Einstein notion of time and the oscillation of the cesium atom

[azoulay]

I just read the thread entitled: "How did Einstein Define Time" and I'm very confused.

At school, I was taught that time was an abstract representation of movement meaning that the word "time" can only be used to represent movements.
For example, when Earth has completed a cycle around the Sun, that is called "one year". So in this example we see that the "one year" (concept of time) represents a movement (the cycle of Earth going around the Sun).
So the definition of time for me has always been that it's an abstract representation of some movement and nothing else.

Now, in the Hafele–Keating experiment where Cesium atomic clocks where used to test Einstein's theory of relativity, they state that the clocks going eastward in the airplane jets "lost time" and the clocks going westward "gain time". These conclusions (of clocks gaining and losing time) can only be considered in regards to a specific definition of the notion of time which I think Einstein has lacked to provide. One thing is for sure, considering the definition of time that was taught to me, it is absurd to think that a clock can gain or lose time, it just makes no sense at all.

What does makes sense tough is that while the air plane jets goes eastward, the speed of the cesium atoms oscillations slows down and when the air plane jets goes westward, the speed of the cesium atoms oscillations increases. But that's it ! Nothing else can be said about that experiment. The jet planes moving eastward or westward has absolutely NO direct effect on the clock, they only affect the speed of oscillation of the cesium atoms and it is that speed of oscillation of the cesium atoms that's speeding or slowing the clock ! So the "time" shown on the clock is totally dependant on the speed of oscillation of the cesium atom.

For Einstein to say that the clocks are "losing or gaining time" relative to those clocks traveling at some speed is to make a direct relationship between "time" and the speed of the oscillation of the cesium atoms. So why bother confusing people using the word "time" instead of simply saying things as they are: "it is the speed of oscillation of the cesium atom that is relative" ?

Time is NOT relative to anything unless your definition of time is : "the speed of oscillation of the cesium atom" !

I think that Einstein biggest problem was to talk about time without ever giving a specific definition of what he considered time to be. He gave the definition of: "time of an event" but that's different from the notion of "time" alone by itself.

Does my above explanations makes sense to anyone ?

regards,
jonathan

 

[QuantumPion]

I just read the thread entitled: "How did Einstein Define Time" and I'm very confused.

At school, I was taught that time was an abstract representation of movement meaning that the word "time" can only be used to represent movements.
For example, when Earth has completed a cycle around the Sun, that is called "one year". So in this example we see that the "one year" (concept of time) represents a movement (the cycle of Earth going around the Sun).
So the definition of time for me has always been that it's an abstract representation of some movement and nothing else.

Now, in the Hafele–Keating experiment where Cesium atomic clocks where used to test Einstein's theory of relativity, they state that the clocks going eastward in the airplane jets "lost time" and the clocks going westward "gain time". These conclusions (of clocks gaining and losing time) can only be considered in regards to a specific definition of the notion of time which I think Einstein has lacked to provide. One thing is for sure, considering the definition of time that was taught to me, it is absurd to think that a clock can gain or lose time, it just makes no sense at all.

What does makes sense tough is that while the air plane jets goes eastward, the speed of the cesium atoms oscillations slows down and when the air plane jets goes westward, the speed of the cesium atoms oscillations increases. But that's it ! Nothing else can be said about that experiment. The jet planes moving eastward or westward has absolutely NO direct effect on the clock, they only affect the speed of oscillation of the cesium atoms and it is that speed of oscillation of the cesium atoms that's speeding or slowing the clock ! So the "time" shown on the clock is totally dependant on the speed of oscillation of the cesium atom.

For Einstein to say that the clocks are "losing or gaining time" relative to those clocks traveling at some speed is to make a direct relationship between "time" and the speed of the oscillation of the cesium atoms. So why bother confusing people using the word "time" instead of simply saying things as they are: "it is the speed of oscillation of the cesium atom that is relative" ?

Time is NOT relative to anything unless your definition of time is : "the speed of oscillation of the cesium atom" !

I think that Einstein biggest problem was to talk about time without ever giving a specific definition of what he considered time to be. He gave the definition of: "time of an event" but that's different from the notion of "time" alone by itself.

Does my above explanations makes sense to anyone ?

regards,
jonathan

The second is defined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom". This is in the reference frame of the cesium atom. If you took two cesium atoms, one on a flying jet and the other on the ground, by the time the atom on the ground produced 9,192,631,770 periods of radiation the one on the jet will have produced say 9,192,631,769 periods of radiation. This is because the atom on the jet experienced less time compared to the atom on the ground.

 

[VantagePoint72]

I think that Einstein biggest problem was to talk about time without ever giving a specific definition of what he considered time to be. He gave the definition of: "time of an event" but that's different from the notion of "time" alone by itself.

