# Time in gravitational reference frame?

• I
Hi,
so Newton said that gravity was like or equivalent to a force?

When I learnt about SR we were talking about the passing of time as defined by a photon bouncing between two parallel mirrors. So when we're sitting our two parallel mirrors in a gravitational field, even though I suppose mathematically the experience of sitting in the field is like accelerating, the mirrors aren't actually moving. So why does the photon bouncing around in them see time change? If the mirrors aren't actually moving?

Thanks

Always provided that your reference frame is small enough, locally there will be no change whatsoever in the way time is measured and experienced; your light clock will continue to operate just as it always did, i.e. it will continue to measure exactly "one second per second". Time dilation becomes apparent only if you step outside your small local frame, and compare the light clock to some other reference clock which is in a different frame - you will then notice differences in the clock readings.

Time dilation is not something that involves local "changes" of any kind, but rather it is a relationship between at least two reference frames in space-time. You can never experience time dilation by using a single, isolated clock. In essence, time dilation is a measure of how events are related in space-time, and that relationship is affected by the presence of sources of energy-momentum - that is an aspect of what we call gravity.

peety
A.T.
Hi,
so Newton said that gravity was like or equivalent to a force?

When I learnt about SR we were talking about the passing of time as defined by a photon bouncing between two parallel mirrors. So when we're sitting our two parallel mirrors in a gravitational field, even though I suppose mathematically the experience of sitting in the field is like accelerating, the mirrors aren't actually moving. So why does the photon bouncing around in them see time change? If the mirrors aren't actually moving?

Thanks
In non-inertial frames time passes at different rates depending on position, not just movement.

Dale
Ibix
2020 Award
so Newton said that gravity was like or equivalent to a force?
Newton described gravity as a force. It's not at all clear how light and gravity interact in a Newtonian picture. Einstein describes gravity in terms of curvature of spacetime.

When I learnt about SR we were talking about the passing of time as defined by a photon bouncing between two parallel mirrors. So when we're sitting our two parallel mirrors in a gravitational field, even though I suppose mathematically the experience of sitting in the field is like accelerating, the mirrors aren't actually moving. So why does the photon bouncing around in them see time change? If the mirrors aren't actually moving?
What do you mean by the mirrors "not actually moving"? According to a free-falling observer the mirrors (and the ground) are accelerating upwards. This is a particular case of a more general point - "not actually moving" is not a well defined concept, not even in Newtonian physics.

You will not see any difference in operation of your light clock, whether you place it at the bottom of a mountain or the top. However, if you use a telescope to observe some other guy's clock at the top of the mountain from the bottom, you'll notice his clock ticking fast. You can interpret this as being because you are in an accelerating rocket, and are "catching up" with the other guy's clock (more precisely, compared to some inertial frame you were going faster at the second tick than the first) or because you are deeper in a gravitational field and are subject to time dilation due to the curvature of spacetime. But neither interpretation involves the photons in the light clock "seeing time change".

Thanks for the replies!

Ok so I'm floating in space (minding my own business as a non-interial frame of reference), then a planet with a photon clock on it falls towards me. As the planet is falling towards me the mirror face that is furthest from the planet's surface is moving away from the planet, towards me, so it will take longer for the photon to reach that top mirror? Thus, I see the planet's clock tick slower than the photonic-Fob watch chained to my pocket?
So is that one ANALOGY for how it works, but the actual explanation is that the more distorted spacetime is from a large mass, the 'time' part of spacetime gets accelerated from the perspective of a non-enertial frame of reference?

[Mentor's note: some personal theorizing in violation of the Physics Forums rules has been removed from this post]

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Ibix
2020 Award
Ok so I'm floating in space (minding my own business as a non-interial frame of reference),
If you're floating in space then you're in an inertial frame. The simple test is: if I stand on a spring balance, does it say I weigh anything? If the answer is no, I'm free falling and in an inertial frame.

then a planet with a photon clock on it falls towards me. As the planet is falling towards me the mirror face that is furthest from the planet's surface is moving away from the planet, towards me, so it will take longer for the photon to reach that top mirror? Thus, I see the planet's clock tick slower than the photonic-Fob watch chained to my pocket?
That's a slightly different scenario from two clocks in a tower. But assuming you are only moving radially with respect to the Earth, yes. If you're moving tangentially as well, I think it depends on how deep in the field you and the other clock are (I think).

