Gravity vs Acceleration: The Impact on Clocks in Reference Frame R

In summary: The same happens to the clock under G force.This is not equivalent. If you apply a force to a stationary clock, the clock will go slower. However, if you apply a force to a moving clock, the clock will go slower according to the principle of relativity, but not according to the law of gravity.
  • #36
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  • #37
calinvass said:
the mistake was that the horizontal line from SRL should've intersected the dotted blue line not the helping acceleration path

Yes.

calinvass said:
that path goes beyond c

It shouldn't if you generated it correctly. You need to use the ##\cosh## and ##\sinh## functions.
 
  • #38
Yes, I understand. I've used constant Newtonian acceleration in flat spacetime but that is not the trajectory in frame F0.
 
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  • #39
A.T. said:
It's not an illusion, and it's not symmetrical like kinetic time dilation.
Please explain what you mean by not symmetrical.
 
  • #40
David Lewis said:
Please explain what you mean by not symmetrical.
Gravitational time dilation is asymmetrical in the sense that if B's clock is running slow relative to A's clock as observed by A, it is also running slow (or equivalently, A's clock is running faster) as observed by B. In physical terms: If B is deeper in a gravity well than A, and they exchange light signals from identically constructed (so the emission frequencies are the same) light sources B will receive a light signal that is blueshifted to a higher frequency than his own source, while A will receive a light signal that is redshifted to a lower frequency than his own source.

The speed-based time dilation is symmetrical: as observed by A, B's clock is running slow relative to A's clock but as observed by B, A's clock is running slow relative to B's clock. If they exchange light signals they will both receive either blue-shifted or red-shifted signals according to whether they are approaching one or another or moving apart.
 
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  • #41
Many thanks. Is it correct to say gravitational time dilation is asymmetric under interchange of observers?
 
  • #42
David Lewis said:
Many thanks. Is it correct to say gravitational time dilation is asymmetric under interchange of observers?

Yes, it's asymmetric.

But it's actually a little complicated as to what "gravitational time dilation" means. What's definitely true is that if you use a curvilinear, noninertial coordinate system, then in general the value of [itex]\frac{d \tau}{dt}[/itex] (where [itex]\tau[/itex] is the elapsed time on a standard clock, and [itex]t[/itex] is coordinate time) will be position-dependent, as well as velocity-dependent, while in SR, using inertial Cartesian coordinates, it is only velocity-dependent.
 
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  • #43
So a satellite clock, having higher gravitational potential, would appear to tick faster than an Earth clock, and (assuming the satellite is moving with respect to the Earth clock) SR time dilation would make the satellite clock appear to tick slower than the Earth clock. I suppose you would add the two effects together to arrive at the net dT/dt.
 
  • #44
David Lewis said:
So a satellite clock, having higher gravitational potential, would appear to tick faster than an Earth clock, and (assuming the satellite is moving with respect to the Earth clock) SR time dilation would make the satellite clock appear to tick slower than the Earth clock. I suppose you would add the two effects together to arrive at the net dT/dt.
Yes, and we have several older threads that show how to do this calculation. Getting it right is kinda important for the GPS system...
 
  • #45
There is also frame dragging effect thus the orbiting rotation direction or whether it is geostationary should influence the difference in tick rates.
 
  • #46
PeterDonis said:
if we have two observers inside a rocket accelerating in flat spacetime ("accelerating" meaning "experiencing proper acceleration"), at rest relative to each other (as measured by them exchanging round-trip light signals and seeing that the round-trip travel time by each of their clocks remains constant), the observer at the bottom of the rocket will be time dilated (clock running slower) relative to the observer at the top (as measured by noting the elapsed time on both of their clocks between two successive round-trip light signals).
Reading this old thread I would ask for a clarification: observer A sends a light signal reflected back from B and using his own clock measures the round-trip travel time; the observer B does the same. If the results of both measurements remain constant then we claim both observers are at rest each other.

Furthermore if in the above procedure each observer sends/encodes in the reflected light signal the reading of his own clock (when the signal is reflected back), the receiving observer can evaluate the difference between the encoded times and the readings of his own clock between the receipts of two successive round-trip light signals.

This way both observers will evaluate a non-zero difference (i.e. the observer at the bottom will be time dilated).

Is the above correct ? Thank you.
 
