Question about gravity and time

[ParanoiA]

If the scale of time and its relation to gravity was exaggerated to the point that one person could stand in a 20 foot hole and their time frame move twice as fast relative to someone standing at the edge of it....would we even notice? I don't understand how light relates with gravity to determine if we could *see* someone moving faster because their time frame is faster relative to our time frame.

 

Since the speed of light is constant, it seems like we could definitely see each other moving faster or slower, in our different time frames, but is that true?

 

I'm sure I'm not asking that right. But maybe someone knows what I mean?

[IM Egdall]

I believe it works like this: Say Tina Top is at the top of the hole, and Barry Bottom is at the bottom of the hole. Time for Barry runs slower than time for Tina because gravity is stronger at the bottom of the hole. So Tina Top sees Barry Bottom moving in slow motion. Conversely, Barry Bottom sees Tina Top moving in fast motion.

 

And there is a light effect. The slower time at the bottom is equivalent to longer light frequency. (The regular up-down motion of the light's electromagnetic wave is a kind of clock.) So Tina Top sees light from the bottom shifted towards the red (longer frequency). And conversely Barry Bottom sees light from the top shifted towards the blue (shorter frequency).

Edited December 24, 2010 by I ME

[Zarnaxus]

time moves slower the larger the gravitational field you are in. also, time moves slower the faster you are going. I believe that since your example is exaggerated, the person on the outside (farther away from the center of Earth's spin) is travelling faster than the person in the hole (closer to the center of the Earth's spin). From a certain perspective, the time would move slower for the person outside of the hole for the reason that person is moving faster.

[swansont]

time moves slower the larger the gravitational field you are in.

 

Larger gravitational potential (depth of the well), not field (slope of the walls of the well)

[timo]

If the scale of time and its relation to gravity was exaggerated to the point that one person could stand in a 20 foot hole and their time frame move twice as fast relative to someone standing at the edge of it....would we even notice?

Absolutely. You'd think twice whether to store your potatoes in the cellar or below the rooftop.

 

I don't understand how light relates with gravity to determine if we could *see* someone moving faster because their time frame is faster relative to our time frame.

The whole issue has nothing to do with light at all (except that light is the most common method for observing things). It only matters where you store your potatoes, not whether you leave the light on or not. You can think about what you visually see, but that's merely an additional level of complication, and not what is meant by time passing differently.

 

It may be somewhat surprising that light has nothing to do with relativity considering that the "speed of light", the maximum speed possible (with some restrictions), seems to play such a prominent role. The reason is historic, I believe. Light was known to travel with this speed before it was realized to be the maximum speed. So it was called "speed of light". Had that not been known by the time it was discovered to be the maximum speed, it would probably be called "maximum speed" today - which is probably a more appropriate name.

 

Since the speed of light is constant, it seems like we could definitely see each other moving faster or slower, in our different time frames, but is that true?

Ignoring the process of bringing the potatoes into or out of the cellar/attic, which takes very little time, anyways: Yes, you'd see the potatoes rot with at a different rate. And in some weird color, too.

 

EDIT (new version, hopefully less confuing):

The potatoes do rot with a different rate in the sense that if you leave some lying around in the attic and some in the cellar for some time and then bring both bags into the kitchen, you'll find that the potatoes in the two bags will have aged differently. There is no light or "seeing" involved (imagine measuring the water content and giving it out via a speaker if you want to be really anal about the "no seeing involved" - it's not going to change the fact). Now, of course you could insist on watching your potatoes through your glass floor/ceiling while they rot in the cellar/attic. In this case, the striked-out sentence above would apply, i.e. you would observe them rot at a different rate. The effect why you see them rot at a different rate is not due to the transmission of light, though. That merely adds an additional layer of complication.

To re-emphasize this point: Light has as much to do with time dilatation due to gravity as it has with the mechanical stability of the house you live in.

Edited December 25, 2010 by timo

[gnarledreaper]

If time can be slowed by gravity then does that mean time might have some physical substance, since gravity "pulls" on things?

 

Forgive my lack of understanding if i am talking nonsense, i am not a scientist of any sort.

