Why does gravity affect time in space?

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i dont understand why gravity affects time, and why does it do that?
 

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Drakkith
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The explanation requires that you learn a lot about Special and General relativity, two difficult, counter-intuitive theories that give plenty of people trouble. Are you prepared to do that?
 
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yes
 
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PeterDonis
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i dont understand why gravity affects time, and why does it do that?

As Drakkith said, to really understand this, you need to spend considerable time learning SR and GR. However, there is a simple thought experiment that might at least help you to see why it's worth making that effort.

The thought experiment is due to Einstein; it's one of the first ones he constructed while trying to work out how to extend SR to include gravity. Suppose we are inside an accelerating rocket, standing on the bottom of the rocket so that we feel an acceleration of 1 g, just as if we were standing on the surface of the Earth. Also, suppose that the rocket is entirely enclosed and we have no way of seeing or making any measurements of anything outside it; we can only see and make measurements of things inside the rocket. In that scenario, Einstein said, no experiment that we can run will enable us to tell whether we are actually inside an accelerating rocket, or are instead standing inside an enclosed room that is at rest on the surface of a planet (like the Earth) with a 1 g gravitational field. This is called the "equivalence principle".

But Einstein went further. Suppose that we have two clocks, one at the bottom of the rocket and one at the top. At some instant, the bottom clock sends a brief flash of light of a known frequency towards the top clock. What frequency will a detector co-located with the top clock measure when it receives the light flash? Einstein analyzed this scenario in an inertial frame in which the rocket is momentarily at rest at the instant the bottom clock emits the flash. By the time the flash reaches the top clock, the rocket has accelerated upward by some amount, so the top clock is moving away from the light flash, and therefore the detector will measure the frequency to be Doppler redshifted. By the equivalence principle, the same thing will happen if we have two clocks in an enclosed room at rest in a gravitational field: light emitted from the bottom clock will be redshifted when it is measured at a detector co-located with the top clock.

So far we haven't said anything directly about time; but consider what the frequency of the light pulse actually means. If we treat the pulse as a classical wave (which has limitations, but it will do for this discussion), then the frequency is just the rate at which wave fronts are emitted or detected. So consider: we have a light pulse consisting of some fixed number of wave fronts, which takes some time ##T_{\text{bottom}}## to be emitted (the number of wave fronts divided by the emission frequency) and some time ##T_{\text{top}}## to be detected (the number of wave fronts divided by the detected frequency). So we have ##T_{\text{bottom}} = N / \omega_{\text{emitted}}## and ##T_{\text{top}} = N / \omega_{\text{detected}}##, and since ##\omega_{\text{emitted}} > \omega_{\text{detected}}##, we must have ##T_{\text{bottom}} < T_{\text{top}}##. That is, the redshift implies that there is a difference in "rate of time flow" between the two clocks, since they register different elapsed times for a fixed number of wave fronts.

As I said, this is all just a simple thought experiment to make it seem plausible that gravity could affect time. But to really understand why, you'll need to spend the time learning the details.
 
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Drakkith
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It always amazes me how something as simple as an accelerating rocket and two clocks is a profound thought experiment for gravity and time.
 
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As Drakkith said, to really understand this, you need to spend considerable time learning SR and GR. However, there is a simple thought experiment that might at least help you to see why it's worth making that effort...

Something has always bothered me about this thought experiment. The equivalence principle upon which it depends is only valid for a small enclosure where gravity is essentially constant i.e. no tidal effects. Yet we end up concluding that the time at the top of the enclosure is different from that at the bottom, implying gravity is different in these two locations and therefore contradicting the assumptions of the equivalence principle. If as we assume gravity is constant in the enclosure, then the time would be the same everywhere inside it, no?
 
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PeterDonis
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The equivalence principle upon which it depends is only valid for a small enclosure where gravity is essentially constant i.e. no tidal effects.

Yes.

Yet we end up concluding that the time at the top of the enclosure is different from that at the bottom, implying gravity is different in these two locations

No, it doesn't. It only implies that the "rate of time flow" is different. The argument based on the equivalence principle does not require there to be any change in acceleration from the bottom to the top of the enclosure; it goes through perfectly well if the bottom and top are both accelerated exactly the same, which means the "acceleration due to gravity" of a free-falling object dropped at the bottom is the same as that of one dropped at the top, i.e., there is no change in gravity from bottom to top.

If as we assume gravity is constant in the enclosure, then the time would be the same everywhere inside it, no?

No. See above. Basically, the difference in time flow is due to a difference in altitude in the (constant) gravitational field between the bottom and top, not due to a difference in the field itself.
 
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Thanks for clearing that up.
 
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In the above mentioned models time is not independently defined. Time is something that clocks measure. Gravity does not directly effect time. It effects how the clocks that measure time function.
 
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phinds
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In the above mentioned models time is not independently defined. Time is something that clocks measure. Gravity does not directly effect time. It effects how the clocks that measure time function.
No, it does not. Regardless of whether you are traveling at near c relative to me or you are in a much deeper gravity well than I am, your clock ticks at exactly the same one second per second as mine does. What is it DOES affect is our path through space-time, which determines how MANY ticks our respective clocks perform so that in both of those instances if we meet up again we will disagree on how much time has passed and we will both be right.
 
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In order for your example to be complete you have to describe how these clocks are keeping time. What is ticking and how is it being measured? You are just assuming that they both "tick" the same.
 
  • #15
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Time is something that clocks measure.
Yes, and this one of Einstein's most powerful insights: "Time is what a clock measures".
In this context, a "clock" is any time-dependent process: The graying of my hair, the passage of sand through an hourglass, the movement of the earth on its axis and about the sun, the decay of radioactive nuclei, the growth of tree rings, the swings of a pendulum in a traditional clock, the oscillations of a carefully designed quartz crystal.... They're all "clocks", although some have much greater accuracy and resolution than others.
Gravity does not directly affect time. It affects how the clocks that measure time function.
This is not right, although it is a fairly common misunderstanding. Consider that all of the clocks I described above display the same amount of gravitational time dilation, even though they operate by very different mechanisms (chemical, biological, electromagnetic, nuclear, mechanical). It would be weird if gravity affected how all of these clocks work by exactly the same amount, especially because in some cases (the quartz crystal and nuclear decay, for example) there is no remotely plausible theory for how a gravitational field could have any effect at all on the mechanism.
Another consideration is that gravitational time dilation is not a function of the local gravitational forces. It is a function of the difference in the gravitational potential between the locations of the two clocks. If I place two clocks in earth orbit at different heights, both clocks will be in freefall and experience no gravitational force at all, but there will still be gravitational time dilation and exactly as much as would be produced if either or both were held at rest and hence feeling substantial force (as in the Pound-Rebka) experiment, where both clocks were on the surface of the earth so subject to a force of 1G).

The simplest experimentally supported explanation for these facts is that gravity does "affect time" so that all clocks, regardless of construction and susceptibility to gravitational effects, are measuring this effect; because they're all measuring the same thing, they're all equally affected.
 
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Just one comment on "why": physics cannot answer "why" questions on a fundamental level.
The description with curved spacetime leads to very accurate descriptions. It does not mean the universe would have to be like that, and it does not explain at all why curved spacetime is a good description. The theory was developed to match experimental observations, not the other way round.
 
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  • #17
phinds
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In order for your example to be complete you have to describe how these clocks are keeping time. What is ticking and how is it being measured? You are just assuming that they both "tick" the same.
I am assuming that they are some kind of standard clock. This is a normal assumption in such situations.
 

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