# Questions regarding traveling speed in time and gravity as a force

• I
• ffp
In summary, the speaker, an engineer with knowledge of physics and calculus, has limited understanding of relativity from university and has gained most of their knowledge through personal research online. They are skeptical about some concepts they have encountered, such as the idea that everything travels at the speed of light, and do not see empirical evidence or logical sense in this claim. They also question the explanation of gravity as the curvature of spacetime and believe it is treated as a spatial dimension, which they do not agree with.

#### ffp

I am an Engineer, so I have some knowledge about physics and calculus. I've seen relativity in university years ago but only briefly. The majority of my knowledge in SR and GR, which isn't much, are from reading, studying and searching online myself.

I have seen some definitions that I am not sure it's true, due to internet being a pace full of wrong facts. So, here I ask my doubts about relativity:

1- I've seen more than once people saying that we (as everything in the universe) travel at the speed of light. Just that inertial objetct travel with the speed of light in time and moveing objects travel with less speed in time and more in space. I understand that spacetime interval are invariant, but they aren't necessarily always equal to c, right? Also, the ct time-component of the metric are a convention thing, right? So that this coordinate get a unit of space? Anyway, I've seen no good reason or proof to believe that everything travel with c in spacetime.

2- I know that in GR gravity is not a force, but the curvatre of spacetime. However, while I can see why a moving object would be attracted to a massive object like the Earth (follwing the geodesic path), I can't understand why a still object would start moving toward the ground, if there isn't a force pulling it to Earth. I've seen videos and explanations saying that this happens due to the curvature of spacetime, especially the time axis and that since we are always traveling in time, and the time axis is cuved due to the massive mass of a planet, then we travel toward the Earth
I think this is a terrible explanation, because they are treating time as a spatial dimension, and it isn't. As i understand, the "bending" or "curving" of time means time passing faster or slower to an object, and not affecting the object position in space. So, if someone could give me a light about this one would be very nice.

ffp said:
Anyway, I've seen no good reason or proof to believe that everything travel with c in spacetime.
Neither do I. Except mass zero particles nothing moves with speed c.

vanhees71
ffp said:
I've seen more than once people saying that we (as everything in the universe) travel at the speed of light.
The "everything travels at ##c##" comes from the standard normalisation of the four velocity to have length ##c##. Interpreting that choice of normalisation as meaning "everything travels at ##c##" is circular, yes - all four velocities have the same magnitude because that's how they are defined. And it's not true for light anyway, where the tangent vector to its worldline is null so cannot be normalised to length ##c##.

However, the "##ct## thing" is not just a convention. Essentially, ##c## is a natural conversion factor between units of time and units of length. Not including it, or using a different speed, is analogous to taking a rectangle that's 1m on one side and 1000mm on the other and asserting that the diagonal must therefore be ##\sqrt{1^2+1000^2}## long.

ffp said:
I can't understand why a still object would start moving toward the ground, if there isn't a force pulling it to Earth.
Unfortunately the explanations you've seen are more or less correct. The point is that even when you aren't moving (by some definition) you are advancing in time. And spacetime near a mass is curved, and the unaccelerated path of an object in that spacetime gets closer to the object as a result.
ffp said:
I think this is a terrible explanation, because they are treating time as a spatial dimension, and it isn't.
Time is a dimension, but it is distinct from spatial ones. There is some crosstalk, though, in that the direction in spacetime that I call "time" you might call a mixture of time and some spatial direction.

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Dale
ffp said:
As i understand, the "bending" or "curving" of time means time passing faster or slower to an object, and not affecting the object position in space.
In weak limit of gravity, metric component ##g_{00}## and gravity potential have relation ##g_{00}=1+2V## where ##V=-\frac{GM}{Rc^2}## for our daily ground Earth case.

##g_{00}## decides not only time passing pace but also potential of attracting acceleration i.e.
In lower place time passing slower and gravity potential is lower. In higher place time passing faster and gravity potential is higher. Bodies even at still get acceleration of ##-\nabla V##.