There is indeed a difference between time as something that locates an event in space-time ("coordinate time") and time as something measured by clocks ("proper time"). Einstein understood—as do all physicists who are now acquainted with relativity—the difference, specifically that only the latter is physically significant, and was very clear on this point.

What does makes sense tough is that while the air plane jets goes eastward, the speed of the cesium atoms oscillations slows down and when the air plane jets goes westward, the speed of the cesium atoms oscillations increases.

That is not what happens. According to either reference frame, time is running slowly in the other frame. This is possible precisely because of the difference between coordinate and proper time. However, when all the clocks are brought back together for comparison, it is found that different amounts of proper time elapsed for each.

Time is NOT relative to anything unless your definition of time is : "the speed of oscillation of the cesium atom

It doesn't matter what physical process you define time to elapse by. It is not just the Cesium clocks that disagreed with one another. Any clocks aboard one jet would have disagreed with clocks on the other jet by the same amount, were they precise enough. The pilot who flew eastward aged less than the pilot who flew westward by the same amount as the two clocks disagreed. Note that were also general relativistic effects that had to be taken into account (gravity also causes time dilation) but the overall effect was the same as that predicted by special relativity alone. Time dilation isn't something that just happened to the atomic clocks; it happened to every dynamical process.

Of course, it's always good to bring a critical eye to new concepts since that often brings better understanding; however, I think you have the wrong attitude. You're not going to disprove Einstein—if indeed he is wrong—without many years studying advanced physics. I'm sorry, but it's just not going to happen. I understand that these are challenging ideas because they're so different from every day life. However, these are ideas that have withstood some very critical inquiry by some very smart people for a long time, and you're not going to get anywhere if you decide right off the bat that these ideas are wrong. You just have to accept that you might not always understand things as well as you might like. If you do that, perhaps it will motivate you to work a bit more at it until they do make sense. We all went through it. On the other hand, folding your arms and going, 'Hmph, well Einstein was wrong,' will not lead to understanding.

 

[Dale]

So the definition of time for me has always been that it's an abstract representation of some movement and nothing else.

Now, in the Hafele–Keating experiment where Cesium atomic clocks where used to test Einstein's theory of relativity, they state that the clocks going eastward in the airplane jets "lost time" and the clocks going westward "gain time". These conclusions (of clocks gaining and losing time) can only be considered in regards to a specific definition of the notion of time which I think Einstein has lacked to provide. One thing is for sure, considering the definition of time that was taught to me, it is absurd to think that a clock can gain or lose time, it just makes no sense at all.

Why is it absurd? The definition of time according to you is "an abstract representation of some movement". To the best measurements possible today, any movement that you would care to measure slows down the same amount as the atomic clock. So in what sense is it absurd under your own definition of time?

I think that you are having a visceral reaction to the idea of time slowing down, rather than a reasoned response. It is understandable, I think that every student of relativity has faced that same reaction at some point. It is counterintuitive, but the data supports it very strongly.

 

[Bhumble]

You seem to be ignoring the fact that speed is a function of position (magnitude only) over time. So any change in speed means that there was either a force exerted or something not quite right with perceived time. Einstein defined time as a part of a fourth dimension cT. An observers perception of time varies based on their relative speed to each other.
The interesting thing is how the two clocks observe the other.

 

[azoulay]

... This is because the atom on the jet experienced less time compared to the atom on the ground.

QuantumPion, what is your definition of "time" ? I cannot understand objectively what you're saying when you mention that the atom on the jet experienced "less time" (I understand where you want to bring me with this explanation but it still makes no sense to me).

On the other side, I think I've come up with an (probably not doable but interesting) experiment that could maybe prove that “time being relative” is simply a misunderstanding of what is really going on. I hope this doesn’t sound pretentious; I’m open to any suggestion.

Let's assume we’re measuring Earth position (around the Sun) in the precision of a billionth of a meter, let’s say Earth is at position (x1,y1,z1), and at the same moment (in regards to Earth position) we’re taking note of the “time” displayed on the reference atomic cesium clock on Earth. We then ask 2 air plane jets (having on board atomic clocks that’s showing exact same time as the reference one on Earth) to take off (one Eastward the other one Westward) and after, let’s say, 48 hours of flight (Earth position measured to be (x2,y2,z2)) we press on a button that would stop all three clocks (the one on Earth, the one in the plane going Eastward and the one on the plane going Westward) at the exact same moment, what will each clock show?