  • #47
cianfa72 said:
Reading this old thread I would ask for a clarification: observer A sends a light signal reflected back from B and using his own clock measures the round-trip travel time; the observer B does the same. If the results of both measurements remain constant then we claim both observers are at rest each other.

Furthermore if in the above procedure each observer sends/encodes in the reflected light signal the reading of his own clock (when the signal is reflected back), the receiving observer can evaluate the difference between the encoded times and the readings of his own clock between the receipts of two successive round-trip light signals.

This way both observers will evaluate a non-zero difference (i.e. the observer at the bottom will be time dilated).

Is the above correct ? Thank you.
You could do it that way. Alternatively, each observer sends out a signal once per second, say. They each receive their own signals back at one second intervals. But, receive the other's signals with a longer or shorter time interval.
 
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  • #48
PeroK said:
Alternatively, each observer sends out a signal once per second, say.
yes, once per second according their own clocks.

PeroK said:
They each receive their own signals back at one second intervals. But, receive the other's signals with a longer or shorter time interval.
Again, as measured by their own clocks.
 
  • #49
cianfa72 said:
Reading this old thread I would ask for a clarification: observer A sends a light signal reflected back from B and using his own clock measures the round-trip travel time; the observer B does the same. If the results of both measurements remain constant then we claim both observers are at rest each other.
Quite the opposite. All inertial observers say that there is some relative motion. They might call it "length contraction motion". I am guessing that "we" are inertial observers.
cianfa72 said:
This way both observers will evaluate a non-zero difference (i.e. the observer at the bottom will be time dilated).
Yes, according to those non-inertial people the bottom people are time dilated. Different inertial observers have different opinions about the time dilation.
 
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  • #50
jartsa said:
cianfa72 said:
Reading this old thread I would ask for a clarification: observer A sends a light signal reflected back from B and using his own clock measures the round-trip travel time; the observer B does the same. If the results of both measurements remain constant then we claim both observers are at rest each other.
Quite the opposite. All inertial observers say that there is some relative motion. They might call it "length contraction motion". I am guessing that "we" are inertial observers
If "we" are inertial observers, you are right, but I suspect what cianfa72 meant to say was "each observer claims the other is at rest relative to themself", and, in that case, that is true.

EDIT: Just to clarify possibly ambiguous language:
  • Observer A claims that Observer B is at rest relative to Observer A
  • Observer B claims that Observer A is at rest relative to Observer B
Both these claims are true; they can be taken as a definition of what "at rest relative to a non-inertial observer" means.
 
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  • #51
DrGreg said:
If "we" are inertial observers, you are right, but I suspect what cianfa72 meant to say was "each observer claims the other is at rest relative to themself", and, in that case, that is true.
That's what we all meant! Starting with:
PeterDonis said:
The precise way of putting it is this: if we have two observers inside a rocket accelerating in flat spacetime ("accelerating" meaning "experiencing proper acceleration"), at rest relative to each other (as measured by them exchanging round-trip light signals and seeing that the round-trip travel time by each of their clocks remains constant), the observer at the bottom of the rocket will be time dilated (clock running slower) relative to the observer at the top (as measured by noting the elapsed time on both of their clocks between two successive round-trip light signals).
 
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  • #52
DrGreg said:
EDIT: Just to clarify possibly ambiguous language:
  • Observer A claims that Observer B is at rest relative to Observer A
  • Observer B claims that Observer A is at rest relative to Observer B
Both these claims are true; they can be taken as a definition of what "at rest relative to a non-inertial observer" means.

Last sentence is ambiguous. It should be said like this: Both these claims are true; they can be taken as a definition of what "at rest relative to a non-inertial observer, according to the observer himself" means.

Relative to what, and according to who.
 
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  • #53
jartsa said:
Last sentence is ambiguous. It should be said like this: Both these claims are true; they can be taken as a definition of what "at rest relative to a non-inertial observer, according to the observer himself" means.

Relative to what, and according to who.
I think in relativity, when you say "A is at rest relative to B" it is automatically assumed it's "...according to B". Or in other words, it means "A is at rest in B's coordinate system". I think it's a bad idea to say "A is at rest relative to B according to C". I'm not even sure it has a well-defined meaning. It would be better to say "A and B have the same velocity relative to C", if that's what you mean, or "A and B have a constant separation as measured by C". The details depend on exactly how C chooses to do the measurement. It may also depend on whether spacetime is curved or flat. ("Same velocity" doesn't always make sense.)
 
