Time dilation and 2 identical clocks

[Ross Arden]

So we seem to have this situation:

When the egg cooker's velocity vector points towards the egg timer, the egg cooks faster.
When the egg cooker's velocity vector points away from the egg timer, the egg cooks slower.

But let's not ignore egg timer's velocity vector:

When the egg timer's velocity vector points towards the egg cooker, the egg cooks faster.
When the egg timer's velocity vector points away from the egg cooker, the egg cooks slower.

I always wondered why I had such difficulty cooking uniform boiled eggs, finally a plausible explanation, the velocity of my kitchen thru space :-)

 

[Mister T]

I may be wrong but it appears to me event one is the start of the heat and event 2 is the end of the heat and the egg timer is present at both events ?

all events/timing etc occur at the same place ie inside the rocket and next to the observer

It looks like you've got it right.

So now we have the problem of measuring the elapsed time between events using a clock that is not present at both events, that is, a clock that's moving relative to the rocket ship. Such a clock cannot be present at both events, it can be present at one of them, but then it won't be present at the other. So how will you use such a clock to measure how long it took to cook the egg?

Let's say Clock 1 is moving relative to the ship and is present for the start of the egg-cook. Clock 2 is at rest relative to Clock 1 and is present at the end of the egg-cook. How will you use these two clocks to measure the elapsed time of the egg-cook? You will need to synchronize them, and when you do that you will find that they measure an elapsed time for the egg-cook that is longer than the elapsed time measured by the rocket clock.

But an observer at rest aboard the rocket ship will not agree that Clocks 1 and 2 are properly synchronized. He will observe that the clocks are out of sync, stay out of sync by the same amount during the egg-cook, and that they are running slow. He will therefore attribute the effect mentioned at the end of the previous paragraph to that errant synchronization!

 

[Ross Arden]

the clocks don't need to be synchronised. Any observer can determine which clock ran slow and which ran fast by simply checking which egg is undercooked and which isnt?

 

[Mister T]

the clocks don't need to be synchronised. Any observer can determining which clock ran slow and which ran fast by simply checking which egg is undercooked and which isnt?

In the scenario described in my post there was only one egg cooked. And if it wasn't under-cooked then it wasn't under-cooked, it makes no difference which clocks were used to measure the time that elapsed while it was cooking.

If the clocks weren't synchronized I don't how you would be able to tell, using the readings on Clocks 1 and 2, how much time elapsed while the egg was cooking. (Remember, neither Clock 1 or 2 is at rest relative to the egg, so neither clock alone can be used to measure that elapsed time. If Clock 1 reads $t_A$ as it passes the egg at the beginning of the cooking, and Clock 2 reads $t_B$ as it passes the egg at the end of the cooking, then $t_B - t_A$ means what if the two clocks are not synchronized? It certainly doesn't tell you how much time the egg spent in the cooker.)

 

[Ross Arden]

In the scenario described in my post there was only one egg cooked. And if it wasn't under-cooked then it wasn't under-cooked, it makes no difference which clocks were used to measure the time that elapsed while it was cooking.

If the clocks weren't synchronized I don't how you would be able to tell, using the readings on Clocks 1 and 2, how much time elapsed while the egg was cooking. (Remember, neither Clock 1 or 2 is at rest relative to the egg, so neither clock alone can be used to measure that elapsed time. If Clock 1 reads $t_A$ as it passes the egg at the beginning of the cooking, and Clock 2 reads $t_B$ as it passes the egg at the end of the cooking, then $t_B - t_A$ means what if the two clocks are not synchronized? It certainly doesn't tell you how much time the egg spent in the cooker.)

I have no idea what you are talking about, maybe see the diagrams with the OP. In the OP there are 2 eggs 2 egg timers, 2 counters, 2 light tubes, 2 stoves, 2 identical arrangements. 1 arrangement is in a space ship, one is at rest wrt an single observer. The spaceship is purported to be moving relative to the observer.

 

[Mister T]

I have no idea what you are talking about, maybe see the diagrams with the OP

I saw them. Sorry I'm not making sense to you. Perhaps if you could explain what part or parts of what I said you don't understand we could get somewhere.

 

[Ross Arden]

elapsed time is measured by the egg. If the time is brief the egg is under cooked. if the time is long the egg is over cooked.

I fail to see why anything needs to be synchonised. If one cooking process starts after the other so what, regardless the egg will still be over or under cooked depending on if the pulses in the light tube ran slow,fast or otherwise.