[michel123456]

would we even notice?

 

I am not sure. Only math can tell. It is not answerable through logic or intuition.

 

The whole issue has nothing to do with light at all (except that light is the most common method for observing things). (...)

anyways: Yes, you'd see the potatoes rot with at a different rate. And in some weird color, too.

(emphasis mine)

 

Are you sure? Light may not have to do with gravity (is that so?), but light has certainly to do with observation.

Edited December 25, 2010 by michel123456

[timo]

If time can be slowed by gravity then does that mean time might have some physical substance, since gravity "pulls" on things?

No. That's not the standard point of view. Also, the term "time" is slightly ambiguous, anyways. The closest you get to "physical substance" is possibly the concept of ageing, which is called "proper time" in the context of relativity. It is a real physical property in some sense (in particular in the sense that it is not "relative"), but not a substance.

 

Forgive my lack of understanding if i am talking nonsense, i am not a scientist of any sort.

That's cool as long as you don't run around claiming you knew better than the professionals because of that. And that your ideas are actually the sages' stone, and all those idiots disagreeing with you merely lack the creativity/intelligence/karma to realize that. Believe it or not: not only do such people exist, they are in fact rather common on the Internet.

 

Are you sure?

About what I wrote? Yes, except for grammar and some words (e.g. "attic") that I had to look up in an online-translator.

 

Light may not have to do with gravity (is that so?),...

Yes. Unless you want to get philosophical, because ultimately light has to do with taking a shower, of course.

 

 

Anyways: I already had my doubts that my post could be a bit hard to understand when I wrote it. The problem is that this fixation of people on the action of visually seeing things is so strong that question like the one in this thread are "would we see X" rather than "would X happen". That makes it hard to give answers because what actually happens is relatively easy to describe but not what was actually asked for. And answering what is literally asked for ("what we see") is possibly not helpful, since it distracts from the crucial point. I tried to answer both. But seeing that it did seem to cause confusion, I've rewritten it.

[swansont]

Are you sure? Light may not have to do with gravity (is that so?), but light has certainly to do with observation.

 

Observation = measurement. Which can be done electronically.

[michel123456]

I believe the crucial point is always what we see, and never what happens. If you were in the cellar with your potatoes, would you notice anything? No, of course, because the effects of time upon your potatoes would be the same upon you. The question arises when the observator is not in the cellar, and it has all to do with observation, curvature of spacetime under strong gravitational potential, S.O.L. and all that kind of stuff.

 

The potatoes do rot with a different rate in the sense that if you leave some lying around in the attic and some in the cellar for some time and then bring both bags into the kitchen, you'll find that the potatoes in the two bags will have aged differently.

 

IMHO it is a wrong interpretation of Relativity. It does not take into count all the parameters, like the displacement & enormous acceleration of the potatoes when you placed them in the attic (with the help of a rocket) & the cellar, and when you took it back to the kitchen with a crane & much difficulty, remember the gravity well has been immensily exaggerated.

Edited December 25, 2010 by michel123456

[timo]

Making a problem that already is over your head more complicated does not necessarily prove your point or help understanding. I think from a scientific viewpoint my answer to the original question, an explicit example how we could notice a difference in the passing of time, is more than Paranoia could have hoped for on sfn. I don't want to spend time explaining to you (Michel) why the transfer process is irrelevant in this case.

[ParanoiA]

Well thanks for all the feedback. It's been helpful.

 

Timo, I get your point about "seeing" things as opposed to "what actually happens". My questions in speculations are about fiction projects I fiddle around with. Apparently I like writing about things I know nothing about!

 

I was curious about what is "seen" because that's crucial to presentation. Imagine how different a story would have to be told if we lived in different time frames but didn't realize it all, as opposed to living in different time frames and very much obviously noticing the effect. That would change pretty much everything about how life interacts, not just with humans.

 

But "what actually happens" is every bit as important, obviously. I hadn't actually thought of perishables in such a scenario. Awesome.

 

And now I'm fascinated about color and how things would change color as they ascended from my time pit to merge into the time frame of those looking down in the pit. Very cool. Any ideas how the colors from each time frame would change with respect to other time frames? I think someone mentioned a slower time frame producing a longer wavelength, resulting in more red?