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Dale
anuttarasammyak said:
In weak limit of gravity, metric component ##g_{00}## and gravity potential have relation ##g_{00}=1+2V## where ##V=-\frac{GM}{Rc^2}## for our daily ground Earth case.
That much is always true (outside an event horizon, and assuming your zeroth basis vector is the timelike Killing vector). Where the weak field low speed stuff comes in is in showing that the Einstein field equations reduce to Poisson's equation.

horacio torres and anuttarasammyak
ffp said:
As i understand, the "bending" or "curving" of time means time passing faster or slower to an object, and not affecting the object position in space.
Forgot to say this earlier - you can't think of "the curving of time". It's always the curving of spacetime. Space and time are both aspects of spacetime.

LBoy
I'm an engineer and I have knowledge of physics and calculus, even saw something about relativity in university, but not much. The majority of info I have about the topic I got from my own readings, studying and research online.

Here are a couple of concepts that I read more than once and that I find hard to understand:

1- I've seen people saying that everything is always traveling at the speed of light. It just happens that still objects are traveling at that speed in time, while moving objects are traveling at a combination of that speed in time and space. Now, I don't believe this is true, since I see no empyrical evidence of proof for such a claim. Also there makes no sense in saying that you travel in time with the speed of light (which unit is m/s). We travel in time by the rate of 1 second per second. I think people that say that might be getting a wrong concept from the time coordinate from the metric "ct". Isn't that c just a human convention, that is there to make the time coordinate unit spatial? Couldn't it be anyvalue?

2- Regarding gravity, I know that in GR gravity is not considered a force, but the curvature of spacetime. I can see why a moving object that goes in the way of a massive mass like a planet would have its trajectory changed by the curvature of spacetime to follow the geodesic path. However, I don't see why a still object in the presence of such massive mass would begin moving toward it, since there is not any force acting upon it.
The explanations I found were that everything is always traveling through time, and time is "curved" by the mass so it "bends" in the direction of the planet. This makes no sense to me, since time is not a spatial dimension, and while i understand it can be curved, since spacetime is one unified thing and mass curve spacetime, the "bending" of space, as I see, is just affecting the flow of time. Time curving means time flowing slower or faster for that object, and not making it travel in space.
I also saw explanation of how time would flow diferently inside the very object. So, if a ball is traveling parallel to Earth, the atoms of the side of the ball that is closer to Earth travel in time slower than the ones of the other side. This would cause the ball to turn and be "attracted" by Earth. Yet, I don't see this working with a still object and how it would start moving. Also, I find the explanation very hard to believe, since the difference in time flow in one side of the ball from the other would be ridiculously small. It don't seem suficient to give an aceleration of 9.8 m/s2. This is even worst the smaller the object you use.

I guess this is it for now.

Please don't post messages on the same topic in different threads. I have merged the new thread with the existing one. Keep future messages on this same topic here in this thread, please.

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ffp said:
Time curving means time flowing slower or faster for that object, and not making it travel in space.
Here is a good quick video that really shows the point effectively

The apple is initially at rest, staying at a constant position due to the force acting on it. Then, when that force is removed it travels in a straight line and the curvature of spacetime results in it starting to fall even though it was initially at rest.

LBoy
Ibix said:
The "everything travels at ##c##" comes from the standard normalisation of the four velocity to have length ##c##. Interpreting that choice of normalisation as meaning "everything travels at ##c##" is circular, yes - all four velocities have the same magnitude because that's how they are defined. And it's not true for light anyway, where the tangent vector to its worldline is null so cannot be normalised to length ##c##.

However, the "##ct## thing" is not just a convention. Essentially, ##c## is a natural conversion factor between units of time and units of length. Not including it, or using a different speed, is analogous to taking a rectangle that's 1m on one side and 1000mm on the other and asserting that the diagonal must therefore be ##\sqrt{1^2+1000^2}## long.Unfortunately the explanations you've seen are more or less correct. The point is that even when you aren't moving (by some definition) you are advancing in time. And spacetime near a mass is curved, and the unaccelerated path of an object in that spacetime gets closer to the object as a result.

