B Time dilation and 2 identical clocks

[Ross Arden]

Hi

Couldnt figure this out

U have 2 identical clocks where a pulse of light goes from a light source (a), reflects off a mirror (b) and goes to the end (c)

A person is stationary wrt one clock and another clock is in a spaceship moving, relative to the observer, in the direction v at velocity v

The clock in the spaceship is shown at time t1, t2 and t3

Theory says the observer should see the clock in the spaceship ticking slower than the clock at rest wrt the observer.

If the height of the clock is H and its length is L the observer will deduce the clock in the spaceship ticks at 2H/c. The observer will deduce the stationary clock will tick at some time greater than 2H/c ...is that right?

 

[Ibix]

You can't make a clock with a pendulum that swings one way and then stops. So that isn't a clock, unless you put a mirror at point c so that the light comes back to point a, in which case more analysis of the return tick is needed.

If you aren't aware of the relativity of simultaneity, you should google that term.

 

[Ross Arden]

its not a pendulum clock!

 

[Ross Arden]

there is no pendulum in an hour glass

 

[Ibix]

its not a pendulum clock!

It's not a clock full stop, unless it has a mirror at c. It doesn't complete a cycle so there's no way to compare any other clock to it without invoking a simultaneity convention.

there is no pendulum in an hour glass

True. But it measures one unit of time at a point (the neck of the glass). If you want to measure any more than that you need to turn it over, then turn it over, then turn it over. And there you have your cyclic motion.

Your design does not measure time at a point because a and c are not co-located. So it doesn't work as a sand timer since it mixes up space and time, and interpreting its results depends on your simultaneity convention (did you google the relativity of simultaneity?). And it doesn't work as a regular clock because it doesn't cycle.

 

[Sorcerer]

Ibix, what you're saying is that it only works as a clock if the start of the cycle ends at the same location in space with respect to the person using it to measure time, correct?

 

[PeroK]

Hi

Couldnt figure this out

U have 2 identical clocks where a pulse of light goes from a light source (a), reflects off a mirror (b) and goes to the end (c)

A person is stationary wrt one clock and another clock is in a spaceship moving, relative to the observer, in the direction v at velocity v

The clock in the spaceship is shown at time t1, t2 and t3

Theory says the observer should see the clock in the spaceship ticking slower than the clock at rest wrt the observer.

If the height of the clock is H and its length is L the observer will deduce the clock in the spaceship ticks at 2H/c. The observer will deduce the stationary clock will tick at some time greater than 2H/c ...is that right?

Ah, I see what you have done. The light clock is supposed to fire light vertically upwards and be reflected vertically back down. This is what happens when the clock is at rest with respect to an observer. The distance traveled by the light is $2H$; hence the time for an up and down light trip is $2H/c$.

But, if the light clock is moving with respect to an observer, then the light will travel in a triangle, hence further. And, since the speed of light is invariant, this will take longer and the observer will conclude that the moving light clock is running slow.

But, to an observer moving with the light clock, the light will be going up and down vertically and the clock will be running normally.

 

[Ibix]

Ibix, what you're saying is that it only works as a clock if the start of the cycle ends at the same location in space with respect to the person using it to measure time, correct?

Yes - that's a clearer way to phrase it. So you can just about get away with calling a sand timer a clock because you can talk about the proper time between the events of the sand starting to slide through the neck of the glass and finishing sliding through. You can also talk about the proper time between the events "light leaves a" and "light arrives at c", but this doesn't correspond to the proper time of anyone at rest with respect to the device.

So I suppose one could argue that it's a clock (in the narrow sense of a one-shot sand timer) for a very specific observer, one who happens to be passing a at the time the light is emitted and happens to be passing c at the time the light is received. And time dilation will work out as usual if this frame is used as the rest frame. But that's a bit odd - that isn't the rest frame of the device.

On balance, I stand by "that is not a clock". A lot of highly specific caveats must apply to regard it as a clock.

 

[Sorcerer]

As suspected. Then, correct me if I'm wrong, it makes no sense to talk about measuring time unless you are either next to both the clock and the event or have some means of synchronization with the clock that is next to the event. In other words the interval of space through which the event transpires should be zero as you measure the time (unless there is some method of synchronization).

Nor does it make any sense to talk about a length unless the interval of time through which the object moves is zero as you measure the length (unless you again have some method of synchronization).

Yes? No? In the ball park?

