What is the "rate" of the "passage of time"? How does a physicist define and measure time?

Question

I'm trying to separate common concepts of time from the use of time as a standard measurement in physics.

One thing I'm struggling to define is the "rate of the passage of time". For example, commonly we might say that something happens, or has the rate of, "every day". But "every day" isn't a rate "of time".

Let's use the example of a CPU clock "speed". "Speed" is loosely defined in physics as the distance traveled per unit of time. In the case of CPU clock speeds, the speed is the number of clock cycles the CPU can perform per second. But a second isn't a measurement of time. A second is a measurement of the rotation of the Earth. Therefore, the CPU clock speed is more accurately defined as, "the number of clock cycles the CPU can perform in 1/86,400th rotations of the Earth". It's simple substitution. The second is a portion of a minute, is a portion of an hour, is a portion of a day. A day is defined as 1 rotation of the Earth. Any relationship that the rotation of the Earth has to another "dimension" or "force" called "time", seems to be an assumption.

According to my understanding of physics, the current belief is that "time" is passing at varying rates "all the time" depending on different circumstances. "Time is passing more slowly" for objects that are larger (or vice-versa) or time is passing more quickly for objects that are experiencing more gravity (or vice-versa). So, if we've had this assumption that the Earth's rotation happens at a constant rate of the passing of time, which rate of passing time have we been... standardizing the Earth's rotation against? If 1 rotation of the Earth is equal to x units of a force called time "passing by", then are we using the rate at which time passes when it's experiencing more gravity or less gravity?

So, my conclusion thus far is that we've just been confusing time with the relatively constant motion of physical objects. Like two lights blinking at different but consistent rates. They don't blink in rates of time, they blink in rates of each other, because each of them is relatively constant. The fast light blinks 3 times for every 1 blink of the slow light. And somehow we've assumed that there's a third underlying force which is also passing by at a consistent rate where really none exists.

So, what instrument have we used to measure the rate at which a fourth dimension passes by? We have devices that compare the rates of one object in the three dimensional world with the rates of other objects in the physical world, but as far as I can tell we're always comparing the rate of one object in the three dimensional world against the rate of another object in the three dimensional world. I can't tell where a 4th dimension fits into the equation. Examples:

Carbon 14 has a half life of 5,730 revolutions of the Earth around the Sun.

The gestation period for a human baby is approximately 252 rotations of the Earth.

2,091,450 rotations of the Earth is approximately the half life of a Carbon 14 atom.

At this point Microsoft Excel would throw a "Circular Reference" error. What is physics doing differently?

"Any relationship that the rotation of the Earth has to another "dimension" or "force" called "time", seems to be an assumption." Who says that there has to be a "force" called "time"? — BioPhysicist, Nov 13 '18 at 03:44
Possible duplicate of What is time, does it flow, and if so what defines its direction? — BioPhysicist, Nov 13 '18 at 04:16

score 3 · Answer 1 · answered Nov 13 '18 at 04:10

Imagine that you and I have identical boxes filled with precisely the same amount of some radioactive isotope. By measuring how much of the radioactive material has decayed, we can (in principle) get a spectacularly accurate measure of how much time has passed.

Now I take my box in my rocket ship and jet around the galaxy at relativistic speeds. When I return, we compare boxes and find that we no longer have exactly the same amount of material; while almost none of my material has decayed, you've lost a very substantial amount. It's important to note that neither you nor I experienced anything weird during my trip - despite the fact that very little of my material has decayed, I didn't experience my trip in some kind of sci-fi slow motion. Everything was normal, it's just that our clocks no longer agree.

Gravitational time dilation is a different effect. We'll start again with equal amounts of radioactive material, but this time, instead of traveling at relativistic speeds, I climb with my box to the top of a very high mountain (that is to say, I go to a region of increased gravitational potential). After admiring the view for a while, I climb back down and meet you at the base of the mountain. This time, when we compare our boxes, it is yours which has more radioactive material left. Once again, neither one of us had any weird, time-bending experiences during this experiment; it's just that our clocks once agreed, and now they don't.

The reason we're using the decay of radioactive isotopes to keep time is that such "clocks" depend on absolutely no external factors. Talking about the digital watch on my wrist would leave open the possibility that the time mismatch is due to something happening to the electrons moving through the wires; this is absolutely not the case here.

If the mismatch happens even with our radioactive clocks (which again, are affected by nothing external), then the mismatch will happen with all clocks, biological ones included. When we meet after my relativistic space journey, I will have physically aged less than you have. When we meet after my trip up the mountain, I will have aged more.