Time is a dimension, but it is distinct from spatial ones. There is some crosstalk, though, in that the direction in spacetime that I call "time" you might call a mixture of time and some spatial direction.
I disagree about the first part. Your rectangle example is treating two "different" units (meter and milimeters). We could just replace c by any chosen velocity (still in m/s) and still have the equations to work.

While we call spacetime and know that they are somehow realted, time is still the passing of time and shouldn't affect the direction an object travels in space. I can't grasp how affecting time can change the trajectory of an object. I know you will say that it's no affecting time, but *spacetime*.

However, even though spacetime is like one unified thing, it still has two different concepts of a spatial dimension and a time dimension. I can see how bending spacetime would affect how moving objects travel in space (space is literally bent) and how time flows differently (time is bent). But not how traveling in time can affect your position in space.

@anuttarasammyak , sorry I don't understand your post.

@Dale Oh, I'm really sorry. I was trying to post this thread yesterday and got a login failure and I thought I lost it. Then I proceeded to re-write it now, without knowing it worked before. Thanks for mergin the threads, my questions stay basically the same.

About your video, why would the apple fall in the Einstein's example in the first place? I know it has to follow the geodesic path of the curved spacetime, but only if it is moving, right?

ffp said:
I know it has to follow the geodesic path of the curved spacetime, but only if it is moving, right?
No. It has to follow the geodesic path in curved spacetime if it is not experiencing a real force (e.g. as measured by an accelerometer). Whether it is at rest or moving is irrelevant. A geodesic path is the path of a force-free object.

vanhees71
Dale said:
No. It has to follow the geodesic path in curved spacetime if it is not experiencing a real force (e.g. as measured by an accelerometer). Whether it is at rest or moving is irrelevant. A geodesic path is the path of a force-free object.
I know this is the answer, but I can't understand why an object that has no forces acting upon it would move in space. I know it "moves" in time (as time passing), but moving in time won't (or shouldn't) change its position in space.

ffp said:
I know this is the answer, but I can't understand why an object that has no forces acting upon it would move in space. I know it "moves" in time (as time passing), but moving in time won't (or shouldn't) change its position in space.
It isn’t good to think about “moving” in spacetime at all. A Newtonian point particle becomes a worldline in spacetime. You don’t think of the line as moving, it is just a line. That line has, for each value on the time axis, a corresponding value on the space axis.

So the slope of the line (wrt some specified axes) is what we think of as “moving” in Newtonian physics. If the worldline is parallel to the time axis in spacetime then it is at rest per Newton and if it is not parallel to the time axis then it is moving per Newton.

So now, if your time axis is curved then you cannot draw a straight line which remains parallel to it. Go ahead and try it. Print out a picture from the video and draw lots of straight lines. Notice when they become parallel to the time axis and when they do not. That is the Newtonian idea of rest and moving.

A straight worldline that begins parallel to the time axis will necessarily quickly begin to diverge from the axis as the axis curves.

LBoy, sysprog and vanhees71
Dale said:
It isn’t good to think about “moving” in spacetime at all. A Newtonian point particle becomes a worldline in spacetime. You don’t think of the line as moving, it is just a line. That line has, for each value on the time axis, a corresponding value on the space axis.

So the slope of the line (wrt some specified axes) is what we think of as “moving” in Newtonian physics. If the worldline is parallel to the time axis in spacetime then it is at rest per Newton and if it is not parallel to the time axis then it is moving per Newton.

So now, if your time axis is curved then you cannot draw a straight line which remains parallel to it. Go ahead and try it. Print out a picture from the video and draw lots of straight lines. Notice when they become parallel to the time axis and when they do not. That is the Newtonian idea of rest and moving.

A straight worldline that begins parallel to the time axis will necessarily quickly begin to diverge from the axis as the axis curves.
I understand. My issue is that we are representing time (the x axis) as a spatial dimension the moment we bend it. What does it mean to "bend" time? As I see, it means to make the flow of time go faster or slower.
It isn't "wrong" to treat time with the same characteristics of space? Doesn't the concept of spacetime just means that space and time are related, yet not the same thing? For example, let's pretend that masses in our universe only bends time. What would that mean?
I believe my issue is in the concept of spacetime because I can't quite grasp the concept that space and time are the same thing. I can see how they are related, though, but not the same thing.