 

[Herman Trivilino]

As suspected. Then, correct me if I'm wrong, it makes no sense to talk about measuring time unless you are either next to both the clock and the event or have some means of synchronization with the clock that is next to the event. In other words the interval of space through which the event transpires should be zero as you measure the time (unless there is some method of synchronization).

If two events occur at the same location then the time that elapses between them is called a proper time. To an observer moving relative to these two events they will of course not occur in the same place. He can measure the time that elapses between them, but he will need two clocks, one at the location of the first event and one at the location of the second event. If he synchronizes them (this is where the convention that @Ibix mentioned comes in) then he will indeed be able to measure the time that elapses between them, and he will find that elapsed time to be larger than the proper time. This is what's called time dilation.

The twist is that to an observer present at both events those two clocks that the moving observer uses will not be properly synchronized.

 

[Ross Arden]

It's not a clock full stop, unless it has a mirror at c. It doesn't complete a cycle so there's no way to compare any other clock to it without invoking a simultaneity convention.
True. But it measures one unit of time at a point (the neck of the glass). If you want to measure any more than that you need to turn it over, then turn it over, then turn it over. And there you have your cyclic motion.

Your design does not measure time at a point because a and c are not co-located. So it doesn't work as a sand timer since it mixes up space and time, and interpreting its results depends on your simultaneity convention (did you google the relativity of simultaneity?). And it doesn't work as a regular clock because it doesn't cycle.

the purpose of a clock is to measure time whether that be eternity or cooking an egg ... in the scenario I depicted the egg timer in the spaceship would time the cookig of the egg faster than the egg time external to the space ship...is that right?

 

[Ross Arden]

there are many natural, and probably unnatural, phenomena that can be used to measure time, ie the rotation of a neutron star, atomic phenomena, but do not have a feed back loop such as a pendulum. Where it is cast in stone that a device used to measure time must have a "feed back" mechanism such as a pendulum?

another one would be the half life of radioactive materials, time measurement with no feed back mechanism

In the scenario I depicted even if there was only one tick of the clock, say the guy doing the experiment was testing the clock to see if it worked. Even after only a single "tick" of the clock they would have to conclude the clock in the spaceship was going to run fast

 

[Ibix]

the purpose of a clock is to measure time whether that be eternity or cooking an egg ... in the scenario I depicted the egg timer in the spaceship would time the cookig of the egg faster than the egg time external to the space ship...is that right?

You can't use the setup described in your OP to time an egg. Let’s assume the pan is at the "start" end of your tube. You send out the light pulse and start cooking your egg. But when do you stop? It can't be when the light reaches the far end of the tube because you can't know when that happens. You must either have a real clock to tell you when you predict that the light pulse has reached the other end, or you must use a telescope to watch the far end and turn off the pan when you see the light arrive. In the first case your v-tube is not acting as a clock. In the second case you need to factor in the light travel time between "light arrives at end of tube" and "you see it arrive". In either case you will find normal time dilation applies.

there are many natural, and probably unnatural, phenomena that can be used to measure time

But all of these work at a single point and can be used as a clock at that point. Yours doesn’t, unless you add a telescope or some other kind of return leg, so you can't use it as a clock (at least, not in its rest frame) because you can't tell when the end of a tick happens.

 

[Ross Arden]

put the pan at the detector end of the tube. An egg timer is placed at the light source. Each time a grain of sand falls thru the egg time a light pulse is triggered. The egg timer has 500 grains of sand. A counter is placed at the pan. when the counter gets to 500 the heat is tuned off. the egg timer is oriented with the direction of movement of the space ship

If the experiment is conducted million of times the counter in the spaceship will turn off consistently quicker than the one external to the space ship

 

[Ibix]

put the pan at the detector end of the tube. An egg timer is placed at the light source. Each time a grain of sand falls thru the egg time a light pulse is triggered. The egg timer has 500 grains of sand. A counter is placed at the pan. when the counter gets to 500 the heat is tuned off. the egg timer is oriented with the direction of movement of the space ship

So you turn on the heat when you get the flash corresponding to "first grain falls" and turn it off when you get the flash corresponding to "last grain falls"? This is basically watching a standard egg-timer through a telescope. The egg-timer is the only clock in this setup.

 

[Ross Arden]

the counter located in the spaceship turns off/on the heat. As the timer in the spaceship turns off the heat early the egg in the spaceship is not fully cooked , where as the egg external to the spaceship is

l

 

[Ross Arden]

the set up external to the spaceship is identical to the setup internal to the spaceship

 

[Ibix]

I think you need to explain clearly where you have egg timers and where you have pans, and which ones are moving with the rocket and which ones are moving with the stick man.

