first year in graduate school that I actually proved mathematically that the two pictures gave exactly the same results. At the time I showed my proof to the professor we had for introductory quantum mechanics. After about four hours of arguing with him over minor issues his reaction kind of surprised me. He said, “well of course you are right; but don't show it to any of the other students, it will just confuse them!" Being a good obedient student, I never did. Truthfully, I now suspect my solution confused him.

 

Nevertheless, the fact that my picture had no conflicts with quantum mechanics seemed interesting and in many respects was exactly what led me to discover my fundamental equation.

 

So thanks for seeing at least a glimpse of the issue.

 

2 What speed and radius of the centrifuge will give the 59/60 result?

The centrifugal force is given by [math]\vec{F}= mr\omega^2\hat{r}[/math] thus the velocity (which is perpendicular to [math]\hat{r}[/math] has nothing to do with m. Its magnitude is constant and is in fact given by rω.

 

The units of omega in the above are “radians per unit time” which is RPM divided by 2π. Since π = 3.1415 and a meter is 3.2808399 feet, why don't we make the diameter 1.0443 feet, making the radius of the rotating clock about six and a quarter inches (6.2659”), a reasonably sized centrifuge. Then rω = 2πω in meters and is directly represented by RPM

 

The elapsed time (in the rest frame is one hour) the reading on the clock in the centrifuge at roughly 6.2659 inches is given by [math]59=t'=t\sqrt{1-\left(\frac{v}{c}\right)^2} = 60\sqrt{1-\left(\frac{r\omega}{c}\right)^2}= 60\sqrt{1-\left(\frac{“RPM”}{c}\right)^2}[/math].

 

Solving that for “RPM” one has [math]\left(\frac{59}{60}\right)^2=1-\left(\frac{“RPM”}{c}\right)^2[/math]

 

or [math] “RPM” =c\sqrt{1-\left(\frac{59}{60}\right)^2}[/math]

 

where c must be given in meters per minute. That would be 60 times [math]3\;10^8[/math] meters/sec or [math]1.8\;10^{10}[/math] meters/min.

 

The final result is [math] “RPM” =1.8\;10^{10}\sqrt{1-\left(\frac{59}{60}\right)^2}=1.8\;10^{10}\: times \; 0.1818[/math]

 

Roughly, the answer is 3,273,000,000 RPM

 

If your clock weighed one oz. the radial force would be [math]\frac{m}{r}\left(\frac{“RPM”}{60}\right)^2[/math] in ounces.

The “60” gets us back to seconds and “r” is slightly over a sixth of a meter so, since a ton is 32,000 ounces, the approximate radial force would be 557,944,200,000 tons. (I have done the multiplication twice but errors are easy to make so that might be wrong.) A rather strong force to sustain in that centrifuge :P

 

3 Why and how is rotation shortening the rate of time of the rotating clock, where is "the missing minute"?

Because the clock is moving through ordinary space and thus it is advancing faster into the future! As I said above, the fact that “clocks measure time” is a total myth. Their measurements can only be compared to time when they are not moving. Even in Einstein's picture, their measurements are actually always proportional to “proper time” the “invariant interval” of his geometry, their own path length in my geometry. Read my posts, time is nothing more than an ordering parameter and, in my picture, it can be set universally (any rest frame will do) but it can not be actually measured; it's a make believe parameter convenient to calculations!

 

Have fun -- Dick

[sigurdV]

Thank you sigurdV for pointing out something I noticed sixty five years ago (when I read a book my dad had bought). The book was George Gamow's book “One Two Three ... Infinity”. The central theme of the book (or at least the part I found interesting) was his explanation of Einstein's relativity which no one I knew seemed to understand. Being but a child I had no idea of the mathematical constructs of Minkowski's geometry and misinterpreted much of what Gamow said. When he said time was an “imaginary” coordinate, I thought he meant “make believe”. I connected that fourth “imaginary” coordinate with Plato's shadows on the wall comment on what we think we know. That is, the three dimensional world we see is projected out of that imaginary four dimensional geometry of Einstein's picture. With regard to the measurements on the moving train (Gamow's example) my reaction was, “Oh, clocks don't measure time!” (time is make believe). But their measure is proportional to how far we move!