First of all, QuantumPion would probably argue that this experiment resembles very much the Hafele–Keating experiment. One of the difference being that the clocks in the Hafele–Keating experiment were never stopped but only compared to one another after the experiment.
The reason why I would stop all 3 atomic clocks at exactly the same moment (let’s assume that’s possible) is that I would want to see if the “time” displayed on the 3 atomic clocks are different taking into account that they have been running for THE EXACT SAME AMOUNT OF TIME. I’m putting emphasis on the fact that all 3 clocks ran for THE EXACT SAME AMOUNT OF TIME before they were stopped and no one can argue that. Why? Because the time that has elapsed between Earth position (x1,y1,z1) and position (x2,y2,z2) can only take one unique value. Also, we made sure that when Earth is at position (x1,y1,z1) all 3 clocks showed exact same time and we also made sure that when Earth arrives at position (x2,y2,z2) all 3 clocks are stopped at precisely the same moment. So this necessarily implies that the 3 clocks have all experienced THE EXACT SAME AMOUNT OF TIME.

This experiment resemble so much the Hafele–Keating experiment that I’m 100% confident the results would be the same: the clock going eastward in the airplane jet would seem to have "lost time" and the clock going westward would seem to have "gain time" compared to the reference atomic clock on Earth. But that doesn’t mean time is relative. What the LCD screen of the atomic clock is showing is something very different of why it’s showing what it’s showing.
The argument of QuantumPion, following the Hafele–Keating experiment, is that “the atom on the jet experienced less time compared to the atom on the ground” is now, in my experiment, totally invalid because all Cesium atoms (on Earth, on plane 1 and on plane 2) have experienced THE EXACT SAME AMOUNT OF TIME like I explained above. That being said, what could now possibly explain why 3 clocks don’t display the same “time”? Well it’s so obvious to me at least: the ONLY explanation is that the speed of oscillation of the cesium atom has been perturbed during the flights. During the Eastward flight, the speed of oscillation of the Cesium atoms has decreased and during the Westward flight, it has increased.

This increase or decrease of the speed of oscillation of the Cesium atom makes a difference in what is sent to the LCD screen of the atomic clock. Why? Because the electronic board of the atomic clock is programmed to add a second to the time displayed on the LCD screen only when it counted a precise number of periods of the cesium atom (9,192,631,770). So if the speed of oscillation of the cesium atom slows down, like in the scenario where the air plane flew eastward, it then takes more time for 9,192,631,770 periods to occur resulting in the clock giving the impression of “slowing down” or showing to have “lost time” which is not the case. For the other scenario where the air plane flew westward, the speed of oscillation of the cesium atom increased, it then took less time for 9,192,631,770 periods to occur resulting in the clock giving the impression of “speeding up” or showing to have “gain time” which is also not the case.
In the above explanation, I took into assumption, of course, that the definition of “time” is the one I learned in school in which “time” is only an abstract representation of movements. If you take any other definition of time, all the explanations above make probably no sense. It’s interesting to see that it all comes down to definitions!

One last thing, they say the GPS systems are programmed to take into account the theory of relativity. What I think is really happening is that the GPS system in the satellites compensates for the increase or decrease of the cesium atom oscillations (depending on the direction the satellite is moving), that's it ! These GPS system need to be synchronized with atomic clocks on Earth and since the speed of oscillation of the cesium atom is modified on a satellite moving at high speed, if no correction is made, the GPS system on the satellites would lose their synchronization with atomic clock on Earth. But again, this correction (on the GPS system on the satellites) has nothing to do with some fancy notion that, at high speed, "time" is modified. Time is never modified, the GPS system is only compensating for the cesium atom oscillation that is perturbed by satellites moving at high speed.

I'm opened to all comments or suggestion. If you want to throw at me that all of this is crap, you might as well. I'm a truth seeker and I don't believe in any magical non-sense explanation too many times offered by actual science.

regards,
jonathan azoulay

 

[ghwellsjr]

...we’re taking note of the “time” displayed on the reference atomic cesium clock on Earth.

Which one? The ones at Greenwich tick at a different rate than the ones at Boulder due to the difference in gravity at different altitudes.

One last thing, they say the GPS systems are programmed to take into account the theory of relativity. What I think is really happening is that the GPS system in the satellites compensates for the increase or decrease of the cesium atom oscillations (depending on the direction the satellite is moving), that's it ! These GPS system need to be synchronized with atomic clocks on Earth and since the speed of oscillation of the cesium atom is modified on a satellite moving at high speed, if no correction is made, the GPS system on the satellites would lose their synchronization with atomic clock on Earth. But again, this correction (on the GPS system on the satellites) has nothing to do with some fancy notion that, at high speed, "time" is modified. Time is never modified, the GPS system is only compensating for the cesium atom oscillation that is perturbed by satellites moving at high speed.

The GPS system is set up to keep track of a time that no actual clock ticks at.

You haven't been reading the previous posts carefully. You're dreaming. If you want your ideas to be taken seriously, you will have to decide which clock in the universe is going to be the standard and you're going to have to convince every one else in the world why your choice should be taken seriously.

Simple question: which clock is going to be the standard?