So is that one ANALOGY for how it works, but the actual explanation is that the more distorted spacetime is from a large mass, the 'time' part of spacetime gets accelerated from the perspective of a non-enertial frame of reference?
I don't think analogy is the right word. "I'm in a rocket" and "I'm on the surface of a planet" are two competing hypotheses. Locally, both are equivalent. There's no way to tell the difference, whereas an analogy is an approximate description that's evocative rather than precise. If you start to look over a larger region you will notice that the apparent g-field is uniform or not, which will tell you whether you are in curved spacetime or not, and the "in a rocket" explanation is either falsified or not.

I don't think that "the 'time' part of spacetime gets accelerated" makes any sense. How could you describe time being accelerated? What would you differentiate, and with respect to what?

[Mentor's note: quotes of deleted text from a previous post have been removed]

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PeterDonis
Mentor
2020 Award
So is that one ANALOGY for how it works, but the actual explanation is that the more distorted spacetime is from a large mass

No, the analogy is not correct. Your analogy is with a light clock in flat spacetime, but your actual scenario is in curved spacetime (because of the presence of the planet). Flat spacetime and curved spacetime are not the same.

You are also confusing inertial motion with accelerated motion. In the usual light clock scenario in flat spacetime, the light clock is moving inertially. In the usual equivalence principle scenario, the observer is accelerated--he feels weight. Locally he can't tell whether the weight he feels is because he is inside a rocket whose engine is accelerating it, or inside a room at rest on the surface of a planet, with the planet's surface pushing up on him. But neither of those cases is the same as moving inertially. Similar remarks would apply to a light clock sitting on the surface of a planet--you would have to analyze it as an accelerated light clock, not an inertial light clock.

I'd just like a little clarity about the right terminology. Alfred is at rest in a train at a station. On his left Henry is in a train that suddenly accelerates forward with the result that he spills his coffee. Henry concludes that he is at rest in a gravitational field that results in the acceleration backwards of Alfred, along with his train and the platform. None of the passengers in Alfred's train spill their coffee because... they are in free fall, they are in an inertial frame?

PeterDonis
Mentor
2020 Award
Alfred is at rest in a train at a station.

Just to be clear, we are treating the station as floating somewhere out in space, so there is no Earth gravity involved. (Most thought experiments gloss over this, but for this one we need to make it explicit.) The station is in free fall, at rest in an inertial frame.

On his left Henry is in a train that suddenly accelerates forward with the result that he spills his coffee. Henry concludes that he is at rest in a gravitational field

Yes. And being at rest in a gravitational field, he feels acceleration, and can observe acceleration-related effects, such as spilling his coffee.

that results in the acceleration backwards of Alfred, along with his train and the platform.

That results in the coordinate acceleration backwards of Alfred, etc. But coordinate acceleration is not the same as proper acceleration, which is what Henry is experiencing. The term "acceleration" is often used sloppily, in a way that ignores this crucial distinction.

None of the passengers in Alfred's train spill their coffee because... they are in free fall, they are in an inertial frame?

Yes. And they can tell because they don't feel acceleration, whereas Henry does. The felt acceleration, or lack thereof, is an invariant, and doesn't change if we change frames, or if we introduce "gravitational fields" because we've chosen a non-inertial frame (such as Henry's frame when he spills his coffee).

peety
Just to be clear, we are treating the station as floating somewhere out in space, so there is no Earth gravity involved. (Most thought experiments gloss over this, but for this one we need to make it explicit.) The station is in free fall, at rest in an inertial frame.

Yes. And being at rest in a gravitational field, he feels acceleration, and can observe acceleration-related effects, such as spilling his coffee.

That results in the coordinate acceleration backwards of Alfred, etc. But coordinate acceleration is not the same as proper acceleration, which is what Henry is experiencing. The term "acceleration" is often used sloppily, in a way that ignores this crucial distinction.

Yes. And they can tell because they don't feel acceleration, whereas Henry does. The felt acceleration, or lack thereof, is an invariant, and doesn't change if we change frames, or if we introduce "gravitational fields" because we've chosen a non-inertial frame (such as Henry's frame when he spills his coffee).
Thanks - that's very clear and helpful. I always thought setting these thought experiments on the earth confused things, but I like familiar territory.

Its been so long that I'm looking over what I wrote almost as an impartial observer.
I don't think that "the 'time' part of spacetime gets accelerated" makes any sense. How could you describe time being accelerated? What would you differentiate, and with respect to what?