 

I came up with an interpretation which made perfect sense to me. Things moved in that four dimensional universe just as we perceive of them moving in our three dimensional universe except that the fourth dimension was being projected out. If we are standing still, we are actually moving to the future in that "make believe" direction. Since I thought imaginary meant make believe, it never dawned on me that the fourth axis was any different from the other three axes. If we move, we are, in addition, moving in the three dimensions we perceive. Since we cannot tell we are actually moving (i.e., the central thesis of relativity), motion through space must also move us into the future.

 

The net effect? If we go a light year as fast as possible (essentially instantaneously) we will have moved into the future (in spite of the fact that our clock reads zero: i.e., we moved instantaneously) a distance exactly one year (that is the definition of a light year).

 

Work out the mechanics of the thing and you will get exactly the same results for any experiment which are given by special relativity. As a child, I thought I understood relativity. I didn't discover I had “made a mistake” until I got into college and discovered that wasn't at all what Einstein had in mind. On the other hand, my mental construct gave exactly the same answers as his did so, when it came to calculating answers to specific questions I generally used whichever picture was quicker. Sometimes mine was and sometimes his was.

 

I was never able to find a circumstance where the answers ever differed. None the less, one thing bothered me about my picture. I could never come up with any reason for that fourth dimension to be projected out.

 

When I was in graduate school (the first time I ever heard of quantum mechanics) it dawned on me that quantized momentum in that fourth dimension was a perfect mechanism for projecting out that dimension. It was my first year in graduate school that I actually proved mathematically that the two pictures gave exactly the same results. At the time I showed my proof to the professor we had for introductory quantum mechanics. After about four hours of arguing with him over minor issues his reaction kind of surprised me. He said, “well of course you are right; but don't show it to any of the other students, it will just confuse them!" Being a good obedient student, I never did. Truthfully, I now suspect my solution confused him.

 

Nevertheless, the fact that my picture had no conflicts with quantum mechanics seemed interesting and in many respects was exactly what led me to discover my fundamental equation.

 

So thanks for seeing at least a glimpse of the issue.

 

 

The centrifugal force is given by [math]\vec{F}= mr\omega^2\hat{r}[/math] thus the velocity (which is perpendicular to [math]\hat{r}[/math] has nothing to do with m. Its magnitude is constant and is in fact given by rω.

 

The units of omega in the above are “radians per unit time” which is RPM divided by 2π. Since π = 3.1415 and a meter is 3.2808399 feet, why don't we make the diameter 1.0443 feet, making the radius of the rotating clock about six and a quarter inches (6.2659”), a reasonably sized centrifuge. Then rω = 2πω in meters and is directly represented by RPM

 

The elapsed time (in the rest frame is one hour) the reading on the clock in the centrifuge at roughly 6.2659 inches is given by [math]59=t'=t\sqrt{1-\left(\frac{v}{c}\right)^2} = 60\sqrt{1-\left(\frac{r\omega}{c}\right)^2}= 60\sqrt{1-\left(\frac{“RPM”}{c}\right)^2}[/math].

 

Solving that for “RPM” one has [math]\left(\frac{59}{60}\right)^2=1-\left(\frac{“RPM”}{c}\right)^2[/math]

 

or [math] “RPM” =c\sqrt{1-\left(\frac{59}{60}\right)^2}[/math]

 

where c must be given in meters per minute. That would be 60 times [math]3\;10^8[/math] meters/sec or [math]1.8\;10^{10}[/math] meters/min.

 

The final result is [math] “RPM” =1.8\;10^{10}\sqrt{1-\left(\frac{59}{60}\right)^2}=1.8\;10^{10}\: times \; 0.1818[/math]

 

Roughly, the answer is 3,273,000,000 RPM

 

If your clock weighed one oz. the radial force would be [math]\frac{m}{r}\left(\frac{“RPM”}{60}\right)^2[/math] in ounces.

The “60” gets us back to seconds and “r” is slightly over a sixth of a meter so, since a ton is 32,000 ounces, the approximate radial force would be 557,944,200,000 tons. (I have done the multiplication twice but errors are easy to make so that might be wrong.) A rather strong force to sustain in that centrifuge :P

 

 

Because the clock is moving through ordinary space and thus it is advancing faster into the future! As I said above, the fact that “clocks measure time” is a total myth. Their measurements can only be compared to time when they are not moving. Even in Einstein's picture, their measurements are actually always proportional to “proper time” the “invariant interval” of his geometry, their own path length in my geometry. Read my posts, time is nothing more than an ordering parameter and, in my picture, it can be set universally (any rest frame will do) but it can not be actually measured; it's a make believe parameter convenient to calculations!