 

[PeterDonis]

after, let’s say, 48 hours of flight (Earth position measured to be (x2,y2,z2)) we press on a button that would stop all three clocks (the one on Earth, the one in the plane going Eastward and the one on the plane going Westward) at the exact same moment

You can't do this if the clocks are spatially separated. More precisely, if the clocks are spatially separated, stopping them "at the same moment" will be frame-dependent; it can only be done with reference to one particular frame.

One of the difference being that the clocks in the Hafele–Keating experiment were never stopped but only compared to one another after the experiment.

Yes, and the whole point of doing that is to take away the frame dependence; the clocks are all at the same spatial location both before and after the experiment, so any difference in the amount of time elapsed on them is an invariant--it's the same in every frame.

The reason why I would stop all 3 atomic clocks at exactly the same moment (let’s assume that’s possible)

Bad assumption; it's not possible. See above.

 

[Fredrik]

You sure used a lot of words to ask what happens if we stop a clock on a plane after 48 hours of flight. It's a good idea to keep things short if you want people to read your posts.

The answer is that it depends on whose 48 hours we're talking about. If we stop the clock after 48 hours has elapsed on the plane, then the answer is obviously that the clock will show that 48 hours has passed, because we simply chose to stop it when it displayed that number.

But if we wait until a clock on the ground shows "48 hours, minus the time it will take a radio signal to reach the plane", and then send a "stop the clock now" message by radio to the plane, then the clock on the plane will stop before it has reached 48 hours.

 

[ghwellsjr]

...In the above explanation, I took into assumption, of course, that the definition of ?time? is the one I learned in school in which ?time? is only an abstract representation of movements. If you take any other definition of time, all the explanations above make probably no sense. It?s interesting to see that it all comes down to definitions!

Yes, it does come down to definitions and your definition is the one that leads to relativity unless you want to limit it to the movement of the atoms in a single atomic clock.

 

[Dale]

In the above explanation, I took into assumption, of course, that the definition of “time” is the one I learned in school in which “time” is only an abstract representation of movements.

Then you are contradicting yourself. The oscillation of a cesium atom is every bit as valid a movement as the motion of the Earth around the sun. If you consider the latter to be an accurate measure of time then why not the former? You need to use some logic, not just your emotional reaction. You cannot logically say that time is an abstract representation of movements and then escape the inevitable conclusion that time slows down for a clock in motion.

 

[azoulay]

I'm indeed not a specialist of Einstein theory. I still wish to understand his definition of "time" and time only. Maybe that would be the basis of my understanding of his theory.

I found this interesting article on the web (A NEW INTERPRETATION OF THE HAFELE-KEATING EXPERIMENT): http://www.shaping.ru/congress/english/spenser1/spencer1.asp


thanks again for all your comments,
jonathan

 

[mrspeedybob]

I would encourage you to read Einstein's original paper on special relativity. There's nothing particularly hard about the definitions, the concepts, the reasoning, or the math. Special relativity is simple and obvious. If you read the paper and still don't get it, it's because you don't want to get it and you are trying very hard not to. I can't help you with that.

http://www.phys.lsu.edu/mog/100/elecmovbodeng.pdf

 

[Bill_K]

At school, I was taught that time was an abstract representation of movement meaning that the word "time" can only be used to represent movements.

In that case, time is a more general concept than you were taught. It has meaning even in situations where no movement is involved.

Example: a muon at rest lives for about 2 microsecs, and then decays into an electron and a pair of neutrinos. A muon does this without the need for a pocket watch!

 

[Dale]

I still wish to understand his definition of "time" and time only.

You should read section 1 of the paper mrspeedybob linked to.

 

[Salman2]

I have a side question to the OP.

In a few replies I read that time is thought to go either faster or slower in the examples given. However, is it not more appropriate to say that time is either a shorter or longer number relative to some entity that is in faster or slower motion ? That is, if some entity has faster relative motion up to limit of speed of light then time is relatively shorter; conversely, if entity has slower relative motion time is relatively longer. For an entity in motion at speed of light such as photon, time reaches the limit of the concept slow, e.g., time stops. Some help with this appreciated.

Edit: To support my suggestion that it is the entity, and not time, that moves slow or fast, we read in his 1905 paper that Einstein said this..."hence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions." Clearly Einstein claims that the entity, the arms of clock, 'must go more slowly'...not that time must go more slowly. Thus, as the clock arm must go more slowly, time must be longer.

 

[Dale]

Azoulay, one thing that might help the conversation is to distinguish coordinate time and proper time. These are two different, but related, concepts. Proper time is essentially the time as measured by some clock, and it is considered to be the "length" of the clocks path through space-time, and it is only defined on that path. Coordinate time is a number that is assigned to an event to describe when the event happened, events with the same time coordinate are simultaneous.

