# B Pace-of-Time and Gravity

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1. Aug 8, 2015

### Angstrom's Muse

Full disclosure, I am novice and I do not know much of the lexicon associated with physics. Please forgive the vagueness of the language I use as the proper terms are unknown. Insight on the theoretical properties of the question as well as insight on the correct vocabulary is appreciated.

It there a connection between the magnitude of a body's gravity and time?

When I say "time", I mean the pace of time. That is how fast stuff ( Molecules/atoms etc.) decay within a gravitational field. It seems to me that there is a inverse relationship between the magnitude of gravitational force and the pace-to-time. That is on earth we all experience (9.8m/s^2 x our mass) and the pace-of-time has the same impact on all of us, which is why we age (molecular breakdown) at relatively the same rate. I assume if we were in a bigger gravitational feild our body's would under go more stress, we would move slower (in terms of speed) and the pace-of-time would get shorter. As a result our body's would age faster in comparison to earth. Of course, vice-a-versa in the case of a lesser gravitational field, pace-of-time would lengthen and we would age slower.

This of course leads to a whole host of other questions concerning pace-of-time (or whatever the correct term is) in space and how it changes throughout the universe as well as how entropy would have similar effects on our body's or different.

I am pretty sure, there are some blaring misconceptions in this train of thought, the reason for the post.
Thank for considering.

Last edited: Aug 8, 2015
2. Aug 8, 2015

### pellman

Yes. What you are calling pace-of-time physicists call the rate of clocks. The effect of changing rates of clocks is called time dilation. First, forget gravity for a moment. In flat spacetime, consider a clock moving at high speed relative to an observer. The observer will see that the moving clock ticks slower than his own clock. (Since motion is a relative, an observer traveling with the moving clock will see the first observer as the one moving and will say that first observer's clock is the slow one. This sounds like it would lead to contradictions but it can be shown that it doesn't really.)

There is a similar effect due to the gravity. The effect of the curvature of spacetime near the massive body as compared to the flat spacetime far away is similar to that of a moving body compared to one at rest. the clocks near the massive body tick slower. This has been observed directly with respect to the earth using very precise clocks.

Search youtube for "gravitational time dilation" and you will find some good introductory videos on the topic.

3. Aug 8, 2015

### A.T.

Not quite. Gravitational time dilation depends on the gravitational potential, not the gravitational field strength. For example, at the center of the Earth the gravitational acceleration is zero, but the gravitational time dilation is maximal.

The connection between gravitational acceleration and gravitational time dilation is visualized in a simplified manner here:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

4. Aug 8, 2015

### Staff: Mentor

Humans would age differently on different planets, but this has nothing to do with the speed of clocks - it is pure biology.
The gravitational time dilation is tiny for planets, of the order of microseconds per year. You need a neutron star for significant effects, but living on those doesn't work. For an observer outside, time is slower deep down in gravitational wells, so the effect is opposite to possible biological issues.

5. Aug 8, 2015

### Staff: Mentor

You're mixing up several different things here. In a stronger gravitational field, our bodies would be under more stress, yes, but that in itself doesn't affect the "pace of time"; it means your body will age more in, say, one year of your own experienced time. Neither does the fact that we would move slower in stronger gravity; again, that just means you would be able to cover less distance in, say, one minute of your own experienced time. Neither of those things, in itself, changes how you experience time relative to someone somewhere else; you could put your body under more stress and slow down your movements here on Earth (say, by carrying a heavy backpack around everywhere), and it wouldn't change the rate at which you experience time relative to anyone else.

Gravitational time dilation, the phenomenon in relativity that changes the rate at which you experience time, relative to someone at a different location, does not depend on the "strength of gravity", meaning the force you feel when you are at rest in the field; it depends on gravitational potential--heuristically, how deep you are in the gravity well, not the slope of the well at your location (which is what determines the strength of the force you feel when you stay at rest in the field). The deeper you are in a gravity well, the slower time flows for you compared to someone out in empty space, far away from all gravitating bodies. This makes you age slower than someone out in empty space.

