The Derivative Nature of Time and Its Relation to Earth's Rotation and Speed

In summary, time is a dimension that is modeled as a fourth dimension. Clocks measure displacement in the timelike dimension.
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TL;DR Summary
Is there an example, definition, explanation of time that is not derivative of a physical system like a clock, e.g., that's based on the rotation of the earth? If not. If time is not a stand-alone definable entity how can it qualify as a fourth dimension?
I tweeted this on a Sabine Hossenfelder’s Twitter thread:

Is there an example, definition, explanation of time that is not derivative of a physical system like a clock, e.g., that's based on the rotation of the earth? If not. If time is not a stand-alone definable entity how can it qualify as a fourth dimension?

There was no response.
But I can expand on that tweet here.

The formula for calculating the speed of an object is - Distance/Time = Speed

So, if D = 60 miles and T = 1 hr then S = 60 mph 60/1 = 60 mph

69 miles = 1 degree of the earth’s circumference at the equator. And 60 miles = 0.87 degrees.

15 degrees of rotation = 1 hr - So, 0.87/1 hr = 0.87 degrees per hr which = 60 mph

Now, clocks are slower at sea level than they are at mile high elevations like Denver, Colorado. But time with respect to the rotation of the Earth is always the same. 15 degrees = 1 hour. A clock’s movement can slow down or speed up and, therefore, does not accurately reflect the system from which it derives its seconds, minutes and hours. So, does time slow down at lower altitudes or at high speeds? Or is it merely the timepiece that does so? How ever long or short a clock’s hour might be it is geared to the regularity of the earth’s rotation which it cannot faithfully represent.

The earth’s rotation about its axis and revolution around the sun are its motions and movements through space. Through space only. Not through time. Our notion of time is imposed on the earth. All that is going on is 365 1/4 rotations for one revolution. That’s it. That is all that is happening. We extrapolate from that our notion of time. Time then is a derivative of changes in a physical system. It is not a stand-alone definable entity in its own right.

When time is part of an equation “time x to time y”, for instance, it must refer to a certain arc of Earth's rotation from point x to point y to be an accurate notation with respect to our concept of time.

If we age slower at extremely high speeds it’s not because “time” slows down. It’s because the changes in our bodies that contribute to aging slow down. One’s heart rate, for example, that is normally beat-beat would be beat——beat.
 
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Time doesn’t slow down. That's a poor explanation used in popular science, and reasoning from popularised science is extremely risky because it's, at best, an attempt to say in words things that we don't have words for.

Defining time in fractions of the Earth's rotation period fails for the reason you yourself identified: clocks at different altitudes ascribe a different period to the rotation. Furthermore, to the precision required for modern science, the rotation of the Earth is not well defined. It varies. And there are technical reasons that make it extremely difficult to even define what the rotational period is when you're not near the Earth in a curved and non-stationary spacetime. You need to use local clocks to measure local time

Time is modeled as a fourth dimension because that's how it appears to behave. The Lorentz transforms can be derived from three or four postulates, and Minkowski pointed out that they were equivalent to a claim that space and time formed a single four dimensional manifold. So time is a dimension and clocks measure displacement in the timelike dimension in the same way rulers measure displacement in the spacelike dimensions.
 
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  • #3
sumfor said:
Is there an example, definition, explanation of time that is not derivative of a physical system like a clock
No. Time is the thing a clock measures and clocks are physical systems.

The question is why do you think there should be such a notion of time and what use would such a definition have? Also, why do you think the rotation of the Earth is not a physical system like a clock?

sumfor said:
If time is not a stand-alone definable entity how can it qualify as a fourth dimension?
What does one thing have to do with the other? I don’t see how the two ideas are connected, let alone that one forbids the other. Can you explain your reasoning a bit?

FYI, there are two distinct notions of time being used here. “Proper time” is the thing that a clock measures. “Coordinate time” is the fourth dimension. You may want to be explicit about which notion you are asking about.
 
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  • #4
Time is a fourth dimension even in Galilean/Newtonian physics… but there it’s not as intertwined or entangled as it is in special and general relativity.

While historically some units of time (like the year, month, and day) are based on astronomical situations peculiar to the Earth, modern units of time (which are more universal) are based on the frequency of the transition of a particular atom.

Time in [special] relativity (say as measured by a wristwatch) is not tied to the regularity of anyone particular type of clock, in accordance with the principle of relativity.
 