It is an experimental fact that if you set up a coordinate system according to Einstein's convention, then any clock's proper time is slow compared to the coordinate time if that clock is moving in that coordinate system. It is also an experimental fact that if two different clocks take different paths through spacetime between the same pair of events that the amount of proper time they experience may be different.

 

[Dale]

To support my suggestion that it is the entity, and not time, that moves slow or fast, we read in his 1905 paper that Einstein said this..."hence we conclude that a balance-clock 7 at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions." Clearly Einstein claims that the entity, the arms of clock, 'must go more slowly'...not that time must go more slowly. Thus, as the clock arm must go more slowly, time must be longer.

That is Einstein's way of saying that time goes more slowly. Remember his definition of time from section 1. He defined time as the pointing of the hands of a clock, together with a simultaneity convention.

 

[Salman2]

That is Einstein's way of saying that time goes more slowly. Remember his definition of time from section 1. He defined time as the pointing of the hands of a clock, together with a simultaneity convention.

Thank you. Yes, I read that, but Einstein also presented the concept of the time interval related to light path and velocity. By definition, along any path, an interval measurement (such as time) would be long or short, and a velocity measurement, slow or fast. Consider a horse race, and the second place horse is one track length measurement behind winning horse. Do we not say the second horse was slower than the first because it took a longer time to reach the finish line ? I do not see why Einstein would grant 'time' as a concept the same physical status as 'horse' and say that both move slow or fast ? Sorry for being so dense.

 

[Dale]

Thank you. Yes, I read that, but Einstein also presented the concept of the time interval related to light path and velocity.

Of course. It would be hard to have velocity without time.

Do we not say the second horse was slower than the first because it took a longer time to reach the finish line ? I do not see why Einstein would grant 'time' as a concept the same physical status as 'horse' and say that both move slow or fast ?

The words slow and fast do not exclusively refer to velocity. You can have a song with a slow or fast beat, nothing has a higher velocity. You can have slow or fast chemical reactions, but no higher velocity (at least not macroscopically).

Slow and fast refer to rates of change wrt time. It can be the rate of change of position or volume or chemical concentrations.

Time slows down because the rate of change of proper time wrt coordinate time goes down.

 

[ghwellsjr]

I have a side question to the OP.

In a few replies I read that time is thought to go either faster or slower in the examples given. However, is it not more appropriate to say that time is either a shorter or longer number relative to some entity that is in faster or slower motion ? That is, if some entity has faster relative motion up to limit of speed of light then time is relatively shorter; conversely, if entity has slower relative motion time is relatively longer. For an entity in motion at speed of light such as photon, time reaches the limit of the concept slow, e.g., time stops. Some help with this appreciated.

Edit: To support my suggestion that it is the entity, and not time, that moves slow or fast, we read in his 1905 paper that Einstein said this..."hence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions." Clearly Einstein claims that the entity, the arms of clock, 'must go more slowly'...not that time must go more slowly. Thus, as the clock arm must go more slowly, time must be longer.

Is there any entity, according to your suggestion, that we can use to keep track of time?

 

[Salman2]

Time slows down because the rate of change of proper time wrt coordinate time goes down.

But, because the rate of change of proper time wrt coordinate time is SLOWER (e.g., goes down), time is LONGER for the clock that measures proper time wrt the clock that measures coordinate time..correct ?

 

[Nugatory]

But, because the rate of change of proper time wrt coordinate time is SLOWER (e.g., goes down), time is LONGER for the clock that measures proper time wrt the clock that measures coordinate time..correct ?

All clocks, by definition, measure proper time.
There's no such thing as a clock that measures coordinate time (except in the trivial sense that there is always some coordinate system in which the coordinate time between two events is equal to the proper time between them, so the clock measuring proper time will happen to report coordinate time in that coordinate system, for those two events).

 

[Dale]

But, because the rate of change of proper time wrt coordinate time is SLOWER (e.g., goes down), time is LONGER for the clock that measures proper time wrt the clock that measures coordinate time..correct ?

I don't know what you mean by longer. The English doesn't matter, what matters is the math. If τ is the proper time on a clock and t is the coordinate time in an inertial frame where the clock is moving then dτ/dt is less than 1. Call that what you will in English.

 

[Salman2]

Is there any entity, according to your suggestion, that we can use to keep track of time?

Is this a trick question ? I'll assume you are asking about entities internal to humans, and not clocks, etc ? Not sure how humans internally keep track of time. However, there is a gene in some plants called ELF4 that allows the plant to keep track of time based on day length, long periods of daytime vs short periods. For a plant, the amount of time that the sun shines in a 24 hour period is NOT fast or slow, it is long or short duration. The only suggestion I make is that time is not a measure of fast or slow wrt to motion of entities, it is either (1) a measure of long or short, or (2) a measure of many or few, depending on what sense of time is being discussed as relates to motion.