If, instead of representing spacetime as two axis we represent a 3 axis spatial place repeatedly as in frames of a movie, what would bend time mean?

ffp said:
I disagree about the first part. Your rectangle example is treating two "different" units (meter and milimeters). We could just replace c by any chosen velocity (still in m/s) and still have the equations to work.
And if you do, you will find that your chosen velocity is now the one that is the same in all frames (which means that your revised model no longer matches reality), or else that your invariant interval isn't invariant while the one using ##c## remains invariant. This is exactly analogous to the situation where you measure ##x## distances in one unit and ##y## distances in another - "lengths" defined this way are not invariant under rotation, or if I wish to keep "length" invariant I need to introduce scaling along with rotation, which is not what happens in reality.
ffp said:
My issue is that we are representing time (the x axis) as a spatial dimension the moment we bend it.
No we are not. We are treating all four dimensions in the same way, except that the metric signature picks one out as different from the other three. That signature difference is what defines the timelike direction. Having any curvature at all entails curvature in a timelike plane - since there is no unique time direction you cannot have curvature that only affects planes perpendicular to time.

LBoy, sysprog, vanhees71 and 1 other person
ffp said:
My issue is that we are representing time (the x axis) as a spatial dimension the moment we bend it.
This is incorrect. Including time as part of spacetime does not mean that we are treating it as a spatial axis.

In any case, this "issue" isn't a scientific objection. The scientific question is: Does the resulting theory match the experimental data? It does. Even if we were treating time as a spatial dimension (which we are not), if the resulting theory gave correct results then it is correct to do so.

ffp said:
Doesn't the concept of spacetime just means that space and time are related, yet not the same thing? ... I can't quite grasp the concept that space and time are the same thing. I can see how they are related, though, but not the same thing.
Space and time are not the same thing. They are related, but not the same.

The relationship is expressed in the metric which (in an inertial frame) can be written ##ds^2= -c^2 dt^2 + dx^2 + dy^2 + dz^2##. So in the metric you can clearly see that there are two important distinctions that make time different from space. First, there is only one time dimension and there are three spatial dimensions, and second the time has a different sign in the metric than space.

This preserves the distinction between time and space. For example, because of the difference in signs intervals with ##ds^2 < 0## are measured with a clock while intervals with ##ds^2>0## are measured with a ruler. Because of the difference in the number of dimensions you can draw a closed spacelike loop but not a closed timelike loop.

Because clocks measure ##ds^2## (or more specifically they measure ##\sqrt{-ds^2}##) it is clear that this spacetime (which has the above relationship between space and time) has physical significance. You cannot treat time or space separately, but they are different parts of the same Lorentzian manifold.

ffp said:
What does it mean to "bend" time?
It means exactly what is shown in the video. It means that the time axis is not a straight line.

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LBoy, Nugatory, vanhees71 and 2 others
@Ibix I understand. You are saying that if we replace the c in the time coordinate of the metric for another chosen number, than the speed limit would be that of the new number and not c, which is incorrect. I got it right? And does this means than that we are indeed...travelling throught time.. with the speed of light? What would that even mean? I would love to know the answer in a theory way, not mathematically, so I can understand that related to our universe.

@Dale Ok, let's just try to leave the equations aside for a moment and try to see what meaning this have in our physical universe. What does "bend time" means? Axis and worldlines are things to ilustrate and help understanding the concepts. But in our 3 spatial dimensional and 1 time dimensional universe what does it mean to bend time?

I already know the answer will be: it's not bending time, but bending spacetime. Let me rephrase it then:
Bending spacetime will have effects on how space works and on how time works. A bent space means that your trajectory will bend, because space is where you move spatially. So, what effect in time (and our perception of it) does bending spacetime has?

ffp said:
I got it right?
Yes.
ffp said:
And does this means than that we are indeed...travelling throught time.. with the speed of light?
No. That is popsci nonsense, albeit often promulgated by Brian Greene.