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  • #5
sumfor said:
Summary: Is there an example, definition, explanation of time that is not derivative of a physical system like a clock, e.g., that's based on the rotation of the earth?
The concept of a clock in SR is intentionally kept vague. ANY physical process that can be used to measure time is some sort of clock. The rotating Earth is certainly one such process. It obeys all the SR conclusions for a clock. If the Earth was passing you (or you pass it) at nearly the speed of light, it would appear to you to rotate very slowly,
sumfor said:
If not. If time is not a stand-alone definable entity how can it qualify as a fourth dimension?
Our problem with defining it may not change its existence as a dimension. Two events can happen at different times but at the exact same position in three-dimensional space. That means that time is a fourth dimension, no matter how much trouble we have defining it.
 
  • #6
Ibix said:
Time doesn’t slow down.

Defining time in fractions of the Earth's rotation period fails for the reason you yourself identified: clocks at different altitudes ascribe a different period to the rotation.
If time doesn't slow down but clocks do as you indicate in the next sentence then time must be something independent of clocks even though we use clocks to tell the time.

And clocks have no effect on the rotation of the earth. And even if they could how could any clock ascribe a different period to the earth’s rotation when one clock is running slower than another? Clocks are based on that rotation. A clock is a mechanical sundial.

Also, can you provide an example, definition, explanation of time that is not derivative of changes in some physical system?
 
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  • #7
sumfor said:
time must be something independent of clocks even though we use clocks to tell the time
Of course. Time is the thing that clocks measure, time is not clocks.

sumfor said:
Also, can you provide an example, definition, explanation of time that is not derivative of changes in some physical system?
I already told you “no”. Time is defined as the thing that clocks measure. Again, the question that you have not answered is why do you think there should be a non-physical notion of time and what use would such a definition have?

sumfor said:
how could any clock ascribe a different period to the earth’s rotation when one clock is running slower than another?
Very easily. The relative seasonal variation in the rotation rate is on the order of ##10^{-8}##. Modern clocks are orders of magnitude more precise than that.
 
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sumfor said:
If time doesn't slow down but clocks do
Clocks' proper time does NOT slow down. It ALWAYS ticks away at one second per second. What you don't seem to get is that the NUMBER OF TICKS can vary depending on the path of the clock through space-time. I think this is where your confusion is coming from. Well, that and you unwillingness to accept the simple truth that time is what clocks measure.

Get clear on the concepts of time dilation vs differential aging --- I think that will help your understanding.
 
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  • #9
sumfor said:
And clocks have no effect on the rotation of the earth. And even if they could how could any clock ascribe a different period to the earth’s rotation when one clock is running slower than another? Clocks are based on that rotation. A clock is a mechanical sundial.
Your question boils down to "which is the worse clock?". It's the Earth. And you're assuming it isn't/that Earth is The Standard. It's really not. Have you not heard of leap seconds? In fact:
https://www.forbes.com/sites/jamiec...test-day-since-records-began/?sh=5791d8c78561
Also, can you provide an example, definition, explanation of time that is not derivative of changes in some physical system?
No. Why should there be? Describe "blue" without invoking the concept of light.
 
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I'd like you to describe blue even with the concept of light. Also, space has its own definition. Its not something derived from the physical changes of something else. So, why shouldn't we expect the same with regard to the fourth dimension?

I'm not assuming anything. The first clocks were sundials and time depended on the position of the Earth with regard to the sun. Mechanical clocks replicate that.
 
  • #11
@sumfor I have a question for you. Are you here to learn or to argue? You have joined a forum where there are a lot of people who know what they are talking about and yet you persistently ignore what you are being told and just repeat the same useless argument. I get that you have a point of view that you are loath to discard, but you are being told by people who understand the concepts that you point of view is just wrong. The sooner you can let it go, the sooner you can begin to understand the actual physics.
 
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  • #12
phinds said:
Clocks' proper time does NOT slow down. It ALWAYS ticks away at one second per second. What you don't seem to get is that the NUMBER OF TICKS can vary depending on the path of the clock through space-time. I think this is where your confusion is coming from. Well, that and you unwillingness to accept the simple truth that time is what clocks measure.

Get clear on the concepts of time dilation vs differential aging --- I think that will help your understanding.
Well, we could just as well say that a clock measures distance with respect to degrees. A clock face is 360 degrees with the second hand moving 6 degrees with every tick.
 