 

[Bhumble]

@OP
It seems intuitive for most people that there is an absolute or god's reference frame in which there is an infinitely fast transfer of information so that the appropriate time for all events can be recorded properly. This is likely because of how we are used to seeing this in our daily lives, as I'll explain below.

Unfortunately that does not seem to be the universe we live in. And there appears to be a limitation on the speed it takes for information to be sent from a source to a destination.

Einstein's theory of special relativity is regarding how an observer views events from some source and how that observation changes depending on the speed at which those events are traveling towards or away from the observer.

It is best to start from the Galileon view of relativity.
e.g. Let's say an observer is standing still and there is someone running away at say 50 miles per hour then he will observe them as running away at 50 miles per hour.
Now if that same observer were running at 20 miles per hour then they would perceive the person running away as traveling 30 miles per hour. Which is just the difference in speed between the two with the observer's reference frame traveling at 20 miles per hour with him so that he perceives himself as staying still.

v_observed = v_runner - v_observer = 50 mph - 20 mph = 30 mph

For a lot of what we observe in our daily lives this seems to work great as a model because the time that it takes for information to travel short distances and at the relatively low speed differences (compared to the speed of light) is practically negligable.

According to Einstein the perceived speed is
It seems intuit for most people that there is an absolute or god's reference frame in which there is an infinitely fast transfer of information so that the appropriate time for all events can be recorded properly.

Unfortunately that is not the universe we live in and there is a limitation on how long it takes for information to be sent from a source and destination.

Einstein's theory of special relativity is regarding how an observer views events and how that observation changes depending on the speed at which those events are traveling towards or away from the observer.

It is best to start from the Galileon view of relativity.
e.g. Let's say an observer is standing still and there is someone running away at say 50 miles per hour then he will observe them as running away at 50 miles per hour.
Now if that same observer were running at 20 miles per hour then they would perceive the person running away as traveling 30 miles per hour. Which is just the difference in speed between the two with the observer's reference frame traveling at 20 miles per hour with him so that he perceives himself as staying still.

v_observed = v_runner - v_observer = 50 mph - 20 mph = 30 mph

For a lot of what we observe in our daily lives this seems to work great as a model because the time that it takes for information to travel short distances and at the relatively low speed differences (compared to the speed of light) is practically negligable.

According to Einstein the perceived speed for the observer and runner is
\begin{align}
v_{observed} &= \frac{v_{runner} - v_{observer}}{1- \frac{v_{runner} * v_{observer}}{c^2}} \approx \frac{50 mph - 30 mph}{1 - \frac{50*20}{67061520^2}} \approx \frac{30}{0.99999999999977764176691477773854} mph \\
&\approx 30.000000000006670746992558151139 mph\end{align} Reinforced with this on a daily basis in seems intuitive that Galileon relativity is correct and in low speed situations it is definitely a reasonable approximation. The problem is that when we either observe events at very long distances or that the speeds observed are not negligable, compared to the speed of light, these errors are compounded and it becomes apparent that Galileon relativity is not correct.

Imagine that same approximation above but at astronomical distances in the order of light years. Approximately 1 light year = 5.87849981 × 10^12 miles. Then even at that relatively low speed you can see notable differences.

You can make the argument that the runner is actually traveling at 50 mph because we stated that, but the theory really boils down to perspective and what we as observers see, which is the entire reason it's called relativity.

It is okay for you to cling to the idea of an absolute reference frame but just realize that you or no other person will ever be able to make observations that way and for the sake of predictability and our actual perception of the universe Einstein's special theory of relativity has consistently been tested and proven with many experiments.

There are a few different ways that you can take this theory. Some of us reconcile better with time dilation than others. I personally like to view it as not so much that time is actually altered but that this is the ability for us to observe given our medium of information transferred from source to destination.

And who knows maybe Einstein's theory doesn't hold true for all matter, but just like Galileo's relativity during his time, it is the best theory we currently have available because it fits well with what we observe experimentally.

 

[ghwellsjr]

All clocks, by definition, measure proper time.
There's no such thing as a clock that measures coordinate time (except in the trivial sense that there is always some coordinate system in which the coordinate time between two events is equal to the proper time between them, so the clock measuring proper time will happen to report coordinate time in that coordinate system, for those two events).

Unless I'm totally misunderstanding what you are saying, it is not true "that there is always some coordinate system in which the coordinate time between two events is equal to the proper time between them". In fact it is only true for events with a time-like spacetime interval between them, correct?

But even for those cases where it is true, isn't it misleading to say that such a clock is measuring coordinate time when you may have to switch to a different coordinate system to apply that measurement?

