The "why" behind time dilation

[Cody Richeson]

Feel free to correct anything I state here. I'm trying my best to understand some rather complex (for me) ideas about time dilation.

So if I understand correctly, increasing velocity compresses time, causing you to exist more slowly relative to anyone not moving at that velocity. Similarly, the greater the gravitational attraction of an object, the more time will compress as you near its center of gravity. This is why a great deal of time could conceivably pass on Earth compared to someone orbiting very quickly around a neutron star or a black hole for the same amount of (relative) time, i.e. an hour near a black hole versus a thousand years passing on Earth.

The question is: Why is this? Do we know why extreme gravity and extreme velocity cause dilation? What is it about those particular properties that affects the rate at which time ticks? If the universe is composed of subatomic particles, why is it that these particles oscillate more slowly or more quickly depending on velocity and gravity? Is there something special about these properties that unavoidably alters the rate of oscillation?

 

[RyanC]

Have we ever measured time without periodic motion of bodies? I start here

 

[weirdoguy]

Why is this?

Because that's the way Universe works. We can talk about Lorentz transformations, and other stuff like this, but in the end we'll end up with conclusion that I stated in the beginning.

 

[Nugatory]

The question is: Why is this? Do we know why extreme gravity and extreme velocity cause dilation? What is it about those particular properties that affects the rate at which time ticks? If the universe is composed of subatomic particles, why is it that these particles oscillate more slowly or more quickly depending on velocity and gravity? Is there something special about these properties that unavoidably alters the rate of oscillation?

That's not the best way of thinking about time dilation. If you and I are moving relative to one another, your clock will be dilated compared to mine but mine will also be dilated compared to yours, and that can't be explained by saying that one set of particles is oscillating more or less rapidly than the other.

Instead, try understanding time dilation as a result of the relativity of simultaneity (and if you are not familiar with that concept, stop right now and google for "Einstein train simultaneity" - it's essential for understanding time dilation, length contraction, and just about all the other "paradoxes" of special relativity).

When I say that "your clock is running slow compared to mine", I'm really saying something like "Your clock read noon at the same time that mine read noon; and your clock read 12:30 at the same time that mine read 13:00; therefore your clock is slow by a factor of two". But note that this depends on using my notion of "at the same time" and because of the relativity of simultaneity you might describe the situation differently. I say that the events "my clock reads 13:00" and "your clock reads 12:30" happen at the same time, but you will just as correctly conclude, using your notion of simultaneity, that my clock read 12:15 at the same time that your clock read 12:30, and therefore that my clock is the one that is running slow.

(There are some pitfalls here though. First, how did we arrive at the initial agreement that both clocks read noon at the same time? Either we both were at the same place at noon so that we could put the clocks side by side to compare them, or we had to do something complicated like Einstein clock synchronization.

And second, the famous twin paradox in which one of us leaves the other on a high-speed round trip journey and returns less aged than the other is a different phenomenon, not just time dilation.)

 

[SiennaTheGr8]

Do we know why ... extreme velocity cause[s time] dilation?

This one is a consequence of the surprising fact that the speed of light ($c$) is invariant. That means that all inertial observers agree that all beams of light travel at speed $c$, regardless of the observers' motions relative to each other. In special relativity, that's the one counterintuitive phenomenon that you must accept. The other "strange" effects like time dilation follow logically from there.

Do we know why extreme gravity ... cause[s time] dilation?

The basic idea here is Einstein's equivalence principle:

• if you were in a sealed room with no windows, and you felt weightless, you wouldn't be able to tell whether the room was drifting in the vacuum of space or free-falling in a gravitational field;
• along the same lines, if you were in that sealed room but you could stand steady on the floor, you wouldn't be able to tell whether the room was being accelerated "upward" at a constant rate or resting on the surface of a planet.

If this is true, then it follows that phenomena you'd observe in the accelerated room would also occur in the room resting on the surface of a planet. One such phenomenon is the Doppler effect: in the accelerated room, shine a beam of light with initial frequency $f$ from the floor to the ceiling, and you'll find that a detector fixed to the ceiling measures the light's frequency to be greater [EDIT] less than $f$ (because the detector on the ceiling has gained velocity "toward" [EDIT] "away from" the light by the time of detection).

Well, the speed of light is invariant, so a "shift" in its frequency is indicative of time actually running at different rates for the source of the light (the floor) and the detector (the ceiling). By the equivalence principle, this same phenomenon must occur in the room resting on the surface of a planet, too: time runs slower at lower altitudes.

That's the gist of it, anyway. But I think you need to understand general relativity to really make sense of it. That theory describes gravity not as a force, but rather as the curvature of spacetime.