  • #13
phinds said:
@sumfor I have a question for you. Are you here to learn or to argue? You have joined a forum where there are a lot of people who know what they are talking about and yet you persistently ignore what you are being told and just repeat the same useless argument. I get that you have a point of view that you are loath to discard, but you are being told by people who understand the concepts that you point of view is just wrong. The sooner you can let it go, the sooner you can begin to understand the actual physics.
I haven't been given a definition of time per se that is not derivative of something else. A stand-alone definition of time in its own right. And it's not just me. I've listened to physicists argue about whether there really is such a thing as time.
 
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  • #14
sumfor said:
I'd like you to describe blue even with the concept of light.
No, it's your bad question.
Also, space has its own definition. Its not something derived from the physical changes of something else. So, why shouldn't we expect the same with regard to the fourth dimension?
Be...cause time is what you use to measure change over time. If you want to measure intervals in space, you use a meter stick. And yup, some meter sticks are better than others.
I'm not assuming anything. The first clocks were sundials and time depended on the position of the Earth with regard to the sun. Mechanical clocks replicate that.
No, mechanical (and later atomic) clocks replace that. I'm not sure when the problem was first noticed, but even if people at one time believed the Earth's rotation kept perfect time, they were wrong.
 
  • #15
sumfor said:
Well, we could just as well say that a clock measures distance with respect to degrees. A clock face is 360 degrees with the second hand moving 6 degrees with every tick.
That description doesn't contain a rate/time.
sumfor said:
I haven't been given a definition of time per se that is not derivative of something else. A stand-alone definition of time in its own right. And it's not just me. I've listened to physicists argue about whether there really is such a thing as time.
That's not an answer to the question @phinds asked you. We get that you don't like the answers you've gotten. The question is, would you accept any answer that requires you to change your position on the subject (would you accept that the question itself is ill-formed?)? I think the answer is no.
 
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  • #16
On StackExchange, I gave a possibly abstract answer to the question
"On mathematical level, what exactly is time in Newtonian mechanics?"

In short,
based on a passage from Gravitation by Misner, Thorne, and Wheeler:
"Time is defined so that motion looks simple." - Misner, Thorne, and Wheeler in Gravitation, p.23.
...
"Good clocks make spacetime trajectories of free particles look straight"... p.26

For more details, refer to
https://physics.stackexchange.com/q...-what-exactly-is-time-in-Newtonian-mechanics/
 
  • #17
russ_watters said:
No, mechanical (and later atomic) clocks replace that.
This is absolute key to understand. The Earth’s rotation was once the gold standard for a clock. It is not any more. There are much much preciser clocks around.

One also needs to separate the definition of time from the definition of units of time. Originally, units like days, years, hours, and seconds were introduced as multiples and fractions of a full daily cycle of the Sun. Then people noticed that the Earth’s rotation was a bad clock relative to other clocks that could be constructed. It then makes no sense to use the rotation to define the units any more and therefore the definition was changed. Today the second is defined as the time of 9192631770 oscillations of the radiation emitted by the hyperfine transition of the Cs-133 ground state. This is a priori decoupled from the rotations of the Earth. Of course, the number 9192631770 was chosen such that the old units were reproduced within the errors of the previous definition. Anything else would have been confusing. However, this is all about the definition of time units - which is distinct from the definition of time, which is what a clock measures just as a distance is something that a ruler measures.
 
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sumfor said:
Also, space has its own definition. Its not something derived from the physical changes of something else.
Please define space.
 
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FactChecker said:
The concept of a clock in SR is intentionally kept vague. ANY physical process that can be used to measure time is some sort of clock. The rotating Earth is certainly one such process. It obeys all the SR conclusions for a clock. If the Earth was passing you (or you pass it) at nearly the speed of light, it would appear to you to rotate very slowly,

Our problem with defining it may not change its existence as a dimension. Two events can happen at different times but at the exact same position in three-dimensional space. That means that time is a fourth dimension, no matter how much trouble we have defining it.
Can two events happen at the exact same position in space? I'm sitting in a room and the space seems to always be consistent, unchanging. But it's position is ever changing for being located on a spinning revolving planet.
 
  • #20
sumfor said:
Can two events happen at the exact same position in space? I'm sitting in a room and the space seems to always be consistent, unchanging. But it's position is ever changing for being located on a spinning revolving planet.
Your view of what space is is wrong and as such this question is badly formed as well. There is no unique way of defining the same position at different times. It all depends on the frame you choose to adopt (and as you have noted, one choice means you are at the same position all the time when you sit down - that is the Earth’s rest frame - and another that you are not). You must therefore abandon the notion that there is a unique way of identifying position that is independent of your chosen frame of reference. The ”same place” is only defined with respect to a frame of reference.
 