 

Have fun -- Dick

THANK YOU!

Im happy for a change! Someone takes me seriously...Im delirious so here I go:

 

Honestly: I like your texts, but I will not pretend I understand them.

All I will say about your solution is that I certainly NOT find it ridiculous!

Therefore I feel free to also give my possibly somewhat "far out" solution:

(Ill go slow for once.)

 

1 The answer cant be inside the theory of Relativity...

them Relativisians are competent "in-the-box-thinkers" and they would have found it already if it was there!

2 Where might it be? In the other Masterpiece of science: Quantum Theory? If so I cant find it :(

3 Hey! Time is related to movement, and movement is related to energy, and energy is quantized!

4 Speed makes time as a distance shorter but that surely makes minutes shorter as well...OH NO!

Not if they consist of quanta that cannot be compressed!

Meaning theres no longer room for more than 59 minutes in the spacetime interval!

So there IS no missing minute ;)

 

Thanks again Dick...I had one more speculative point in mind

when I designed the experiment...

 

Now when the math seems satisfyingly done: What if the lab is the universe

and the clocks represent all clocks and clocklike entities in it?

If clocks in the lab has been there for an equally long time

independently of what their "internal clock" shows,

will then not all parts of the universe be of the same age

independently of what time they show it is?

[sigurdV]

The centrifugal force is given by [math]\vec{F}= mr\omega^2\hat{r}[/math] thus the velocity (which is perpendicular to [math]\hat{r}[/math] has nothing to do with m. Its magnitude is constant and is in fact given by rω.

 

The units of omega in the above are “radians per unit time” which is RPM divided by 2π. Since π = 3.1415 and a meter is 3.2808399 feet, why don't we make the diameter 1.0443 feet, making the radius of the rotating clock about six and a quarter inches (6.2659”), a reasonably sized centrifuge. Then rω = 2πω in meters and is directly represented by RPM

 

The elapsed time (in the rest frame is one hour) the reading on the clock in the centrifuge at roughly 6.2659 inches is given by [math]59=t'=t\sqrt{1-\left(\frac{v}{c}\right)^2} = 60\sqrt{1-\left(\frac{r\omega}{c}\right)^2}= 60\sqrt{1-\left(\frac{“RPM”}{c}\right)^2}[/math].

 

Solving that for “RPM” one has [math]\left(\frac{59}{60}\right)^2=1-\left(\frac{“RPM”}{c}\right)^2[/math]

 

or [math] “RPM” =c\sqrt{1-\left(\frac{59}{60}\right)^2}[/math]

 

where c must be given in meters per minute. That would be 60 times [math]3\;10^8[/math] meters/sec or [math]1.8\;10^{10}[/math] meters/min.

 

The final result is [math] “RPM” =1.8\;10^{10}\sqrt{1-\left(\frac{59}{60}\right)^2}=1.8\;10^{10}\: times \; 0.1818[/math]

 

Roughly, the answer is 3,273,000,000 RPM

 

If your clock weighed one oz. the radial force would be [math]\frac{m}{r}\left(\frac{“RPM”}{60}\right)^2[/math] in ounces.

The “60” gets us back to seconds and “r” is slightly over a sixth of a meter so, since a ton is 32,000 ounces, the approximate radial force would be 557,944,200,000 tons. (I have done the multiplication twice but errors are easy to make so that might be wrong.) A rather strong force to sustain in that centrifuge :P

 

 

Because the clock is moving through ordinary space and thus it is advancing faster into the future! As I said above, the fact that “clocks measure time” is a total myth. Their measurements can only be compared to time when they are not moving. Even in Einstein's picture, their measurements are actually always proportional to “proper time” the “invariant interval” of his geometry, their own path length in my geometry. Read my posts, time is nothing more than an ordering parameter and, in my picture, it can be set universally (any rest frame will do) but it can not be actually measured; it's a make believe parameter convenient to calculations!