6. Aug 9, 2015

### Markus Hanke

Maybe I am being pedantic, but from what I have learned about the theory of relativity over the years, concepts such as "rate of clock", "speed of time" etc do not seem to be very meaningful. Every clock taken in isolation ticks at exactly 1s per second, if that makes sense. Time dilation - be it kinematic or gravitational - makes sense as a concept only if one compares two or more clocks - to me, it is a relationship between clocks, not something that "happens" to one single clock.

Or is my understanding off on this point ? I'm just an amateur, so please correct me if I'm wrong on this.

7. Aug 9, 2015

### Staff: Mentor

Right - we are comparing the clocks in gravitational wells with clocks "far away in space" here.

8. Aug 9, 2015

### Staff: Mentor

Yes, this is correct. For gravitational time dilation, we are comparing two clocks which are both at rest in a gravitational field, but at different altitudes. (Or one clock might be "at infinity", which is an idealized way of saying "so far away from the gravitating body that it can be approximated as being unaffected by its gravity". But the clocks being compared should still be at rest relative to each other for a proper comparison.)

9. Aug 15, 2015

### Angstrom's Muse

Ok. Thank you all for the help. Specifically (Marvin the Martian 10,007) Some of these concepts I understand after gathering information and others I am still processing. I have an idea that is tough to articulate and gaining the vocabulary is proving to be the big challenge. Having said that, I find a smaller problem with the inauthentic ways of explaining these concepts. Most of the informative videos and visual diagrams that are widely used to explain these concepts are (what I feel) misrepresenting the concepts completely and creating more misconceptions in my head. An example of this, is the picture of the earth sitting in a x y grid en.wikipedia.org as a relevant image to explain space-time. What the heck?! I find my own understanding is clouded with these images. Is this a fair assumption?

Now,
Back to biology and physics connection. Before I spoke of time being defined as the rate at which molecules decay (ie. humans aging), this seems to be an unorganized way of looking at time and I understand that there are some misconceptions I have there. However, I am not sure if the "speed of clocks" definition is same as what I mean by "the pace of time.".... again vocabulary is the missing link here. I will attempt to present a series assumptions that may frame my question better.

1) I assume that our brains have evolved to take a series of freeze frame shots many times per second, which allows us to view life as is. (app. 24 frames /second for movies)

2) I assume that this evolution is guided by the "pace at 'which' time" proceeds (possibly speed of clocks) here in this position in earth's gravitational field. - referring back to (#5 Aug 8th) if understood correctly.

3) I assume that many other animals have evolved to do the same and at the same rate as we do, thus the ability to interact with different species in the same time frame. (check out article is interested)

Getting to the physics of this.
For the sake of exploration...
If I was to go to a planet with huge gravity (say 10, 000 times earth's) and was in DEEP so that my position in the gravitational field had a noticeable affect on time. Would the pace of time mimic that of earth? Assuming my brain matches this pace, what would it look like? slower/ faster/ backwards/ the same/ NOTA

What would this effect have on the speed of clocks?

My goodness. Thank you for baring with me on this. Hopefully this provokes some thoughtful conversation and is not too trivial.

p.s.
Which seems to be untrue according to this link
http://www.extremetech.com/extreme/...ow-motion-or-why-your-puppy-is-so-hyperactive

10. Aug 15, 2015

### pervect

Staff Emeritus
I would agree with your observation that pop-science, though well intentioned, can be misleading or even very misleading. I would go so far as to say that it's not infrequent for pop-science to interfere with a true understanding of the real underlying issues :(.

Time is measured in seconds, and it might be helpful to look at the SI definition of the second to get a better appreciation of time. See for instance http://physics.nist.gov/cuu/Units/current.html
Cesium atoms don't actually "vibrate" like tuning forks, but the pop-sci analogy is too seductive here for me to resist, in spite of the fact that it's probably ultimately misleading. The misleading parts of the analogy probably won't be a problem unless/until you get into quantum mechanics, though. So, for the purposes of special relativity it's probably not a truly awful anology.