 

[martinbn]

I think part of the problem comes from the word time, which the way you use it is loaded with classical prejudices. What do you mean by time and that it dilates? It seems that you are, without realizing, thinking of absolute time that somehow by magic flows differently for moving clocks. Thus the exclamation "how come". You have to understand that there is proper time, and coordinate time and they need not be the same. You have to put in the effort and read how they are defined and what they mean. In an inertial reference frame a clock at rest will have the same proper time as the coordinate time, that's why usually they are not explicitly distinguished. A moving clock will have different proper time than the coordinate time.

 

[Cody Richeson]

I probably took a somewhat glib approach to describing time. Perhaps I should share what I believe time is, and if I don't have it right, please correct me.

I performed a thought experiment in which X subject is orbiting quickly around a gravity well for an hour (relative to X), and Y subject is standing at ground level on Earth for an hour (also relative to X). Let us say the speed is sufficient enough that Y subject ages by 10 years (relative to X). If the simultaneity of the situation implies that both subjects experienced an equal amount of time passing, then that must mean that the oscillations of the subatomic particles of X are equivalent to the number of subatomic oscillations of Y, but the rate at which they oscillate can appear to be different depending on who is the relative subject for comparison. But objectively, the same number of oscillations occur, which would explain why X would be contracted, both physically and temporally, compared to Y, in order to maintain this equivalency. So I concluded that time is the observation of oscillations being contracted or expanded depending on their velocity/gravity. Is this accurate?

 

[jbriggs444]

Y subject ages by 10 years (relative to X)

The notion "ages by 10 years" is proper time. It is not relative. It is absolute (or, more properly, "invariant"). If Y ages by 10 years between two fixed events, all observers in all frames will agree that Y ages by 10 years between those two events.

 

[vanhees71]

Have we ever measured time without periodic motion of bodies? I start here

The unit of time, as it is defined in the SI, is not defined/measured by periodic motion of bodies in the literal sense, because that's waaaaaaaaaayyyyyyyyy too unprecise. Rather one uses a hyperfine transition of Cs and the corresponding frequency of the em. waves.

 

[phinds]

So I concluded that time is the observation of oscillations being contracted or expanded depending on their velocity/gravity. Is this accurate?

You are getting hung up on how to measure time, not on what is actually happening. Go back to first principles. The speed of light is invariant across all inertial reference frames. Use that and just do the math (Lorentz transforms). Your original post asks WHY does time dilation happens and you seem to be looking for some answer beyond "because the speed of light is invariant across all inertial reference frames" but there really isn't one nor does there need to be.

 

[litup]

Have we ever measured time without periodic motion of bodies? I start here

Yes, atomic clocks like the hydrogen maser relies on a particular wavelength that is very stable which is then counted down to produce clock ticks. My job during Apollo days was Apollo tracking and timing, timing was three clocks, one cesium beam atomic clock made by Hewlett Packard, and a second not as accurate, Rubidium atomic clock and a third, an advanced quartz crystal much more accurate than our watches of today. The tracking part was a transponder onboard Apollo that received a special digital code transmitted from ground stations and the transponder returne the signal to the ground and combining the two codes told them how far away from Earth Apollo was. The hydrogen maser clock was just coming onboard when I was at Goddard Space Flight center.

Since then, optical clocks have gotten so accurate that now they are off one second in the age of the universe or so. The cesium beam clock was good for about one second in 2000 years. They needed that accuracy because of the fact that as Earth turns a particular ground station would go beneath the horizon and lose signal so they had a spec, 100 nanoseconds, that we got to switch from one ground station to the next and that was where the timing part came in, to co-ordinate switching between ground stations, say from Australia to Goldstone in Barstow California (I was offered a job there after Apollo died) it was sad lopking at the new floor tiles put in place when all the Apollo hardware was removed.

 

[Nugatory]

The thought experiment that you are describing has almost nothing to do with time dilation, which is what you started this thread asking about. It is also much more complex than it looks because the gravitational field brings in general relativity and all the counterintuitive properties of curved spacetime. So if you want to develop an intuition for how time really works and how it passes at different rates for different observers you would be much better off starting with problems that don't include any gravity; once you have the Lorentz transformations, Minkowski space, and the standard "paradoxes" (twin paradox, bug-rivet, pole-barn) down cold you'll also have the answer to your original question and you'll be ready to consider problems that include gravity. (This approach also has the advantage of not needing any math beyond ordinary high school algebra). But with that said...

I performed a thought experiment in which X subject is orbiting quickly around a gravity well for an hour (relative to X), and Y subject is standing at ground level on Earth for an hour (also relative to X). Let us say the speed is sufficient enough that Y subject ages by 10 years (relative to X).

You're already letting hidden assumptions sneak in when you toss off that "(also relative to X)" bit without considering what it means. There's no problem saying that if X starts his clock, waits until it reads one hour, and then stops it then one hour will have passed for X between the the start event and the stop event. There's no problem saying that if Y starts his clock, waits until it reads ten years, and then stops it then ten years will have passed for Y. All observers everywhere will agree about how often the subatomic particles that make up X and his clock and everything else moving along with him have oscillated; and that number will be what you expect for one hour having passed All observers everywhere will agree about how often the subatomic particles making up Y and his clock and everything moving along with him have oscillated; and that number will be what you expect for ten years having passed.