 

Have fun -- Dick

Ive given your post a second reading and want to add a few remarks:

I didnt really expect ordinarily clocks to survive in there...

Let experienced experimentators change parameters if they wish to experiment.

"There ARE no elevators in space Mr Einstein!"

 

What if the centrifugal axis is parallell to earth axis? Will there be detectable periodic variations?

We cant find the fastest time,they say, but what if the fastest time we can find has detectable periodic variations?

Then how would One explain them?

 

And thank You again for Your kind attention!

[Rade]

A few comments based on above posts.

 

1. Time is not a parameter that can be measured, time is what measures simultaneous events. Time is not MEASURED by a clock, time is what a clock MEASURES, fundamental difference.

 

2. Time is not fast or slow. Time is long or short. So to look for the fastest time is to look for the make believe. The duration of time is infinite.

 

3. Because time is nothing more than a number, it can be viewed as a parameter as number that orders simultaneous events. All order parameters in physics are numbers.

 

4. A watch spinning on its axis is not moving 'through' space to some future moment from past or present moment, it is moving 'within' space at the present, past, and future moments simultaneously. Space is the inner boundary of that which contains motion. Time is that which is intermediate between moments. Put concepts together:

 

Space-time is the inner boundary of that which contains motion intermediate between moments.

Edited April 13, 2013 by Rade

[sigurdV]

Concerning what you observed, I would say you do not observed BOTH clocks for BOTH of two number measures of time (60 & 59).

Hopefully you are correct since its no fun to admit to 59=60!

But the problem is that I actually see both arrows on the clocks move simultaneously

and i notice that the stationary clock is first to reach a full minute

at a moment when the arrow of the moving clock is not quite at the one minute mark...

so at the end of the experiment the choice of what clock correctly measures time might be questioned.

 

I want to thank you for sharing my experiment...taking it seriously!

But it seems to me we are examining the clocks simultaneously (Whatever that really means?)

We could film the clocks and project their pictures beside each other at the wall.

I suspect we need the concepts of "internal" and "external" time

in order not to confuse our descriptions and measurements of time.

 

Suppose we ask how old a statue is? Then we should be careful in interpreting its "age":

Do we ask how old all the energy the statue contains is or at what moment the artist said:

"There! Now the statue is finished?". We must take care to understand what, what we state or question means!

 

Time is the number of motion and also of rest of an entity, time is the number of motion that is intermediate between moments. In your experiment the moments are the start and stop events of watch. What you observed between those two moments are two watches each in some state of motion at some (x,y,z) location on flat table and each has independent moments associated with them (e.g., it takes two hands to start two watches)

(Not necessarily so: One handed persons are surely also able to start the clocks at the same time.)

 

 

The watch on table has motion = 0 units of measure between the two moments of start and stop. The watch spinning in centrifuge some motion > 0. Motion that can be measured by time does not have to be linear, such as from location A to B where there is a change in (x,y,z) coordinates. Rotation or spinning in place, where (x,y,z) space locations do not change, also is a type of motion that time can measure. What you observe are independent watches that record independent records of time between two moments (start and stop of watches) of two entities with different motion.

I like your analysis. Motion surely is an indication of time!

But there are differend kinds of motion as you point out:

Instead of rotating the clock we surely in principle could have oscillated it

in very small but very fast movements back and forwards...

so minute that all we would notice is the slowness of the clock itself!

 

And there might be a problem with that...

Surely the constituents of the clock moves relative to each other?

What effect has its internal movements on the clock as a whole?

Must we invoke Thermodynamics?

 

A word of caution:

Please understand that I am not attacking the Beautiful Theory of Einstein.

(Who in my eye is the leading Philosopher of Time in all written History!)

 

I am only trying to make sense of our observations of our world!

IF Theory does not fit observations THEN Goodbye Theory!

(or goodbye theory of observations.)

 

And another:

My Total Commitment to Reality has made internet people

considering me as the King of Trolls!

Declaring me to be the worst threat to Sanity on the Internet there is.

 

This really hurts! But there is nothing I can do about it.

Except continuing my attempts to explain thingz as I obzerve them.

Sometimes getting my threads closed and myself banned in the process...

 

 

As said above, there is no missing minute,

Im very sorry but I disagree! A basic fact is: 60-59=1.

