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I have heard that even atomic clocks lose a second every billion years or so. That raises the question, is it even theoretically possible for a perfect clock to exist, one that never gains or loses time?

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    $\begingroup$ A different point of view would be to say that there are many perfect clocks, and it is just man's interpretation that is imperfect. An atomic clock vibrates at a certain rate; it is that rate that is correct, not our imperfect measurement of it. The earth goes round the sun in exactly one year; it is our clocks and calendars that are incorrect, the earth turns in exactly 24 hours, regardless of how we measure it. Human clocks are merely attempting to measure something that occurs in nature. $\endgroup$ Commented Feb 4, 2021 at 23:20
  • $\begingroup$ A clock is a measurement device. ALL measurement devices have a finite precision. $\endgroup$ Commented Feb 4, 2021 at 23:46
  • $\begingroup$ @foolishmuse, Re, "The Earth goes round the Sun in exactly one year." Are you defining the word "Year?" Or are you claiming that the Earth-Sun system is a perfect clock? $\endgroup$ Commented Feb 5, 2021 at 0:07
  • $\begingroup$ @foolishmuse, Re, "the earth turns in exactly 24 hours." Actually, that's not true--at least, not if "hour" means exactly 3600 international seconds. en.wikipedia.org/wiki/Day_length_fluctuations $\endgroup$ Commented Feb 5, 2021 at 0:10
  • $\begingroup$ @SolomonSlow What is the original definition of one year; the time it takes for the earth to circle the sun. What is the original definition of one day; the time it takes for the earth to complete one rotation. What is the original definition of 1 second: 1/60th of 1/60th of 1/24th of one day. Yes, these amounts very from day to day and from year to year, but that's the real world. I didn't put this as an answer because I know that it doesn't match modern thinking. But any real clock would only match what occurs in the real world. $\endgroup$ Commented Feb 5, 2021 at 16:41

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The words "perfect" and "exist" are not compatible. The only way we can imagine perfect things is in our imagination, not in anything that exists. For things that exist, we can ask how close they are to being perfect, but even that question will not have a perfect answer. The best we can do is to estimate how close they are to being perfect. Losing 1 second in a billion years is pretty darn close to being perfect (since it is 1 part in 31,557,600,000,000,000) but it is not perfect and nothing physical can ever be perfect.

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I have heard that even atomic clocks lose a second every billion years or so.

That would be a small misunderstanding on your part. The second now is defined by atomic clocks. So, if all atomic clocks were consistently slow, then that would mean that the definition of a second was wrong... by definition.

That doesn't make sense.

What you read probably said that an atomic clock can not be regulated to better accuracy than plus or minus so-many seconds per billion years. That is to say, if you built an ensemble of atomic clocks, and you let them all run for a billion years without ever correcting them, then you could expect their counts to differ by some small number of seconds at the end of that time.

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  • $\begingroup$ Primary atomic clocks are not regulated or corrected. $\endgroup$ Commented Feb 5, 2021 at 11:23
  • $\begingroup$ @MassimoOrtolano Can you expand that comment? My understanding is that there's still measurement uncertainty; so the atomic frequency is accurate and precise (because that's how time units are defined), but actually measuring it in an atomic clock is not. Also I think the "without ever correcting" in the answer refers to cross-calibrating different clocks when their measurement uncertainties accumulate, no? $\endgroup$
    – uUnwY
    Commented Feb 5, 2021 at 13:34
  • $\begingroup$ @MassimoOrtolano, That would be a deliberate choice, not a physical necessity. In principle, any clock can be adjusted if its owner chooses to do so. What procedures actually are followed by the owners of the various clocks whose average define International Atomic Time is beyond my knowledge. $\endgroup$ Commented Feb 5, 2021 at 13:48
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    $\begingroup$ Solomon, I made the remark because it's actually within my knowledge: in general, they really neither regulate nor correct primary clocks (some corrections are applied by evaluating certain systematic effects, e.g. the relativistic effect due to the altitude). @Stephan There's no cross-calibration either, but the explanation would be really too long for comments (and I'd hardly find the time for an answer to a question). Audoin's book which I referenced in this answer is a good source of information about these topics. $\endgroup$ Commented Feb 5, 2021 at 14:02
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    $\begingroup$ @MassimoOrtolano Perhaps my comment was unclear. What you say is what I already know. This wasn't what I meant, and it's not how I understand Solomon's answer. To clarify: Do you agree that if we build two or more atomic clocks and let them run for a billion years, they will differ by some small amount? This will not be relevant for any human timescale and the point was not whether clocks in practice are corrected or not, but that in principle there are will be uncertainties. $\endgroup$
    – uUnwY
    Commented Feb 5, 2021 at 19:59
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Well, there is no concept of absolute time or a perfect ' tick tock ' in the universe. Phenomena happen at their own rate.

You can't quantify their 'perfection'. You can quantify the errors you made while measuring their physical aspects.

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Imagine a totally perfect clock. It measures the time in the place where it is situated. Its own proper time. But due to general relativity the speed of time is affected by nearby objects, gravitational fields, spacetime curvature, speed of motion and gravitational waves.

The ideally perfect clock would look not that perfect for anyone who is located in a different place, surrounded by different bodies that curve the spacetime, and moves around at different speeds.

So, even ideally perfect clock would be not that much useful because it would measure its own proper time, in its own reference frame and in its own place relative to other objects, which is surely different than the proper time of any other object.

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To say that something is perfect, accurate or absolute, is in itself a lie if we consider the realm of our cosmos being governed by the laws of physics - be it classical, modern, or others. The most convenient way to say is that nothing is absolute in this real world ( ha! I know that the speed of light is constant in vacuum. But, yes, the truthfulness is just unachievable ). Even space and time is not just, because we know the instances where space-time is just not as accurate as it seems to be. The theories and their related phenomena, of length contraction, time dilation, red/blue shift in macro physical words and gravitational lensing, gravitational waves and much else more in the quantum level, suggests and portrays a world that we live in as something of a ever changing and ever revealing Pandora's box.

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It seems as though you are asking if a "clock" can exist that isn't impacted by relativity/time dilation. At the moment, nothing we can observe in the universe is free of time dilation. We would need to be able to observe or measure a property of the universe or particle that does not suffer any impact of time dilation.

Unfortunately, there are few possible extra-relativistic properties we can even indirectly observe in the universe (quantum entanglement being on the short list). We would need to have a better understanding and direct measurement capacity of such a property to devise such a "perfect" time dilation free measurement or apparatus.

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