Wouldn't a better statement to make be:

There's no such thing as a clock that measures coordinate time (except in the trivial sense that a clock that is stationary in some coordinate system can only measure the Proper Time, which is equal to the Coordinate Time, between two events that are colocated with the clock).

 

[ghwellsjr]

I have a side question to the OP.

In a few replies I read that time is thought to go either faster or slower in the examples given. However, is it not more appropriate to say that time is either a shorter or longer number relative to some entity that is in faster or slower motion ? That is, if some entity has faster relative motion up to limit of speed of light then time is relatively shorter; conversely, if entity has slower relative motion time is relatively longer. For an entity in motion at speed of light such as photon, time reaches the limit of the concept slow, e.g., time stops. Some help with this appreciated.

Edit: To support my suggestion that it is the entity, and not time, that moves slow or fast, we read in his 1905 paper that Einstein said this..."hence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions." Clearly Einstein claims that the entity, the arms of clock, 'must go more slowly'...not that time must go more slowly. Thus, as the clock arm must go more slowly, time must be longer.

Is there any entity, according to your suggestion, that we can use to keep track of time?

Is this a trick question ? I'll assume you are asking about entities internal to humans, and not clocks, etc ? Not sure how humans internally keep track of time. However, there is a gene in some plants called ELF4 that allows the plant to keep track of time based on day length, long periods of daytime vs short periods. For a plant, the amount of time that the sun shines in a 24 hour period is NOT fast or slow, it is long or short duration. The only suggestion I make is that time is not a measure of fast or slow wrt to motion of entities, it is either (1) a measure of long or short, or (2) a measure of many or few, depending on what sense of time is being discussed as relates to motion.

No, it's not a trick question. I'm trying to figure out what you mean by "entity". I'm not making any assumptions, especially not about genes in a plant or parts internal to humans.

Einstein would answer my question, yes, a clock is an entity that keeps track of time. But you don't say that. You say, the arms of a clock are an entity, not the clock, and they go around the clock at different speeds, like horses going around a race track at different speeds, but in neither case are they keeping track of time. Your suggestion seems to deny that clocks keep track of time. If that's the case, then I'm wondering what does keep track of time.

 

[WannabeNewton]

Indeed if ##p## is an event, ##C## is the light-cone of ##p##, and ##q\notin \text{int}C##, then there is no time-like world-line that can connect ##p## to ##q## so there is no way to define a proper-time in between those two events.

 

[ghwellsjr]

...Einstein's theory of special relativity is regarding how an observer views events and how that observation changes depending on the speed at which those events are traveling towards or away from the observer.

Events don't have speeds. And an observer's view of events does not change depending on anything.

It is okay for you to cling to the idea of an absolute reference frame but just realize that you or no other person will ever be able to make observations that way and for the sake of predictability and our actual perception of the universe Einstein's special theory of relativity has consistently been tested and proven with many experiments.

Clinging to the idea of an absolute reference frame does not change any observations. It also does not change any predictions (as long as you have a correctly working theory based on an absolute reference frame). That sounds like a modern incarnation of Lorentz's Ether Theory. You should be clearer when making statements like this, as is, they sound confusing.

There are a few different ways that you can take this theory. Some of us reconcile better with time dilation than others. I personally like to view it as not so much that time is actually altered but that this is the ability for us to observe given our medium of information transferred from source to destination.

If you want to take Einstein's special theory of relativity, then you must reconcile with time dilation. It's not an option. And it is more than simply our ability to observe, given our medium. Are you talking about Ether?

And who knows maybe Einstein's theory doesn't hold true for all matter, but just like Galileo's relativity during his time, it is the best theory we currently have available because it fits well with what we observe experimentally.

You sound like you're on shaky ground.

 

[Salman2]

Your suggestion seems to deny that clocks keep track of time. If that's the case, then I'm wondering what does keep track of time.

OK, now I understand. Yes, I agree that all clocks (with or without arms) can keep track of time by recording a number related to the motion of some entity. The number of time makes motion continuous. Time is not fast or slow just as the motion of the second hand on a clock (tick-tick-tick...) is not fast or slow, there are either few or many such ticks between two moments and if few the time is short and if many the time is long.

I do not understand why Einstein would not agree with this explanation, given that in his 1905 paper he said "hence we conclude that a balance-clock at the equator must go more slowly" ?...e.g., he said the clock goes more slowly (it had fewer ticks), he did not say time goes more slowly. Imo, he implies with this statement that because the clock goes more slowly (has fewer ticks) then time is relatively shorter because the motion at the equator is faster.

 

[Dale]

Yes, I agree that all clocks (with or without arms) can keep track of time by recording a number related to the motion of some entity. ... Time is not fast or slow just as the motion of the second hand on a clock (tick-tick-tick...) is not fast or slow, there are either few or many such ticks between two moments and if few the time is short and if many the time is long.