I use the Metaphor:

"The Missing Minute",

 

to refer to the discrepancy of the distances in time the clocks imply.

This discrepancy is REAL and needs to be understood and explained!

 

 

 

 

what is missing is the ability of human eye to observe how space-time is modified for a watch sitting on a table compared to a second one next to it on same table spinning like a top between two moments (start and stop events). The rest motion of watch #1 and the non-rest motion of watch #2 informs space-time how to behave independently for each watch, while simultaneously, the space-time informs each watch how to move. For me, this is the beauty found in the GR equation of Einstein, the word simultaneously.

 

There is no TIME if there are not SIMULTANEOUS events that are the limits of TIME as moments.

 

This is how I understand your experiment. If I error please inform.

LOL! My Friend! If I may call you so...

I have no IDEA if youre in error or not!

ALL I see is that you cautiously explore my thought experiment

in order to understand it and its consequences.

 

I took the Liberty to somewhat "improve" on Einsteins Twin Experiment

in order to make some problems I see appear in sharper focus.

 

I dont "understand" the experiment,yet,

thats why I publish in here...to get help in that!

 

Were it the case that I understood, I wouldnt be here...

I would have moved on towards "higher questionz"!

[sigurdV]

A few comments based on above posts.

 

1. Time is not a parameter that can be measured, time is what measures simultaneous events. Time is not MEASURED by a clock, time is what a clock MEASURES, fundamental difference.

 

2. Time is not fast or slow.

I think "the velocity of" time can be defined as its degree of dilation?

 

In my own words:

The rotating clock has the dilation factor of 59/60 relative to the stationary clock.

Your personal time might accordingly be dilated with respect to some "outside" time,

if so then the dilation factor with respect to the outside time is the quotient:

 

(t2-t1) / (u2-u1),

 

of an outside segment of time (u2-u1) as the divisor of your corresponding segment of time (t2-t1).

(Meaning that u1 corresponds to t1, and u2 corresponds to t2.)

 

If the dilation factor is less than one then the outside time is "faster" than your personal time,say:

the time you would experience sitting within the revolving clock.

 

This is NOT what theory told me to expect...

This is what I observe in the experiment!

Do you observe something different?

Edited April 13, 2013 by sigurdV

[Rade]

But the problem is that I actually see both arrows on the clocks move simultaneously and I notice that the stationary clock is first to reach a full minute at a moment when the arrow of the moving clock is not quite at the one minute mark...so at the end of the experiment the choice of what clock correctly measures time might be questioned.

? I do not understand how you can claim to actually see the arrow on the spinning clock, the rotational spin would demand that the arrow vanishes from human vision. Thus in your experiment you can only actually see the slowly moving arrow on the clock on the table that is not spinning. What am I missing ? I mean your thought experiment is only as valid as it matches facts of reality.

 

I want to thank you for sharing my experiment...taking it seriously!

And I want to thank you for dialog without insult. My goal here at this forum is the learn and also provide input by throwing many darts of thought with the hope that a few at best stick to reality and truth.

 

But it seems to me we are examining the clocks simultaneously (Whatever that really means?)

For me, all it means in context of your experiment is that you do examine both clocks simultaneous, twice in fact, first when you start the two clocks and look at two arrows, second when you stop them. Time is nothing more than a number associated with these FOUR simultaneous events related to movement of arrows and acts of starting and stopping clocks.

 

I suspect we need the concepts of "internal" and "external" time in order not to confuse our descriptions and measurements of time.

I find this to be an interesting comment, here is how I answer. For me, external time would be that which is intermediate between two moments, a number that is a measure of motion. So, do we look in a book at the library to find this number between moment? No, we can use sundial or a clock or some other physical object that can measure motion. Internal time is a more abstract concept for me. I view it has being the duration of any moment within external time, and this internal time duration of a moment I give duration of Planck Time, which by definition is outside the possibility of human measurement due to uncertainty principle (HUP). Does this make sense to you as relates to your thought experiment ?

 

Suppose we ask how old a statue is? Then we should be careful in interpreting its "age": Do we ask how old all the energy the statue contains is or at what moment the artist said:

"There! Now the statue is finished?". We must take care to understand what, what we state or question means!