We typically normalise the tangent vector to a worldline to have length ##c## and call this the four velocity, since it's the derivative of your four position with respect to your proper time. This is a velocity in the geometric sense of the word (a normalised vector tangent to a curve), but not really in the physics sense of speed.
ffp said:
What does "bend time" means?
Nothing. It's spacetime that's curved.
ffp said:
A bent space means that your trajectory will bend, because space is where you move spatially. So, what effect in time (and our perception of it) does bending spacetime has?
You can't separate curved spacetime into curved space and curved time. Curvature is measured in terms of what happens to a vector transported around a small loop. A loop has 2d extent, and necessarily includes both spatial and temporal extent. (Edit: it's possible to have a purely spatial loop, although a change of coordinates can make it not purely spatial, but there is only one timelike dimension.)

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LBoy, vanhees71 and ergospherical
ffp said:
What does it mean to "bend" time?
It means exactly what the video shows. It means that the time axis is not straight.

ffp said:
Axis and worldlines are things to ilustrate and help understanding the concepts. But in our 3 spatial dimensional and 1 time dimensional universe what does it mean to bend time?
In this case the axis and worldline thing is more important than you are implying, and cannot be dismissed from the discussion. The reason is that your whole question is based on trying to understand why curved spacetime can make something that is initially at rest begin to move. But there is no such thing “in our 3 spatial dimensional and 1 time dimensional universe” itself that corresponds to the concept of “at rest” or “still”.

The concept of “at rest” means that you have a time axis and a worldline and they are parallel. There is nothing in the universe that corresponds to “at rest” without drawing that time axis. So you cannot divorce axes and worldlines from a question about objects at rest. They are part of the question itself.

So, once again, “curved time” means that the time axis is not straight. In other words, you have chosen a definition of “at rest” such that accelerometers at rest do not read 0.

ffp said:
I already know the answer will be: it's not bending time, but bending spacetime.
I differ slightly with my colleagues here. I have no objection to talking about bending time. It is, as I said, having a time axis which is not straight. This is a concept that does not exist without defining an axis, which is an arbitrary thing, not part of the universe. So it is a fine concept but it is “relative” or “frame variant” and thus not part of nature itself.

In contrast, bending spacetime means that there is tidal gravity. And this is an invariant concept that can be defined without reference to some reference frame.

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PeroK and vanhees71
Hm as @Ibix already said, "curved time" doesn't mean anything; curvature is a property of a manifold and is characterised by the change ##\Delta X_{\nu} = \displaystyle{\oint} \Gamma^{\mu}_{\nu \rho} X_{\mu} dx^{\rho} = \dfrac{1}{2} R^{\mu}_{\nu \rho \sigma} X_{\mu} \Delta S^{\rho \sigma}## of a vector ##\mathbf{X}## after parallel transport around an infinitesimal closed contour. Non-vanishing of the tensor ##R^{\mu}_{\nu \rho \sigma}## implies the manifold is curved!

[##R^{\mu}_{\nu \rho \sigma} := \partial_{\rho} \Gamma^{\mu}_{\nu \sigma} - \partial_{\sigma} \Gamma^{\mu}_{\nu \rho} + \Gamma^{\mu}_{\alpha \rho} \Gamma^{\alpha}_{\nu \sigma} - \Gamma^{\mu}_{\alpha \sigma} \Gamma^{\alpha}_{\nu \sigma}## is called the Riemann tensor.]

LBoy and vanhees71
Dale said:
It means exactly what the video shows. It means that the time axis is not straight.

I wanted to know what it means physically, in our real world. math is a tool that we use to help us comprehend , discover and work with theories. Including things that are abstract.
I don't know you guys, but for me, to really, trully understand a theory or concept in physics I must be able to understand what that concept means in our real world. I can't be satisfied with just the abstract math, even though I know it is really important for better understanding and even developing those concepts.