[Mentor's note: quotes of deleted text from a previous post have been removed]

Yeah I agree with you. I think what I was saying was: it's like time is a 'thing that happens' and when spacetime is warped, the time thing just does it's thing, but faster. However I agree, that time is only 'a thing' when relative to more than one reference frame, so yeah you're right.

Also, For the life of me I can't remember what I wrote, do you remember what my 'personal theorising' was?

So if I'm in a rocket accelerating at 9.8m/s/s, does that locally warp spacetime?

No, the analogy is not correct. Your analogy is with a light clock in flat spacetime, but your actual scenario is in curved spacetime (because of the presence of the planet). Flat spacetime and curved spacetime are not the same.

You are also confusing inertial motion with accelerated motion. In the usual light clock scenario in flat spacetime, the light clock is moving inertially. In the usual equivalence principle scenario, the observer is accelerated--he feels weight. Locally he can't tell whether the weight he feels is because he is inside a rocket whose engine is accelerating it, or inside a room at rest on the surface of a planet, with the planet's surface pushing up on him. But neither of those cases is the same as moving inertially. Similar remarks would apply to a light clock sitting on the surface of a planet--you would have to analyze it as an accelerated light clock, not an inertial light clock.
could you please explain what inertial motion is? Is it just moving at a constant speed?
and the difference between coordinate acceleration and proper acceleration?

Thanks

Ibix
2020 Award
Also, For the life of me I can't remember what I wrote, do you remember what my 'personal theorising' was
It'd just get deleted again even if I could remember.

So if I'm in a rocket accelerating at 9.8m/s/s, does that locally warp spacetime?
No. In both cases you feel a "force of gravity" because the floor is pushing you out of your natural free-fall path. The curvature of spacetime is why you are falling into the floor when you're on a planet. In the rocket, you are falling into the floor because there's a rocket motor pushing the floor upwards. No spacetime curvature needed.

could you please explain what inertial motion is? Is it just moving at a constant speed?
Motion with no forces acting on you. So rockets off, no electromagnetic fields, not moving through a medium (remember gravity is not a force in relativity).

and the difference between coordinate acceleration and proper acceleration?
Proper acceleration is something you measure with an accelerometer. Stand on a weighing scale. Do you weigh anything? If yes, you're undergoing proper acceleration.

Coordinate acceleration is when the rate of change of your coordinates isn't constant. If I pick a coordinate system where x=0 here, x=1 is 1m away, x=2 is 1.5m away and x=3 is 1.75m away, then you walk along at constant speed (no proper acceleration - hold a weighing scale vertically in front of you and ask if it shows anything) then you get from x=1 to x=2 in less time than from x=0 to x=1. But this is just an artifact of the coordinate system, not anything real.

That was obviously a contrived example. But non-trivial coordinate systems do arise in curved spacetime and it's important to distinguish between "my coordinate system isn't the best for what I want to measure" and "I am actually accelerating".

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PeterDonis
Mentor
2020 Award
The curvature of spacetime is why you are falling into the floor when you're on a planet.

More precisely, the curvature of spacetime is why people all over the planet can be "falling into the floor", even though "into the floor" is a different direction in different parts of the planet. There's no way to reproduce that global effect in an accelerating rocket, no matter how large you make it.

Proper acceleration is something you measure with an accelerometer.

And just to add a clarification, this measurement is how we can tell, physically, whether or not something is moving inertially. If an accelerometer attached to an object reads zero, that object is moving inertially; if not, not.

The curvature of spacetime is why you are falling into the floor when you're on a planet

What if our planet were an (almost) infinite plane? Would the curvature of spacetime still be the reason why we are falling into the floor?

More precisely, the curvature of spacetime is why people all over the planet can be "falling into the floor", even though "into the floor" is a different direction in different parts of the planet. There's no way to reproduce that global effect in an accelerating rocket, no matter how large you make it.
Could you reproduce that global effect with millions of accelerating rockets, one for each person?

Ibix
2020 Award
What if our planet were an (almost) infinite plane? Would the curvature of spacetime still be the reason why we are falling into the floor?
I'm told you can't make a uniform gravitational field. I think that this is because there are limits to material strength in relativity that you can't ignore and a disc bigger than a certain diameter will simply collapse under its own weight. So there's always curvature - even at the symmetry axis of such a disc there are non-zero second derivatives.

Might be worth waiting for (e.g.) @PeterDonis to confirm that...