Seems to me we can equally ask for both ages, both questions are valid to ask and of course they must provide different ages. It depends on definition of 'finished', which takes two forms: (1) when finished by living human and (2) when finished by what I will call non-living space-time. So, suppose artist is dead (lack of life) for some period of time and statue he made is in museum and called Statue of David, and we ask the curator a question...how old is that Statue of David? The answer given will be relative to the statue being 'finished' by space-time, when the statue becomes a pile of atomic elements that once were in the form of a slab of hard rock.

 

(Not necessarily so: One handed persons are surely also able to start the clocks at the same time.)

Only if they have two thumbs on one hand :) But, sounds like an interesting experiment for a physics class.

 

I like your analysis. Motion surely is an indication of time!

Yes, and it is very important to define motion. How do you define motion itself ?

 

My Total Commitment to Reality has made internet people considering me as the King of Trolls! Declaring me to be the worst threat to Sanity on the Internet there is.

I share the same commitment and consequences.

 

I'm very sorry but I disagree! A basic fact is: 60-59=1. I use the Metaphor: "The Missing Minute", to refer to the discrepancy of the distances in time the clocks imply.

This discrepancy is REAL and needs to be understood and explained!

OK, it is explained then as a metaphor minute missing, not as a real minute missing...correct ? One clock measures 59, a second 60. They are independent clocks that cannot be viewed simultaneously during the experiment (e.g., you cannot observe the arrow on the spinning clock), only at start and end of experiment. So, in the experiment, the minute is missing or taken away from a clock in the same way life is present or added to a hill, when I use the metaphor in song: :Music: The Hills are Alive, with the Sound of Music. :Music:

 

I took the Liberty to somewhat "improve" on Einsteins Twin Experiment in order to make some problems I see appear in sharper focus.

I find your question to be wonderful. It is my understanding that Einstein was well aware of your question, but never directly published on it. However, after he finished his SR Theory, the question you ask he also asked, and his thinking about it was the key event that lead him to complete his understanding of GR Theory.

[Rade]

I think "the velocity of" time can be defined as its degree of dilation?

This is not my understanding. There cannot be a concept called 'the velocity of time'. Why ? Velocity is a vector, it has both distance and direction, whereas time is a scalar, it lacks direction.

 

But, you could change the wording to "the speed of" time.....; because speed is also a scalar as is time.

 

But, I do not agree that the degree of time dilation is due to the "speed of time", I find that it results from "speed of the clocks". Change or movement is only in the thing that changes, and time is not a thing. Time is equally everywhere and with all things. In your thought experiment it is the change in the motion of clocks that is SLOW or FAST, and it is the change in time relative to motion that is LONG or SHORT. The words fast and slow are defined by time, thus FAST = that which moves much in a SHORT time. SLOW = that which moves little in a LONG time.

 

Consider the various definitions for the word 'dilation' in Webster: To expand, widen, or make longer. So, to say that time dilation is the result of your thought experiment is to say time has been made LONGER for some object in motion that has moved SLOWER (e.g. your number 60) relative to another object that has moved FASTER over the same distance where time has been made SHORTER (your number 59).

 

Consider at speed of light c, we say time stops. OK. For me this means time is the very SHORT indeed, t = 0. In other words, time cannot be a measure of motion of the photon because for time to measure motion the motion must be within time, but the photon is not within time, it is 'within' a moment. Time for a photon is not slow at the c, time is SHORT (the number 0) because the photon is very FAST (the number c). We can say the photon is 'external' to time because it is 'internal' to a moment [recall your suggestion that external and internal relate somehow to time].

 

===

 

The rotating clock has the dilation factor of 59/60 relative to the stationary clock. Your personal time might accordingly be dilated with respect to some "outside" time, if so then the dilation factor with respect to the outside time is the quotient:

OK, the rotating clock has 59/60 = 0.983 factor and stationary clock factor of 1.000, so we say the time is SHORTER for the rotating clock because ratio is smaller due to the motion being FASTER, relative to stationary clock

 

But, why would we have any reason to think the personal time of the observer, sitting next to table and watching experiment for 60 minutes would accordingly be dilated, or dilated at all as the two clocks are, unless the person was spinning slower or faster than the "outside" entity ? You never said in your OP that the observer was in motion relative to something "outside" the experiment. So, I suggest this claim is based on a false premise and thus the rest of your presentation cannot hold true. But, perhaps I did not understand your explanation assumptions.