[timo]

And now I'm fascinated about color and how things would change color as they ascended from my time pit to merge into the time frame of those looking down in the pit. Very cool. Any ideas how the colors from each time frame would change with respect to other time frames? I think someone mentioned a slower time frame producing a longer wavelength, resulting in more red?

The keyword is gravitational redshift.

 

I think the whole concept of gravitational time dilatation is actually rather easy to explain in your scenario (assuming 1 space dimension plus one time dimension for simplicity), so I'll give a try: You have two locations x1 and x2 and a coordinate time t, If you go some coordinate time interval dt forward, then at x1 a proper time tau1=a1*dt passes, and at x2 a proper time tau2=a2*dt passes. Proper time is the "physical time", or "ageing" (both terms are not technical terms, but probably more meaningful than "proper time"). It is the correct time to use for the description of physical processes in the sense that it is not relative. The factors a1 and a2 depend on the gravitational potential (to stay Tom's terminology). Finally, let's assume the gravitational potential does not change with coordinate time (it does of course change with location). Everything ok so far? Then let's go:

 

Gravitational time dilatation:

Assume some event happening at x1 takes a coordinate time dt (meaning that at x1 a proper time tau1=dt*a1 passed) and emits some photons. Since the gravitational well is assumed not to change over coordinate time, all of the photons take the same amount of coordinate time to travel from x1 to x2. The distance in coordinate time between the first and the last photon will be dt when they arrive at x2. So at x2, the process is seen to take a proper time tau2=dt*a2. So at x2 the process seems to take a factor tau2/tau1 = a2/a1 longer than at x1 (btw. if you want to plug in numbers for the Schwarzschild metric, a1 and a2 are the square root of the entry [math]g_{00}[/math] of the metric).

 

Gravitational redshift:

The redshift effect can be easily explained by the dilatation effect. Assume you are sending some monochromatic laser light from x1 to x2. At x1, the time for a certain number of oscillations (e.g. a single one, i.e. the inverse frequency) is tau1, which again corresponds to some coordinate interval dt. Again, this interval dt will be the same when the laser light reaches x2. Again, x2 will perceive a proper time tau2=a2*dt for this amount of oscillations. So again, tau2/tau1 = a2/a1. So the amount of proper time the oscillations take at x1 and x2 are different. And so are the frequencies f1 and f2, then: f1/f2 = a2/a1. And since the frequency of light is perceived as color, the color of the light arriving on x2 will not be the same as it was when it was sent out at x1.

 

Note that in none of the two cases above, energy was explicitly taken into account. The commonly-known relation of converting potential energy into kinetic energy (or vice-versa) when climbing up or down a potential well is somewhat implicit here: a1 and a2 are related to potential energy, and the frequency of light is related to its kinetic energy.

Edited December 25, 2010 by timo

[michel123456]

I thought it was time dilation

 

Also I strongly suggest to read again the gravitational redshift article of wikipedia, in which the role of acceleration is explained. But of course I am probably wrong.

Edited December 25, 2010 by michel123456

[Janus]

I believe the crucial point is always what we see, and never what happens. If you were in the cellar with your potatoes, would you notice anything? No, of course, because the effects of time upon your potatoes would be the same upon you. The question arises when the observator is not in the cellar, and it has all to do with observation, curvature of spacetime under strong gravitational potential, S.O.L. and all that kind of stuff.

 

 

 

IMHO it is a wrong interpretation of Relativity. It does not take into count all the parameters, like the displacement & enormous acceleration of the potatoes when you placed them in the attic (with the help of a rocket) & the cellar, and when you took it back to the kitchen with a crane & much difficulty, remember the gravity well has been immensily exaggerated.

 

The effects you mention are constant regardless of how long you keep the potatoes separated in the attic and cellar. IOW, as long as you keep the potatoes separated for long enough, any time difference caused by bringing them together or originally separating them will be inconsequential compared to the accumulated time difference due to their time spent separated.