 

[Ross Arden]

see pic

 

[Ross Arden]

the setup next to the stick man is identical, minus the rocket of course

 

[Ibix]

According to your illustration you have an egg timer, which sends light pulses down a tube to a cooker which remains on as long as pulses continue to arrive.

There is no clock here except for the egg timer.

Ditto the setup outside. Both eggs will cook; both observers will claim the other one cooked slower.

 

[Ibix]

I invite you to do the full Lorentz transforms if you think otherwise.

 

[Ross Arden]

the egg timer send pulses, the pulses are counted, the cooker starts at the first pulse and turns off at the 500th pulse on the counter. So the cooker in the spaceship starts before the cooker stationary wrt to the stick man. And, the cooker in the spaceship turns off before the cooker stationary wrt to the stick man.

 

[Ross Arden]

first you would need to prove that a LT was the appropriate analysis of this system, as there is no feed back

 

[Ibix]

first you would need to prove that a LT was the appropriate analysis of this system, as there is no feed back

Are you seriously suggesting that this experiment isn't consistent with special relativity? If so, please read the rules on personal theories. If not, you don't seem to be following my verbal explanations of where you are going wrong, so the only thing I can do is suggest that you do the maths. Happy to help if you are having problems with it.

the egg timer send pulses, the pulses are counted, the cooker starts at the first pulse and turns off at the 500th pulse on the counter. So the cooker in the spaceship starts before the cooker stationary wrt to the stick man. And, the cooker in the spaceship turns off before the cooker stationary wrt to the stick man.

You need to use the Lorentz transforms to analyse this correctly.

 

[Nugatory]

first you would need to prove that a LT was the appropriate analysis of this system, as there is no feed back

I'm not understanding this comment. The Lorentz transformation is, by definition, the way get from the statement "Event E happened at position $x$ and time $t$ in one frame" to "Event E happened at position $x'$ and time $t'$ in this other frame". There's no feedback assumed or implied.

 

[Ibix]

Actually, you don't need the full Lorentz transforms. You simply observe that, in the rocket frame, the timer starts at t'=0 and finishes at t'=500, so the egg starts cooking at t'=T and finishes at t'=500+T, where $T=2\sqrt{L^2/4+H^2}/c$ in terms of the sizes given in #1. It's immediately obvious that if the normal time dilation formula applies to the timer's duration, the same scale factor applies to the cooking. You could, after all, add another egg timer beside the pan and start it when the cooker turns on. It'll run out just as the cooker turns off.

So either the standard time dilation formula does not work for any clock or it shows that the egg cooks exactly as I have been saying - both see the other's egg cooking slower.

 

[Ross Arden]

Are you seriously suggesting that this experiment isn't consistent with special relativity? If so, please read the rules on personal theories. If not, you don't seem to be following my verbal explanations of where you are going wrong, so the only thing I can do is suggest that you do the maths. Happy to help if you are having problems with it.
You need to use the Lorentz transforms to analyse this correctly.

I don't know how to do an LT

 

[Ross Arden]

the other interesting aspect of this is if the direction of the rocket is reversed the egg cooks slower!

 

[Ross Arden]

time dilation wrt the egg timer - as mentioned the egg timer is aligned with the direction of the rocket

also I have no allowed for length contraction of the egg timer

 

[Ross Arden]

an exploded view of the egg timer and its orientation wrt the rocket

 

[Herman Trivilino]

there are many natural, and probably unnatural, phenomena that can be used to measure time, ie the rotation of a neutron star, atomic phenomena, but do not have a feed back loop such as a pendulum. Where it is cast in stone that a device used to measure time must have a "feed back" mechanism such as a pendulum?

All clocks measure the time that elapses between two events, and the clock must be present at each event, so the two events have to occur at the same place. Failing to take this into consideration results in confusion over time dilation.

 

[Ross Arden]

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

sorry I misunderstood your post. With an egg timer event 1 is the falling of the first grain and event 2 is the falling of the last grain?

 

[Ross Arden]

a non feed back clock

can you use a very accurate clock to time some non feed back event. For instance use a very accurate clock to time the revolutions of a neutron star and once the revolution timing is accurately known use the neutron star as a very accurate non feed back clock

 

[jartsa]

the other interesting aspect of this is if the direction of the rocket is reversed the egg cooks slower!

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.

 

[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 :-)

 

[Herman Trivilino]

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?

 

[Herman Trivilino]

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.

 

[Herman Trivilino]

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.