[sigurdV]

...not my understanding.

I think we need to compare our conceptual systems! A sort of Mental Clock experiment ;)

You see its awkward for me to replace the words entering my consciousness coming from wherever my thoughts actually gets produced.

I notice I use the undefined word "speed" when I consider time..."Velocity" (besides I think in Swedish mostly)

is a more theory defined concept to me (= distance unit per time unit)

which I expected you to accept without too much hesitation...Ill return to terminology questions later.

 

I think we should improve on the thought experiment so we are assured we contemplate the same experiment!

Instead of imagining a hawkeyed observer able to actually see the arrow on the rotating clock we alter the clock:

It has no visible arrow now, instead it sends a continuous report to something, some advanced computer? ,

able to produce an image of what the clock should tell us if we could observe it directly,

on a screen conveniently placed in front of the observer sitting at the table.

 

Lets do the same for the other clock so theres on the screen pictures of both the clockfaces...and by all means let there also be a superimposed picture so any differences between the speed of the arrows is easily spotted...and let the computer be able to represent the information from the clocks as two parallell arrows growing in the tempo of each clock... or any other interesting and convenient way of presenting the recieved information from the clocks.

 

Maybe we should arrange things on the table so the computer is eggzactly at the midpoint of the segment c1 to c2 in the space of clocks where c1 is stationary and c2 is spinning...but perhaps relativistic effects in transmission of information from the clocks to the computer and into the mind of the observer can be left out of the picture... dont you agree?

 

While we are at it, let the orientation of the rotation axis of the centrifuge be adjustable and let it be perpendicular to the Earth axis at the beginning of the experiment... I think Im done for the moment ...do you have any further suggestions?

 

The question of WHERE the laboratory is...weighs heavily on my my mind...how can one tell? From inside it? Can any "outside" of the lab be demonstrated to exist? Suppose all memory of what has been going on before the experiment is hidden and the talk of the rotation axis of the Earth is sort of left out of the observers understanding... Theres perhaps two knobs to twist if he feels like it? And an unfriendly lab technician able to introduce and improve on any new centrifuges, clocks and computers wherever they are wanted by the observer.

(except, of course, anywhere in the outside)

[Moontanman]

I'm not sure what you mean sigurdV by missing minute, there is no missing minute, both frames of reference are equally valid. I think what Rade said here is important to this understanding.

 

1. Time is not a parameter that can be measured, time is what measures simultaneous events. Time is not MEASURED by a clock, time is what a clock MEASURES, fundamental difference.

 

 

But I think i would have said it a little differently, "Time is not defined by a Clock, time is what a Clock measures"

 

I remember a science fiction book i read once that tried to deal with this by having telepathic twins, one on board a space ship traveling at a high fraction of c and the other on the Earth, they used the twins as radios and assumed that telepathy was instantaneous, it was an interesting take on the problem but I didn't like that they assumed the twins could communicate with no time dilation at all... while at the same time assumed they would experience time dilation in their lives... it was not an elegant solution to the problem...

[sigurdV]

 

OK, the rotating clock has 59/60 = 0.983 factor and stationary clock factor of 1.000, so we say the time is SHORTER for the rotating clock because ratio is smaller due to the motion being FASTER, relative to stationary clock

 

But, why would we have any reason to think the personal time of the observer, sitting next to table and watching experiment for 60 minutes would accordingly be dilated, or dilated at all as the two clocks are, unless the person was spinning slower or faster than the "outside" entity ? You never said in your OP that the observer was in motion relative to something "outside" the experiment. So, I suggest this claim is based on a false premise and thus the rest of your presentation cannot hold true. But, perhaps I did not understand your explanation assumptions.

Im slowly (With pleasure!) reading your comments. It will take me some time to read and think everything through you have said so far. The expression "59/60" to me is the dilation factor of the 59 with respect to the 60. Meaning that 60 times 59/60 gives 59, which is the length of the segment of spacetime, neasured in minutes, that is what we picture time in the centrifuge as being made of.