[michel123456]

The effects you mention are constant regardless of how long you keep the potatoes separated in the attic and cellar. IOW, as long as you keep the potatoes separated for long enough, any time difference caused by bringing them together or originally separating them will be inconsequential compared to the accumulated time difference due to their time spent separated.

 

You have to do the math to say that.

Here an example of my thoughts without maths:

Lets say you are in the kitchen, and you put your potatoes in place. After some time it is 6.00 o'clock in the kitchen, 7.00 o'clock in the attic, and 5.00 o'clock in the cellar (because time clicks slower in the cellar). As seen from the attic, kitchen & cellar are in the past. And the more time elapses, the more in the past they will be. So one could say that time acts exactly as if the distance between the attic, kitchen & cellar was increasing. The observational result is the same. And this result is comparable with what we are observing from Earth looking outside to the universe (instead of looking inside as seen from the attic). Do you agree?

Edited December 26, 2010 by michel123456

[swansont]

You have to do the math to say that.

Here an example of my thoughts without maths:

Lets say you are in the kitchen, and you put your potatoes in place. After some time it is 6.00 o'clock in the kitchen, 7.00 o'clock in the attic, and 5.00 o'clock in the cellar (because time clicks slower in the cellar). As seen from the attic, kitchen & cellar are in the past. And the more time elapses, the more in the past they will be. So one could say that time acts exactly as if the distance between the attic, kitchen & cellar was increasing. The observational result is the same. And this result is comparable with what we are observing from Earth looking outside to the universe (instead of looking inside as seen from the attic). Do you agree?

 

The bolded part is where the problem lies. The differential rates of time owing to relativity are separate from the concepts of past, future and present. It is the present in all frames in this scenario. The issue is how much time has elapsed to get you there.

[timo]

You [Janus] have to do the math to say that [waiting sufficiently long will make the transport process irrelevant]

He did.

[michel123456]

The bolded part is where the problem lies. The differential rates of time owing to relativity are separate from the concepts of past, future and present. It is the present in all frames in this scenario. The issue is how much time has elapsed to get you there.

 

I don't understand. At the moment there is a gap in time, there is what we call past, present, future, or do I miss something?

 

The Moon is there in the sky at a gap that corresponds to about 3 light-seconds. From our point of vue, the Moon is in our past 3 sec ago. When an astronaut goes to the Moon, he walks on the Moon in his present, and in our past. I think that if one goes from the kitchen to the attic, it is the same than traveling from the Earth to Moon. Landing, you will not find the Moon 3 sec ago, and going to the attic, you will not find your potatoes older.

[swansont]

A delay from light travel/communication is not the same thing as the dilated time from relativity. If, owing to the motion and depth of the gravity well, the time on the moon ran fast or slow relative to us, the signal still represents being 3 seconds in the past.

 

There is no "gap," as you describe it, from relativistic effects. An analog signal from any clock would remain continuous; only the frequency would change as you moved it.

[michel123456]

The described situation with rotting potatoes corresponds to a phenomena where the Moon continuously moves away from the Earth. When the distance increases, the gap in time increases too. The 3 sec become 60 sec, then 60 hours and so on, as in the potatoes analogy. Simply distance makes the work of time.

 

In the potatoes analogy, the travel of Neil Armstrong 3 sec in the past has been negligated.

Or

if we had a crane to grasp the Moon and take it close to Earth, we would also make the Moon travel 3 sec in time. It is always true, even if the Moon was 3 billions light years away, in distance & in time.

Edited December 26, 2010 by michel123456

[swansont]

No, I think you are still mixing scenarios. The moon moving away from the earth is not a relativistic phenomenon, and Neil Armstrong never traveled back in time.

[michel123456]

He did.

 

The Hafele-Keating experiment?

[swansont]

Janus described the results of the math one would apply to the problem. Clocks in different potentials have different rates. They accumulate a different amount of phase, which depends on how long they are there, so they are variable — you can make them arbitrarily large by waiting long enough (large [math]\tau[/math]). The effects of moving back and forth between the frames is a fixed effect, which means it can be an arbitrarily small effect if [math]\tau[/math] is large.

[michel123456]

I understand. You must be right.