But how do you leverage these facts about four different events (X start, X stop, Y start, Y stop) into a conclusion about the relative rates of the clocks? To do that you have to somehow assign some meaning to the statement "X and Y started their clocks at the same time" and "X and Y stopped their clocks at the same time" - and there is no objective and non-arbitrary way to do that if they are at different places.

We get around this problem by modifying the thought experiment. Say that X and Y start out together on the surface of the planet and both start clocks while they're standing side by side. Then X is launched into his highspeed orbit, orbits until his clock has ticked off one hour, and then returns to the planet to compare his clock reading with Y's clock reading. Now we only have two events ("Both start their clocks" and "Both set their clocks side-by-side after X returns) and we can make sensible comparisons of the amount of time that has passed for each.

With this change, we can get rid of the planet and the gravity well and we have the much more easily understood classic twin "paradox" of special relativity. You might find this explanation helpful: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html.

 

[FactChecker]

It's more fundamental to consider the definition of "simultaneous" than of time. The relativity of "simultaneous" is at the heart of time distortion. Your definition of time in terms of a periodic process gets complicated when the periodic process is moving. For instance, a pendulum that is moving periodically arrives at the bottom in different positions in a "stationary" frame. So it is first necessary to see if the moving and stationary frames can agree on what is simultaneous at different positions in the direction of relative motion. They can not. Suppose each one synchronizes his clocks in his own time. Then they can not agree on what events are simultaneous if the events are separated in the direction of relative motion.

 

[Cody Richeson]

...once you have the Lorentz transformations, Minkowski space, and the standard "paradoxes" (twin paradox, bug-rivet, pole-barn) down cold you'll also have the answer to your original question and you'll be ready to consider problems that include gravity. (This approach also has the advantage of not needing any math beyond ordinary high school algebra).

I am actually trying to approach this without the math, which I know is stupid, but I took algebra in middle school, high school and college (for a total of I believe 8 or 9 times) and never passed it, even with tutoring. So I'm not sure if I can actually get a grip on this.

 

[russ_watters]

I am actually trying to approach this without the math, which I know is stupid, but I took algebra in middle school, high school and college (for a total of I believe 8 or 9 times) and never passed it, even with tutoring. So I'm not sure if I can actually get a grip on this.

Let's try a geometric analogy. Ever look at a map and see how China is directly west of the USA? Did you know that when people fly to China they actually fly almost directly north, not west? Do you understand why? In our everyday life, the Earth appears flat like a map. If you want to drive west, you drive west. But that's an incomplete/simplified view of how the Earth really looks/works and as it turns out, the shortest distance between two points doesn't follow what you see on a map. The Earth is 3-d, not 2-d and that extra dimension alters how you travel from one place to another when you take it into account. Due to the curvature of the Earth, neither the distance between two points nor the time it takes to travel between them is as clear-cut as at first glance.

Time dilation is rather like that. Time dilation allows you to take a short-cut of sorts on long trips through space. If you take a long trip and return to Earth later and don't take into account Relativity, what you find is that the distance you traveled and the time it took are both shorter than what you expected when you started the trip. It's not an illusion or a thing that effects clocks, it's a literal reality that you traveled a different path than you were expecting before starting the trip. A different path through space and a different path through time.

 

[FactChecker]

A lot of the math of the Lorentz transformation is based on the Pythagorean theorem, A² + B² = C². Suppose a moving person times a light beam traveling at right angles to his motion. A stationary person sees the light beam travel on the hypotenuse of a triangle. The resulting ratio between one side and the hypotenuse gives the Lorentz transformation.

 

[Mister T]

The question is: Why is this?

Why not? If it weren't that we we'd be asking "Why?" about that, too. There really is no way to expect it to be one way or another, we have to take measurements to determine which way it is, there's no other way to figure it out.

 

[Khashishi]

Time dilation is a consequence of (hyperbolic) rotations in 4D. Do you think it is mysterious that a rod becomes shorter in one direction and longer in another direction when you rotate it? Time dilation and length contraction are analogous. The length of a rod doesn't change when you rotate the viewing frame. Similarly, the invariant interval between two points in spacetime does not change when you change the velocity of the viewing frame. But the components change. Time and each spatial direction are just components of spacetime.

 

[Orodruin]

Time dilation is a consequence of (hyperbolic) rotations in 4D.

I would not even say that hyperbolic rotations are what results in time dilation, but the geometry of Minkowski space. Of course, what relates coordinates from different inertial frames are the hyperbolic rotations, but the differential ageing is in the end a coordinate-independent result of the space-time geometry itself, regardless of whether you put inertial coordinates or curvilinear coordinates on top of it.