  • #54
DrGreg said:
I think in relativity, when you say "A is at rest relative to B" it is automatically assumed it's "...according to B".
Actually, I think the proper meaning of "at rest relative to" should be that it is an invariant: the best way to say it is "A and B are at rest relative to each other", and this is to be taken as meaning that, for example, round-trip light signals between them have a constant round-trip travel time, according to either of their clocks, which is an invariant, independent of any choice of coordinates. That is the meaning @cianfa72 was using, and I think it's correct.
 
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  • #55
jartsa said:
All inertial observers say that there is some relative motion.
In coordinate terms, yes. But what invariant indicates "relative motion" in this case? Note that, per my previous post just now, there is an invariant (timing of round-trip light signals between A and B) that says there is no "relative motion".
 
  • #56
PeterDonis said:
In coordinate terms, yes. But what invariant indicates "relative motion" in this case? Note that, per my previous post just now, there is an invariant (timing of round-trip light signals between A and B) that says there is no "relative motion".

Velocity reading on an inertial navigation system bolted on the rocket floor minus velocity reading on an inertial navigation system bolted on the rocket ceiling. That number is the same in all frames.
 
  • #57
jartsa said:
Velocity reading on an inertial navigation system bolted on the rocket floor minus velocity reading on an inertial navigation system bolted on the rocket ceiling. That number is the same in all frames.
You need to compare readings taken at the same time, though. What simultaneity condition are you using? You can get growing, shrinking, or steady distances depending on your choice.
 
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  • #58
jartsa said:
Velocity reading on an inertial navigation system bolted on the rocket floor
Btw, what does a such inertial navigation system actually measure ?
 
  • #59
cianfa72 said:
Btw, what does a such inertial navigation system actually measure ?
The proper acceleration and possibly rotation rates with respect to the Fermi-normal axes, all as functions of the instrument's proper time, and integrals thereof.
 
<h2>1. What is the difference between gravity and acceleration?</h2><p>Gravity is a force that attracts objects towards each other, while acceleration is the rate of change of an object's velocity. In other words, gravity is a force that causes acceleration.</p><h2>2. How does gravity affect clocks in reference frame R?</h2><p>Gravity can affect clocks in reference frame R by causing time dilation, which means that time passes slower in areas with stronger gravitational fields. This is due to the curvature of spacetime caused by gravity.</p><h2>3. What is the relationship between gravity and time dilation?</h2><p>The relationship between gravity and time dilation is that the stronger the gravitational field, the greater the time dilation. This means that time passes slower in areas with stronger gravitational fields.</p><h2>4. Can acceleration also cause time dilation?</h2><p>Yes, acceleration can also cause time dilation. This is known as the principle of equivalence in Einstein's theory of general relativity. Acceleration can create the same effects on time as gravity does.</p><h2>5. How does the impact of gravity and acceleration on clocks affect our daily lives?</h2><p>The impact of gravity and acceleration on clocks is not noticeable in our daily lives because the differences in time dilation are extremely small. However, it is important to consider these effects in certain situations, such as in GPS systems, where accurate timekeeping is crucial for determining location.</p>

1. What is the difference between gravity and acceleration?

Gravity is a force that attracts objects towards each other, while acceleration is the rate of change of an object's velocity. In other words, gravity is a force that causes acceleration.

2. How does gravity affect clocks in reference frame R?

Gravity can affect clocks in reference frame R by causing time dilation, which means that time passes slower in areas with stronger gravitational fields. This is due to the curvature of spacetime caused by gravity.

3. What is the relationship between gravity and time dilation?

The relationship between gravity and time dilation is that the stronger the gravitational field, the greater the time dilation. This means that time passes slower in areas with stronger gravitational fields.

4. Can acceleration also cause time dilation?

Yes, acceleration can also cause time dilation. This is known as the principle of equivalence in Einstein's theory of general relativity. Acceleration can create the same effects on time as gravity does.

5. How does the impact of gravity and acceleration on clocks affect our daily lives?

The impact of gravity and acceleration on clocks is not noticeable in our daily lives because the differences in time dilation are extremely small. However, it is important to consider these effects in certain situations, such as in GPS systems, where accurate timekeeping is crucial for determining location.

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