I think you are getting hung up on the english. You seem to be stuck on "long" and "short" rather than "fast" and "slow". The important part is that dτ/dt<1 for a moving clock, do you understand that?

If so, then the rest is semantics. Fast and slow are equally valid English words as long or short, as long as you are clear that you mean the math above.

 

[ghwellsjr]

Your suggestion seems to deny that clocks keep track of time. If that's the case, then I'm wondering what does keep track of time.

OK, now I understand. Yes, I agree that all clocks (with or without arms) can keep track of time by recording a number related to the motion of some entity. The number of time makes motion continuous. Time is not fast or slow just as the motion of the second hand on a clock (tick-tick-tick...) is not fast or slow, there are either few or many such ticks between two moments and if few the time is short and if many the time is long.

I do not understand why Einstein would not agree with this explanation, given that in his 1905 paper he said "hence we conclude that a balance-clock at the equator must go more slowly" ?...e.g., he said the clock goes more slowly (it had fewer ticks), he did not say time goes more slowly. Imo, he implies with this statement that because the clock goes more slowly (has fewer ticks) then time is relatively shorter because the motion at the equator is faster.

It sounds like you're still denying that clocks keep track of time. It sounds like you are saying that clocks can measure the interval between two events and measure shorter or longer time intervals, but you are not willing to say that if two clocks, present at two events but taking different paths between those two events, measure different intervals, then time is different along those two paths.

So let me ask you about the famous Twin Paradox: if two clocks are present at the same place and at the same time and we set the two clocks to display the same time and then we let them move differently following any arbitrary paths and then eventually reunite them (not necessarily at the same starting location) and we see that they now have different readings on them, would you say that the both legitimately tracked time differently or would you say that one or both of the clocks was influenced by their motions (and/or accelerations) and so did not both keep track of time correctly? Ignore any influences due to gravity or consider the scenario to be carried out far removed from any significant source of gravity.

 

[Nugatory]

I do not understand why Einstein would not agree with this explanation, given that in his 1905 paper he said "hence we conclude that a balance-clock at the equator must go more slowly"...

"Go more slowly" would be a natural way for a turn-of-the-last-century physicist to describe the phenomenon, but (as with the notion of relativistic mass, for example) we've learned that it's not always the best and clearest way of describing it. It's unlikely that Einstein himself would have chosen that description twenty years later and after having developed GR.

It's important to remember that Einstein didn't deliver the modern theory of relativity in a single blinding flash of insight in 1905. The 1905 paper marks the point when the key insights of SR were widely published to the scientific community; but the presentation, mathematical framework, and manner of speaking used by Einstein and others to describe these insights evolved through the following decades.

Thus, we have to be careful about reading too much into the precise wording of a single Einstein quote; we should be approaching his writings the way a historian approaches a historical document, not the way a religious fundamentalist approaches scripture. The fact that Einstein (or anyone else) said something in 1905 means only that that was the clearest way he could find of expressing what he was thinking at the time. (And it doesn't help any that we are often reading English translations of Einstein's German, so we are getting what the translator thought he was saying, not what he actually said).

 

[Salman2]

So let me ask you about the famous Twin Paradox: if two clocks are present at the same place and at the same time and we set the two clocks to display the same time and then we let them move differently following any arbitrary paths and then eventually reunite them (not necessarily at the same starting location) and we see that they now have different readings on them, would you say that the both legitimately tracked time differently or would you say that one or both of the clocks was influenced by their motions (and/or accelerations) and so did not both keep track of time correctly? Ignore any influences due to gravity or consider the scenario to be carried out far removed from any significant source of gravity.

Thank you for the question. In this version of the Twin Paradox there are two simultaneous events for each clock, the first event is when they depart and simultaneously a time is recorded for each, the second event is when they rejoin and simultaneously a second time is recorded for each clock. Thus there are two different frames of reference to keep track of time (1) when and where the clocks depart from each other, and (2) when and where the two clocks unite after each is in motion for some unknown distance and speed.

Let C1 = first clock and C2 = second clock. They depart simultaneously at an event moment M1 and begin an arbitrary motion path and return to a second place simultaneously at a second event moment M2. We observe they record different times during their motions, perhaps C1 records that 100 time ticks during, C2 records 99 ticks.

I would say: (1) because each clock took a unique path of motion between two event moments (M1 = start of motion, M2 = end of motion) they both legitimately tracked time differently because they were synchronized at the start, and because they recorded time simultaneously at two event moments (time measure at event M1 was t=0 for both clocks; time measure at M2 was t=100 for C1 and t=99 for C2).

I also would say (2) the reason the time recorded for C2 was shorter (fewer) than C1 is because C2 moved faster the C1 over identical distances traveled between the two simultaneous events M1 and M2, a result predicted by Einstein relativity theory.