To more directly address the other part of your question, there are processes in nature through which occur with sufficient (essentially perfect) regularity that we can use them as an absolute standard for time. Radioactive decay is one such measure; atomic clocks, which work by a different mechanism, are another. The current SI definition of one second is exactly 9,192,631,770 cycles of a Cesium atomic clock.

One aspect of the theory of relativity is that the passage of time depends on the reference frame of the observer; what that means on an operational level is that two physicists, each armed with a perfect clock, may still measure different time intervals between the same two events (in my first example, these events might be my departure and return to Earth). The observed discrepancy can be precisely calculated based on the relative states of motion of the two observers; such measurements have been done experimentally, and they match the predictions of special and general relativity with exquisite accuracy.

By the way, I am aware of the concepts of acceleration and inertial frames (e.g, https://physics.stackexchange.com/questions/207934/the-twin-paradox-and-positively-curved-space ) but who's to say which of the two frames is inertial? I think this point is usually poorly explained. — mirkastath, Nov 15 '18 at 04:27
Unlike constant velocities, acceleration can be felt. It's what you experience when you're pushed back into your seat when accelerating in your car. See here for an atomic clock experiment using commercial airliners, and here for a NIST paper describing high-precision tests of time dilation. — J. Murray, Nov 15 '18 at 08:17
Thanks for the links! I'll have a look. As for acceleration: 1) I sure can feel it, but how would a single atom "feel" it? ;-) 2) We are routinely told that it is the relativistic speed that dilates time (acceleration is not necessarily mentioned), so my question regarding you and Derek remains... — mirkastath, Nov 16 '18 at 03:40
My point is that an accelerated reference frame can be distinguished from an inertial reference frame by measurements (see accelerometers). Your point was that there is symmetry between me and Derek; my point was to say that there is not. Derek is in an inertial frame (ish) while I am not. More quantitatively, you can tell the difference by calculating the proper time of our respective worldlines (in whatever reference frame you'd like), and you will find that mine will be shorter. — J. Murray, Nov 16 '18 at 03:47
OK then, dime dilates because of acceleration, not because of high speeds... ??? I concede it is impossible to measure the effect of dilation without any acceleration, so we cannot disentangle the two (?). I'll have to check the experiments and brush up my relativity... — mirkastath, Nov 16 '18 at 04:08

JadaLovelace · Answer 2 · 2018-11-13T04:44:48.567

In relativity theory, time is considered as part of the same "thing" as space, called spacetime. Essentially it says that mathematically, there is no difference between a time interval and a distance. Now consider that we can perceive 3 spatial dimensions [x] [y] [z] and 1 temporal dimension [t]. We're used to measuring velocity as [x] [y] [z] per [t], but this is just for practical reasons. There's nothing holding you back from measuring a different type of "velocity", for example [y] per [x]. This has practical applications too - one example would be the glide ratio of an airplane.

The example of the glide ratio immediately tells you what "velocity" is: a ratio. It is the amount of [x] [y] [z] that passes per [t]. We use this ratio because it is practical in our daily lives, nothing more.

The only real universally constant motion that we know of is the speed of light, which is always 3*10^8 m/s, no matter what your frame of reference is. What this means in the context of the above, is that our velocity in spacetime is in fact always constant, no matter which direction we go. Keep in mind that time is also a direction! So, if my velocity is represented by an arrow, and I stand still, then that arrow points only in the "direction" of time. Now if i start moving, my arrow will "rotate" a bit in the direction that i'm moving, which makes the time-component of my arrow a bit smaller and the space-component a bit bigger (i gain speed, but time starts to slow down). The faster i go, the more my arrow has to point to the spatial directions, and the less it can point to the time direction.

I tried to clarify the component thing in this picture:

The blue line and the red line have the same length, but different orientation. If you take the x-axis as movement in time and y-axis as movement in space, you see that when your space-component is bigger, your time-component (indicated in red and blue on the x-axis) gets shorter (and your movement in time becomes slower).

So, in short.

At what "rate" goes time?

This depends on your spatial velocity. The faster you go, the slower time goes.

To what reference is time measured?

To the speed of light. Time is measured as 1 second = the time it takes light to travel 3*10^8 meters.

What is speed?

The ratio of a space interval with a time interval (which are mathematically equivalent, and the concept of speed is a human thing to make our lives easier).

Is there an absolute "rate of time" to which all other "rates of time" are referencing?

No. Relativity tells us that every intertial system is equal, so you can really only say something about your rate of time relative to someone else. In fact, the concept of "simultaneous" is not even a real thing! This is a whole different story, but this in itself tells you that there is no physical "rate of time" that we can measure.

What is the "rate" of the "passage of time"? How does a physicist define and measure time?

2 Answers2