I fail to see why a third clock is required, over an above the 2 egg timers, the counter and the egg.

at each event there is an egg (a clock) and egg timer (also a clock) a light tube (also a clock) and a counter (also a clock) seems to me there are enuf clocks at each event

 

[Pencilvester]

at each event there is an egg (a clock) and egg timer (also a clock) a light tube (also a clock) and a counter (also a clock) seems to me there are enuf clocks at each event

Let’s say Joe has a wristwatch. Every time he sees the second hand on his watch move, Joe takes a bite of a long fruit-by-the-foot candy. Barb is spying on Joe from a mile away using some binoculars, and for every foot of the fruit-by-the-foot that she sees Joe eat, she lights a firecracker. Every time a firecracker blows up a nearby bird gives a squawk. Now, you are free to define anything in any way you want, so you can say that the wristwatch, the length of fruit-by-the-foot, the bag of firecrackers, and the bird’s voice box are all clocks, but you must know that the only clock of any real importance is the wristwatch, as all the other “clocks” in this scenario depend completely on the running of the wristwatch. I think you are really muddying the waters of your thought experiment by calling all of these things clocks.

 

[Ross Arden]

Let’s say Joe has a wristwatch. Every time he sees the second hand on his watch move, Joe takes a bite of a long fruit-by-the-foot candy. Barb is spying on Joe from a mile away using some binoculars, and for every foot of the fruit-by-the-foot that she sees Joe eat, she lights a firecracker. Every time a firecracker blows up a nearby bird gives a squawk. Now, you are free to define anything in any way you want, so you can say that the wristwatch, the length of fruit-by-the-foot, the bag of firecrackers, and the bird’s voice box are all clocks, but you must know that the only clock of any real importance is the wristwatch, as all the other “clocks” in this scenario depend completely on the running of the wristwatch. I think you are really muddying the waters of your thought experiment by calling all of these things clocks.

Hi

In the OP I had an egg timer, each time a grain fell thru the egg timer a flash of light would be released into the light tube. Each egg timer had only 500 grains.

In the OP the egg timer is analogous to the wristwatch?

Which is why I found the last few posts puzzling as they were talking about the third watch to measure time elapsed. But and egg timer traditionally has an elapsed time of 3 minutes, so there is no need to measure elapsed time. Or alternatively the amount of cooking the egg experiences measures the elapsed time.

 

[Pencilvester]

In the OP the egg timer is analogous to the wristwatch?

Yes.

Which is why I found the last few posts puzzling as they were talking about the third watch to measure time.

If I’m following the thread so far, I believe a clock in motion relative to the egg and egg timer was introduced in order to make the 2 events you specified earlier to be in the same location in space relative to this single new clock.

 

[Pencilvester]

If I’m following the thread so far, I believe a clock in motion relative to the egg and egg timer was introduced in order to make the 2 events you specified earlier to be in the same location in space relative to this single new clock.

Ok, never mind that, I wasn’t following closely enough. To which “third clock” are you referring?

 

[Ross Arden]

Ok, never mind that, I wasn’t following closely enough. To which “third clock” are you referring?

Im not referring to a third clock, some other dude who posted introduced a third clock.

 

[PeroK]

Hi

In the OP I had an egg timer, each time a grain fell thru the egg timer a flash of light would be released into the light tube. Each egg timer had only 500 grains.

In the OP the egg timer is analogous to the wristwatch?

Which is why I found the last few posts puzzling as they were talking about the third watch to measure time elapsed. But and egg timer traditionally has an elapsed time of 3 minutes, so there is no need to measure elapsed time. Or alternatively the amount of cooking the egg experiences measures the elapsed time.

I must confess that I don't have any idea what you are trying to say with this experiment. Perhaps you need to rewind and think about reference frames, clocks and time another way.

If your objective is to learn SR, then your thought experiment probably isn't helping you do that.

 

[Ross Arden]

I must confess that I don't have any idea what you are trying to say with this experiment. Perhaps you need to rewind and think about reference frames, clocks and time another way.

If your objective is to learn SR, then your thought experiment probably isn't helping you do that.

to restate my original post - the theorey is a clock inside a MFR should appears to tick slower if observed by an observer external to that MFR who is moving relative to the first mentioned MFR. My query is the timer inside the moving frame of reference will appear to be ticking FASTER , not slower, according to the external observer...It appears I have made a mistake but I don't know where

 

[Ibix]

Your mistake is that you keep trying to treat the v shaped pipe as if it were a clock, rather than a glorified version of the binoculars Pencilvester mentioned in #43.