So, when I asked what does it means to bend time, I'm not asking to bend the axis representation of time. There is no axis in our universe. Axis are just a tool to measure some variable, like a rule.

Dale said:
In this case the axis and worldline thing is more important than you are implying, and cannot be dismissed from the discussion. The reason is that your whole question is based on trying to understand why curved spacetime can make something that is initially at rest begin to move. But there is no such thing “in our 3 spatial dimensional and 1 time dimensional universe” itself that corresponds to the concept of “at rest” or “still”.
I meant still in the spatial dimensions, since no regular object on Earth can be "still" in time.

Dale said:
The concept of “at rest” means that you have a time axis and a worldline and they are parallel. There is nothing in the universe that corresponds to “at rest” without drawing that time axis. So you cannot divorce axes and worldlines from a question about objects at rest. They are part of the question itself.

Again, I don't even know if it is possible to explain (certainly it is not easy) what happens in our physical universe without the axis representation (or math), but it should be. Or else the theory is not what really happens in the universe and is just a tool to calculate relativistics movements. We know that this is not the case for Relativity, since it went through experimental tests.

A way of trying to do that is to work with thougths experiments imagining our real 3D space and a clock. Or just our real 3D space frame by frame as a movie to show the flow of time.

Dale said:
So, once again, “curved time” means that the time axis is not straight. In other words, you have chosen a definition of “at rest” such that accelerometers at rest do not read 0.

I differ slightly with my colleagues here. I have no objection to talking about bending time. It is, as I said, having a time axis which is not straight. This is a concept that does not exist without defining an axis, which is an arbitrary thing, not part of the universe. So it is a fine concept but it is “relative” or “frame variant” and thus not part of nature itself.

In contrast, bending spacetime means that there is tidal gravity. And this is an invariant concept that can be defined without reference to some reference frame.

Are you saying that the "bending" is not a real world thing? Is it just an abstract concept, for the math? @Ibix gave a similar answer about how bending applies to vector and loops. However, one of the major experiments that proved relativity right was the one with the solar eclipse, where the light of stars behind the sun could be seen, since space curved the rays into Earth.

Let's take a step back and see the effects that bending spacetime has on space. What happens to the space around us when a planet like Earth bends spacetime? What's the difference between the space around you if you are on Earth and if you are in deep intergalactic space? What is the physically definition of bending space, since space is continuous and all around us?

I might be asking very silly questions, but I'm just trying to understand the concept applied to our real world.

LBoy and vanhees71
ffp said:
@anuttarasammyak , sorry I don't understand your post.
It is just to give you an idea behind, not to annoy you with mathematics. Length in space is given by Pythagoras theorem say
$$dl^2=dx^2+dy^2+dz^2$$
Similarly world interval, "length" of spacetime, is given
$$ds^2=c^2dt^2-dl^2=c^2dt^2- dx^2-dy^2-dz^2=dx_0^2-dx_1^2-dx_2^2-dx_3^2$$
with ct,x,y,z renamed as ##x_0,x_1,x_2,x_3##. Though strange (+,-,-,-) signs appear, anyway, it is an integrated "length" of spacetime. c is constant of light speed. It is in SR, no curving of spacetime takes place. In GR spacetime is curved so it becomes mingled.
$$ds^2 = g_{00}dx^0 dx^0+ g_{01} dx^0 dx^1+...+g_{33}dx^3dx^3$$
where ##g_{ij}## is metric tensor with 10 different components which denotes how spacetime is curved. For SR, metric tensor is simple, i.e.,
$$g_{00}=-g_{11}=-g_{22}=-g_{33}=1,\ \ \ g_{ij}=0\ \ otherwise$$

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ffp said:
what really happens

Could you define what "really happens" means, and how to distinguish it from "not really"?

ffp said:
I don't know you guys, but for me, to really, trully understand a theory or concept in physics I must be able to understand what that concept means in our real world.
If you only want to talk about "time curvature" then @Dale's answer (the time axis is not a geodesic) is the only one possible. I don't think it's particularly meaningful because it depends on your choice of time axis, but there isn't really any other interpretation of "time curvature" available.
ffp said:
I meant still in the spatial dimensions, since no regular object on Earth can be "still" in time.
"Not moving in space" is a frame dependent concept (a person moving with respect to you says that you are moving), so to be stationary you've picked a definition of space and hence a definition of time. If you accept "still in space" as a real concept you are thereby defining a time axis.