 

Or ...ahem... it does not fit very well with how time appears to me personally. In the picture of time given in the theory of Relativity time is a dimension similar to the three other dimensions but unsimilar enough to get some special treatment,say: dxsquared + dysquared + dzsquared - csquared times dtsquared. I refuse to delve into the subtilities of the (in fact:correct) math formulas of the Theory of Relativity! It surely is not my qualities that are under observation, its my experiment! And I will not even TRY to put my words into the frames of the theory...I will use my own words because they are familiar to me and I KNOW what they are supposed to mean...you translate them if you want and Ill check the result for errors if you like (and if Im able).

 

I was talking about comparing conceptual frames...Is that understandable?

Are you aware of conceptual frames or do I have to prove that they exist? (I can.)

Simply put: you need to understand what my words mean: WHEN INTERPRETED AS INTENDED BY sigurdV!

Dont tell me what they mean in the frame of,say, jiddish!

 

I agree to treat time as a length with end points t1 and t2

and in the experiment two different time segments has been identified

and when compared are found to be of different length. (Which is a surprise to some people!)

The difference being one minute.I refer to the difference as a "Missing Minute" and all Hell breaks loose!

It means I have seen an infected toe and stepped on it intentionally to make the infection noticed...

Metaphorically speaking of course.

 

What I want (besides going through with the experiment to its completion)

is to understand HOW the mechanism shortening the time segment actually works!

What made it shorter? Is it compressed or is it cut? Do you KNOW?

 

Depending on the answer (Given that the answer is NOT simply: "There is no missing minute."

...My words did NOT mean that I myself believe there really exists a "missing minute",

hidden away somewhere,the words were intended to evoke an explanation.) there may be more questions.

 

Enough said about that for now...lets return to the lab. Youre bringing up the matter of personal time...good!

But I dont recall MEANING that the observators personal time is dilated with respect to the lab or its outside...he is just sitting at the table and his dilation factor with respect to the lab should be one. But why not invent his twin sitting in the centrifuge? Equipped with a (mysteriously designed) anti-gravity belt preventing him from experiencing the crushing conditions within the centrifuge? Having a wristwatch showing laboratory time? Or is that too contrafactual to consider?

 

And as last point... In the OP I never said anything about the outside of the lab... so its an open question...but I cant help wondering if it is in some cases possible to detect the existence of an outside by the effects of the outside on objects in the lab... so I include that question among the questions concerning the experiment.

Is the gravity making the observer resting comfortably in his chair a proof of an outside effect? Cant a floor being made of very much denser materials than the rest of the lab account for the effect?

[sigurdV]

I'm not sure what you mean sigurdV by missing minute, there is no missing minute, both frames of reference are equally valid. I think what Rade said here is important to this understanding.

 

But I think i would have said it a little differently, "Time is not defined by a Clock, time is what a Clock measures"

 

I remember a science fiction book i read once that tried to deal with this by having telepathic twins, one on board a space ship traveling at a high fraction of c and the other on the Earth, they used the twins as radios and assumed that telepathy was instantaneous, it was an interesting take on the problem but I didn't like that they assumed the twins could communicate with no time dilation at all... while at the same time assumed they would experience time dilation in their lives... it was not an elegant solution to the problem...

Hi Moontanman and welcome!

 

At the moment the problem of the "Missing Minute" as I call it. gets most of the attention...

There IS more to my thought experiment than that,I think.

But putting that aside: Knowing theory and the radius and speed of the centrifuge

it is possible to calculate the dilation factor (among other things) and that is marvelous!

 

But it does not answer my question!

I want to know WHY the dilation factor becomes whetever it becomes!

How does speed manage to shorten time?

What is the actual mechanism the speed "sets in motion"?

 

Is the mechanism described in the theory of Relativity?

Or must one look somewhere else for it?

Perhaps in Thermodynamics?

Or Quantum Mechanics?

 

"Compression" of distance seems a possibility

I would investigate if being forced for an explanation,

but why doesnt that make also minutes shorter

so theres still sixty of them?

[JMJones0424]

I want to know WHY the dilation factor becomes whetever it becomes!

How does speed manage to shorten time?

What is the actual mechanism the speed "sets in motion"?

 

Is the mechanism described in the theory of Relativity?

Or must one look somewhere else for it?

Perhaps in Thermodynamics?

Or Quantum Mechanics?

 

I'd suggest starting your quest for an answer in one of the first threads you started here almost two years ago, Age and Relativity.