You might like to add a picture of the egg starting to cook and finishing cooking, and the egg timer starting and finishing to your original diagram. You will need four different images.

 

[PeroK]

to restate my original post - the theorey is a clock inside a MFR should appears to tick slower if observed by an observer external to that MFR who is moving relative to the first mentioned MFR. My query is the timer inside the moving frame of reference will appear to be ticking FASTER , not slower, according to the external observer...It appears I have made a mistake but I don't know where

If your clock is an egg-timer, then the postulates of SR don't provide the rules to study this from first principles. The second postulate of SR states that the speed of light is invariant (the same in all inertial reference frames). As speed = diistance/time you can study the nature of time and space using the paths of light rays.

"Appears" may be a dangerous word, since the finiteness of the speed of light can delay the observation of measurements. And, the delay in receiving signals has nothing to do with SR or time dilation. It's the measurement of time that is required, which may be more than the observation of a moving clock.

 

[PeroK]

@Ross Arden For example. Suppose a clock is moving towards you at a speed of $\frac35 c$. In your reference frame that clock runs slow by a factor of $\frac45$. Suppose it reads $t' =0$ when it is $1$ light-second away from you - and emits a light signal at this point. This is all in your reference frame, by the way.

By the time you receive that signal, the clock has moved $\frac35$ of a light-second and is only $\frac25$ of a light-second away. And, due to time dilation, it reads only $t'=\frac45 s$ at this point. Assume it emits a second signal at this point.

That second signal will reach you only $\frac25 s$ after the first.

So, what you "observe" is:

At some time $t$ in your reference frame you observed the moving clock to read $0s$. At some time $t + \frac25 s$ you observed the clock to read $\frac45 s$. These raw observations appear to show the clock running fast.

Note that without time dilation (i.e. in classical physics) it would appear to run even faster.

But, these raw observations do not constitute a measurement of time. To get a measurement, you need (both in classical physics and SR) to take into account the travel time of light. Once you do that you get that the clock is running slow.

Note that this post doesn't explain time dilation itself (it assumes it), but it does show that you need to distinguish between raw observations and measurements of elapsed time between events. And that's why having local measurements and checking simultaneity is important in these thought experiments.

 

[Mister T]

I fail to see why a third clock is required, over an above the 2 egg timers, the counter and the egg.

Let's focus on one egg. If you have more than one egg ignore the others for now. Let's say that one timer is aboard the moving rocket ship with the egg and the other timer is at rest. Explain for us how the timer that's at rest can be used to time the cooking of the egg. If that timer is present when the egg starts to cook, it can't be present when the egg is finished cooking because the rocket will have separated it from the egg. You will need some kind of signalling device that will pass signals from the distant ship to the timer that's at rest.

 

[Dale]

elapsed time is measured by the egg. If the time is brief the egg is under cooked. if the time is long the egg is over cooked.

This is called the egg’s proper time. Here the word proper is in the sense of property, it is the eggs own time. The over/under cooking depends on the eggs proper time.

The other type of time is called coordinate time. This time requires some synchronization convention, and once you have chosen that synchronization convention then you can compare the time of distant events. This time does not belong to an object, but to a reference frame.

Is that clear? If so, then your main question appears to be “which clocks best measure the egg’s proper time”. Do I understand you right?

 

[Ross Arden]

Let's focus on one egg. If you have more than one egg ignore the others for now. Let's say that one timer is aboard the moving rocket ship with the egg and the other timer is at rest. Explain for us how the timer that's at rest can be used to time the cooking of the egg. If that timer is present when the egg starts to cook, it can't be present when the egg is finished cooking because the rocket will have separated it from the egg. You will need some kind of signalling device that will pass signals from the distant ship to the timer that's at rest.

sorry I don't understand what u are trying to say. there is 2 eggs, 2 timers, 2 counters, 2 stoves. Egg timer 1 counts the cooking of egg 1, Egg timer 2 is for egg 2...see the OP

 

[Ross Arden]

This is called the egg’s proper time. Here the word proper is in the sense of property, it is the eggs own time. The over/under cooking depends on the eggs proper time.

The other type of time is called coordinate time. This time requires some synchronization convention, and once you have chosen that synchronization convention then you can compare the time of distant events. This time does not belong to an object, but to a reference frame.