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Nugatory
Mentor
I'm told you can't make a uniform gravitational field. I think that this is because there are limits to material strength in relativity
It's more than that - a uniform gravitational field is not a vacuum solution of the Einstein field equations, you can't arrange matter in a way that produces a uniform field around it.

Nugatory
Mentor
Could you reproduce that global effect with millions of accelerating rockets, one for each person?
You could reproduce the behavior in which dropped objects fall towards the floor of the ship they're in, no matter where on the sphere the ship is. However, objects at rest on the floors of different spaceships will move apart from one another, and this doesn't happen in the gravitational case - so still no global equivalence.

Ibix
2020 Award
It's more than that - a uniform gravitational field is not a vacuum solution of the Einstein field equations, you can't arrange matter in a way that produces a uniform field around it.
I was trying to work out why not. Symmetry suggests the good old infinite thin plane ought to produce a similarly symmetric field, but it would also have to have infinite extent in time too. I presume there's some reason why that doesn't work.

PeterDonis
Mentor
2020 Award
Could you reproduce that global effect with millions of accelerating rockets, one for each person?

No, because the rockets would be accelerating in different directions and so they would move apart, whereas people all standing on the surface of the Earth are at rest relative to each other--they don't move apart.

phinds
Gold Member
What if our planet were an (almost) infinite plane? Would the curvature of spacetime still be the reason why we are falling into the floor?
Yes. What else do you think it could be?

EDIT: that is, in General Relativity (which describes the real world more correctly than Newtonian mechanics) the curvature of spacetime IS gravity.

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PeterDonis
Mentor
2020 Award
Symmetry suggests the good old infinite thin plane ought to produce a similarly symmetric field

It does in Newtonian gravity, but IIRC there isn't a corresponding consistent solution in GR.

I'm told you can't make a uniform gravitational field.

From what I have researched, I am convinced that what you were told is true. There is no uniform gravitational field, and (as I have seen here at PF and elsewhere) gravity is curvature. These two statements, that there is no uniform gravitational field, and that gravity is curvature, are consistent with the statement made by PeterDonis in another post, which is that all curvature is tidal. What is not consistent (or at least is a point of confusion for me) is that people seem to want to qualify certain types of gravity as due to curvature, and other types as not due to curvature, as you have done in post #12, when you say that no spacetime curvature is needed in the case of the rocket.

I could be wrong, but it seems to me that you are saying (and PeterDonis when he points out that globally the two situations are different) that the non-uniformity in the horizontal direction (tangential to the planet) is the cause of gravity for the vertical direction (radial from the center of the planet). That is why I brought up the example of the (almost) infinite plane. I said “almost” because it could not be perfectly infinite, and it would need some depth, so we have an extremely large planet which is not spherical. It’s true that the field is not perfectly uniform in the vertical direction, but in the horizontal direction it is, and it seems to me that the tidal gravity of the kind that you are referring to (that which is due to the spherical nature of the planet) is completely removed. In this scenario, is there a difference, even globally, between the case of the rocket or at the surface of the planet? Objects dropped to the floor in either case will not approach each other.

Yes. What else do you think it could be?

You misunderstand. I agree that spacetime curvature is the reason for gravity in the case of the infinite plane. See my post #23 for the reason I brought it up.

PeterDonis
Mentor
2020 Award
gravity is curvature

More precisely, tidal gravity is spacetime curvature. But the term "gravity" can have meanings other than "tidal gravity". For example, in the case of the accelerating rocket, the "gravity" observed is "acceleration due to gravity" (or more precisely coordinate acceleration due to gravity), which can, as that case illustrates, be present even in flat spacetime. So the issue you are seeing is one of terminology, not physics; the term "gravity" can have different meanings in different contexts, so you have to be clear about which meaning is being used.

the non-uniformity in the horizontal direction (tangential to the planet) is the cause of gravity for the vertical direction (radial from the center of the planet)

No; both of them are manifestations of tidal gravity, i.e., spacetime curvature. Neither one causes the other.

It’s true that the field is not perfectly uniform in the vertical direction, but in the horizontal direction it is

As I and others have commented, AFAIK there is no valid solution to the Einstein Field Equation that has this property. However, we can consider the Newtonian version, at least as some sort of approximate case.

it seems to me that the tidal gravity of the kind that you are referring to (that which is due to the spherical nature of the planet) is completely removed

Not necessarily; you would have to look at how the field varies in the vertical direction. Only one particular kind of vertical variation is consistent with zero tidal gravity, i.e, zero spacetime curvature.