A more abstract idea is that the concept of time is based on periodic changes of state, and we can count the periods, which gives us a notion of "time", much as we could count the physical vibrations of a tuning fork. Atoms are ideal for this purpose, they're all the same, and we can observe their periodic changes of state and use them to create very accurate clocks. Probably there's a lot of room for argument over some of the finer details, but for a rough overview I hope this is simple enough to understand and yet accurate enough to be useful in understanding the SI definition of the second.

So time applies even to atoms. It's more fundamental than atoms, really, but it's convenient for experimental purposes to use atoms to measure time for the reasons already discussed. This property of atoms caries over to molecules, which carries over to chemistry, which carries over to biology, which eventually caries over to your personal perception of "time". But your personal perception of time is more complex than the physical quantities which we measure, and the relationship between your personal perceptions and physics is ultimately a question of philosphy. I won't get into more detail about that,among other reasons of personal preference, philosophical discussions on PF are discouraged as a matter of policy.

The idea of the "rate of time" isn't ultimately physics, or biology, it's a bit more subtle. It is ultimately based on the idea of coordinates. Coordinates are a tool pf physics, but are not in and of themselves physics, there are just one of the tools physicists use. There are some approaches to physics that don't use this tool, i.e. coordinate independent physics.

Abstractly, coordinates are just labels that we assign to events. Time coordinates are labels, usually numbers, that we apply to events to tell "when" they happened. The idea of "when" is subtly different than the idea of clocks. Clocks tell us proper time, the amount of elapsed time between two events, a starting event and an ending event. But they do not have enough structure yet to tell us "when" an event occurs. To do that , you need to introduce an additional layer of abstraction, a coordinate system, that assigns the "when" labels to various events that occur in space-time. Typically, one might start out with some "master clock", co-located with an observer, define some "reference event" that occurs at time 0 on the master clock, then use the concepts of simultaneity to assign a time coordinate to every event.

The fundamental issue is that while we are used to the idea that we can assign coordinates in such a way that the difference in time coordinates between two events is equal to the amount of time a clock, present at both events, would measure, it turns out to be impossible. The reason for this is ultimately very simple, but confusing.

Because time and space turn out to be interdependent, different clocks can be present at the same starting, and ending, events, but measure (or experience) different amounts of proper time.

Therefore, the notion of coordinate time can't be the same as the notion of proper time, that clocks measure. The ratio of the proper time of a particular clock to the difference in the coordinate times turns out to be what we call "time dilation". It also turns out that time dilation depends on the velocity of the clock (as expressed in the coordinate system), and not other factors.

There's another important observation here. I earlier mentioned "observers" and "simultaneity" when I talked about setting up coordinates. Hopefully these are familiar concepts (though it turns out they're trickier than they look - but the tricky parts aren't a problem until one wants to move on to general relativity from special relativity). Anyway, the important observation is that simultaneity depends on the observer in special relativity. There is no "universal" notion of "simultaneity". This is one of the most frequent obstacles to understanding special relativity, in traditional Newtonian physics it is assumed that simultaneity is the same for everyone, and it is very hard to break this habbit of thought once it has been established.

11. Aug 15, 2015

### Staff: Mentor

You're right to be skeptical of that image; it doesn't show spacetime curvature, it only shows space curvature, and the space curvature it shows depends on a particular choice of coordinates. Images like that are often found in pop science sources, but unfortunately, as you are seeing, they don't really help with understanding how spacetime curvature works.

This is more or less correct, but it's a question of biology, not physics. You don't need a brain to keep time, and a brain is much too complex to use as a good simple "test case" for understanding how time works in physics. It's much better to choose a very simple timekeeping device; the one I prefer is a light clock, as explained, for example, here:

http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html

I strongly suggest that you develop an understanding of time from simple devices like this, before trying to understand how brains and other biological systems deal with it. It is true that the "rate of time flow" as defined in physics, for example by the light clock, governs the rate at which all processes take place, including biological processes.