Is that clear? If so, then your main question appears to be “which clocks best measure the egg’s proper time”. Do I understand you right?

the time is compared by the degree of cooking of the egg, simply compare egg one with egg 2. Nothing need to be synchonised. If egg 1 starts to cook after or before or at the same time as egg 2 it makes no differnece the egg will still be over or under cooked

If u cook and egg for 1 minute and then an hour later u cook a second egg for an hour, and then compare them...u can figure the rest out

 

[Mister T]

Egg timer 1 counts the cooking of egg 1, Egg timer 2 is for egg 2...see the OP

Aren't you also interested in how Timer 1 counts the cooking of Egg 2?

Or how Timer 2 counts the cooking of Egg 1?

 

[Ibix]

the egg will still be over or under cooked

Why do you think so? Each egg's cooking is controlled by an egg-timer at rest with respect to it. When it's finished cooking, it's done (assuming the timer is an accurate indicator of how long you need to cook an egg). If you mean "at the same time as one egg finishes cooking, what is the state of the other egg?", then you need a simultaneity convention (i.e., you need to define "at the same time"), which is to say, you need to work out how you are synchronising clocks.

 

[Ross Arden]

Aren't you also interested in how Timer 1 counts the cooking of Egg 2?

Or how Timer 2 counts the cooking of Egg 1?

Im just interested in comparing how under,over, the saem the eggs are cooked timer 1 times egg 1 timer 2 times egg 2...so in short no

 

[Ross Arden]

Why do you think so? Each egg's cooking is controlled by an egg-timer at rest with respect to it. When it's finished cooking, it's done (assuming the timer is an accurate indicator of how long you need to cook an egg). If you mean "at the same time as one egg finishes cooking, what is the state of the other egg?", then you need a simultaneity convention (i.e., you need to define "at the same time"), which is to say, you need to work out how you are synchronising clocks.

If u cook and egg for 1 minute @ 100 degrees C and then 2 hours later u cook a second egg for 50 minutes @ 100 degrees C, in a moving spaceship wrt egg 1, and then compare the eggs...u can figure the rest out ...there is no requirement for synchronsiation...simply compare the eggs...both eggs cooking time is regulated by the egg timer associated with that egg. But if one egg timer is ticking slower than the other one then one egg will be undercooked compared to the other.

How is this a "telescope" scenario when the so called "telescope" is in the space ship? If that is the case isn't Einsteins original thought experiment with a light clock (light at one end, mirror at the other) in a railway carriage also just a "telescope"?

Maybe I am wrong as the heat transfer, to the egg, and heat transfer is a function of time, will be slower in the space ship, as time will be expiring slower in the spaceship so both eggs will be equally cooked ?

But the fact still remains the clock in the spaceship will appear to tick faster, than the external clock, according to the external observer

 

[Ibix]

If u cook and egg for 1 minute and then 2 hours later u cook a second egg for an 50 minutes, and then compare them...u can figure the rest out

But this has nothing to do with any scenario you have presented. I don't understand why you bring it up.

 

[Ross Arden]

Ill start again. See the pic
a = counter
c = light tube
b = egg timer
d is a light that pulses each time a grain falls thru the egg timer
L2 is the length of the light tube
L1 is the length of the egg timer
there are 2 identical arrangements, one in a space ship, one at rest wrt an observer external to the space. The spaceship is moving relative to arrangement 2 at v in the direction of v ...any questions ?

 

[Ross Arden]

the pic, the oval is an egg and the small red line under the egg is a heat source

 

[Ibix]

Your diagram doesn't appear to show length contraction of the apparatus in the moving ship. Assuming you understand that it should be length contracted, or that you've deliberately ignored length contraction for some reason, fine.

 

[Ross Arden]

Your diagram doesn't appear to show length contraction of the apparatus in the moving ship. Assuming you understand that it should be length contracted, or that you've deliberately ignored length contraction for some reason, fine.

I have ignored length contraction

 

[Ibix]

I have ignored length contraction

That may come back to bite, depending on where you're going with this, but fine for now. Go on.

 

[Ross Arden]

so won't the external observer perceive the egg timer in the spaceship to be running faster than the egg timer at rest wrt the observer ?

 

[Vanadium 50]

Ross, can you please use proper English and not text speak? People are already struggling to figure out what you mean; please don't make it any harder.

 

[Ross Arden]

BTW as there is no gravity the egg timer works of pressurized air. So if there is length contraction, as there will be less volume, the egg timer in the spaceship will have a higher pressure than the at rest one

 

[Ross Arden]

Ross, can you please use proper English and not text speak? People are already struggling to figure out what you mean; please don't make it any harder.

okay