  • #21
sumfor said:
Can two events happen at the exact same position in space?
Depending on the choice of reference frame, it can be done. Suppose I am in space and floating with no acceleration. I can say that I am the center of a reference frame in which I never move. So if I snap my fingers twice, they are two events in exactly the same position but at different times.
sumfor said:
I'm sitting in a room and the space seems to always be consistent, unchanging. But it's position is ever changing for being located on a spinning revolving planet.
The Earth-centered, rotating coordinate system is a complicated reference frame to work with. (We do have to work with it sometimes.) There are easier examples.
 
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FactChecker said:
The Earth-centered, rotating coordinate system is a complicated reference frame to work with.
To be fair. It works perfectly easy and well for most daily requirements. Of course this is because at the typically relevant scales the effects of rotation is miniscule.
 
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  • #23
russ_watters said:
No, it's your bad question.

Be...cause time is what you use to measure change over time. If you want to measure intervals in space, you use a meter stick. And yup, some meter sticks are better than others.

No, mechanical (and later atomic) clocks replace that. I'm not sure when the problem was first noticed, but even if people at one time believed the Earth's rotation kept perfect time, they were wrong.
In essence you are saying that time is what you use to measure time. Change happens through space, in space. You can ask what is the rate of change but that is measured by the changes of a clock.
 
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Orodruin said:
To be fair. It works perfectly easy and well for most daily requirements. Of course this is because at the typically relevant scales the effects of rotation is miniscule.
Yes, until you have to figure out the equations for an inertial reference system. Then God help us all. I still suffer from traumatic stress disorder from it. :-)
 
  • #25
sumfor said:
In essence you are saying that time is what you use to measure time.
No, clocks are what you use to measure time.
 
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  • #26
Orodruin said:
Please define space.
Space is the area between the walls of my room and between the objects contained within it. It's filled with air and has a particular volume.
 
  • #27
sumfor said:
Space is the area between the walls of my room and between the objects contained within it. It's filled with air and has a particular volume.
Time is the interval between the start and end of my day and between the events within it. It's filled with air and has a particular duration.
 
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  • #28
FactChecker said:
Depending on the choice of reference frame, it can be done. Suppose I am in space and floating with no acceleration. I can say that I am the center of a reference frame in which I never move. So if I snap my fingers twice, they are two events in exactly the same position but at different times.

The Earth-centered, rotating coordinate system is a complicated reference frame to work with. (We do have to work with it sometimes.) There are easier examples.
Oh sure. I agree with that. Like in my initial post substituting 15 degrees for 1 hour in distance time speed equation worked just fine but it's rather cumbersome.
 
  • #29
Ibix said:
Time is the interval between the start and end of my day and between the events within it. It's filled with air and has a particular duration.
Your day is determined by Earth's rotation to which you can assign a time. And, no, time is not filled with air or anything else.
 
  • #30
@sumfor, I see that you have answered my question. You are just here to argue, not to learn.
 
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  • #31
sumfor said:
Your day is determined by Earth's rotation to which you can assign a time.
You continue to miss the point. Does space not exist in your walls or outside your room? Of course it does - so in your definition you just assigned arbitrary boundaries (the walls), so I did too (the start and end of the day). Essentially, you defined space as "the gap between two arbitrarily chosen surfaces", so I defined time as the gap between two arbitrarily chosen events. If my definition of time is vacuous, as you contend, then so is your definition of space.

Which is kind of the point of operational definitions. We note that clocks are useful and rulers are useful, and that their behaviour implies the Lorentz transforms, which in turn implies that the clocks and rulers are measuring displacements in a 4d manifold with a Lorentzian signature. That's why we say time is the fourth dimension.
sumfor said:
And, no, time is not filled with air or anything else.
Really? What are you planning on breathing today if there's no air between morning and night?
 
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  • #32
"Time does not exist"

Gonna tell my boss that next time I get late to class, I am a physics teacher so who is he to argue with me!?
 
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  • #33
malawi_glenn said:
I am a physics teacher so who is he to argue with me!?
I hope he is not a philosopher …
 
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  • #34
Orodruin said:
I hope he is not a philosopher …
Nah he is a Chemist so he knows his place in scientific discussion with me!
Popular joke amongst us is that I ask how his stamp collection is coming along
 
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  • #35
I guess it's time to move on.
My answer suggested in #16 is probably too abstract.
 

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