What does "mimic that of earth" mean? How would you compare the two?

If you mean, would you see anything different locally, no, you wouldn't. Your experience of "time flowing" would be the same as if you were on earth, and if you had a light clock next to you, it would look and behave the same as it would on earth.

But if you tried to compare what you were seeing locally with what was happening elsewhere, for example on earth, you might see differences. You need to be much more specific about what comparisons you want to make and how you want to make them, in order for questions like this to have meaningful answers.

12. Aug 16, 2015

### Angstrom's Muse

Very informative. Thank you.

I find it very interesting on how time is measured. If I read your definition correctly, a second is measured by a scalar quantity - the periods (cycles/second) of radiation of a specific cesium atom. Which makes me think that we (humans) still do not have a in-depth understanding about the nature of time. That is, it seems the measurement of 'a second' points back to counting the "pulse" of kinetic energy. Is this fair to say?

If so, is time related to temperature (average kinetic energy in a system)?

If not, do you have a good reference that discusses different theories of how time works?

Thank you
pervect

13. Aug 16, 2015

### Angstrom's Muse

Thanks PeterDonis.
I will take a look at the lecture.
I agree trying to mix biology in to this only reduces clarity. I think you are answering my original question despite the verbal awkwardness.

Since the speed of light is a constant - a time clock will never change its pace. This is what I meant by pace-of-time.

I think you are saying that a time-clock will never change its pace (my notion of "pace of time") regardless of its position in a gravitational field, but will be different relative to another time-clock in a different gravitational framework (or traveling at a different speed) which is what we refer to as time dilalation.

This helps. However, I am interested if there are other theories on this.... as taboo as that maybe.

14. Aug 16, 2015

### Staff: Mentor

There is no kinetic energy involved. How else would you define a second, if not "x times the period of some extremely reliable process that we can measure well"?
It is not.
There are no theories that would lead to different results without being excluded by experiments.

15. Aug 16, 2015

### Angstrom's Muse

I realize that your understanding of this is beyond mine, so please view these questions as a yearning to learn. I am trying to gain the best understanding I can and with that, being critical is a habit, possibly a bad habit.

I am not sure of another way to define it and I am not questioning its reliability.
It does seem strange that the definition counts the period which as I understand, is (cycles/second). Usually when defining something, it's definition should not refer to itself. In this case the definition of a {second = x times (cycles/second)}. I know there is a misconception in there somewhere.

Respectfully,
Angstrom's Muse

16. Aug 16, 2015

### Staff: Mentor

No, x is just a number, the number of cycles; it's not a frequency. We define a second as the time it takes for x number of cycles to occur.

17. Aug 16, 2015

### Staff: Mentor

This concept is not new - the original definition of a second was "one day has 86400 seconds" (usually divided in 24 hours per day, 60 minutes per hour and 60 seconds per minute: 24*60*60=86400). Unfortunately, the length of a day is not completely constant.
The radiation emitted by caesium in the transition between two states is more stable, so one second is defined as 9'192'631'770 times the period of this radiation. This is more reliable, and it can be reproduced everywhere, even if the clock is far away from Earth.

Even more precise measurements make it a bit more complicated. Clocks at different altitude run at different speeds due to gravitational time dilation (to come back to the original topic) - this is correct, but computers should agree on the question "which time is it?". Therefore, time is taken as a clock on sea level records it.
The radiation from the caesium has a "long" period, which limits the precision of its measurement. Clocks with different elements can emit visible light with a much higher frequency, improving the stability. Stability doesn't help if you don't know how many periods you have to count, so currently the more precise clocks are gauged with less precise clocks.... it is planned to change the definition of a second to another element to improve the precision of clocks.