You can do physics without coordinates, but you have to let go of notions like "stationary in space" because defining "space" is picking coordinates.
ffp said:
Let's take a step back and see the effects that bending spacetime has on space. What happens to the space around us when a planet like Earth bends spacetime?
If you dig a tunnel through the center of the Earth and measure the length, ##d##, of the tunnel and the circumference, ##C##, of the planet you will find ##C\neq \pi d##. You will also find that clocks held at different altitudes will tick at different rates.

Note that both of these statements involve picking coordinates.

Dale
ffp said:
I wanted to know what it means physically, in our real world.

ffp said:
math is a tool that we use to help us comprehend , discover and work with theories. Including things that are abstract
Why would you avoid using a tool for comprehending if you are trying to comprehend?

ffp said:
for me, to really, trully understand a theory or concept in physics I must be able to understand what that concept means in our real world
Again, that is fine for concepts that are actually "in our real world", but your questions are full of concepts that don't exist in our real world but are only in our theories and math. You asked about time and you asked about space, but the real world only has spacetime. The separation of spacetime into time and space is a human convention (our choice of axes), not part of the real world. You asked about objects at rest, but the state of being at rest is also a human convention and not part of the real world.

The problem here is that you are asking questions about things that only exist in our theories and math and then complaining that the answers are not only about the real world. If you want answers that are only about the real world then you will need to ask questions that are only about the real world. If you ask questions that are a mix of real world and human convention then the answers will necessarily be a mix of real world and human convention.

ffp said:
I can't be satisfied with just the abstract math, even though I know it is really important for better understanding and even developing those concepts.
Frankly, this line of complaint is starting to irritate me. You asked a question and it was answered. Furthermore, I explained explicitly how the mathematical concepts in your question could be directly tied to real experimental result. As I already told you, curved time means that accelerometers which you have arbitrarily designated as being "at rest" read non-zero. If accelerometers at rest measure 0 then time is not curved, if accelerometers at rest measure non-zero then time is curved. I don't know how you can complain about "just the abstract math" when I already tied it into real physical measurements.

ffp said:
I'm not asking to bend the axis representation of time. There is no axis in our universe.
Then according to you there is no time in our universe.

Stop blaming us if you are asking a question that you don't want to know the answer to. I am a physicist, not a psychic. I can't tell what question you actually want answered if you don't actually ask the question.

ffp said:
Again, I don't even know if it is possible to explain (certainly it is not easy) what happens in our physical universe without the axis representation (or math), but it should be.
Certainly, it is possible to explain what happens in our physical universe without the axis representation. The axis representation is about "time", so if you want answers that avoid the axes then you should ask about spacetime (the manifold with its metric) instead of space or time (the axes we arbitrarily draw on that manifold).

I don't think it could be done without math entirely. I think that you should revisit your anti-math stance. Of course, math is not sufficient. You need to also include the link between the math and actual physical experiments. But physics is more than just experimental data, it is also theory, and the theory is built on math. So to get a full understanding you must have both math and experiment.

ffp said:
A way of trying to do that is to work with thougths experiments imagining our real 3D space and a clock. Or just our real 3D space frame by frame as a movie to show the flow of time.
There is no such thing as our real 3D space. What is real is 4D spacetime.

ffp said:
Are you saying that the "bending" is not a real world thing?
I am saying that "bending of time" requires the specification of an arbitrary human convention of "time". This is done by declaring certain objects to be at rest. But there is no universal truth to what objects are at rest. Once you have made that arbitrary human specification of which objects are declared to be "at rest" (thereby fixing the time axis), then the real-world meaning of "time bending" is that accelerometers at rest do not read 0.

ffp said:
Let's take a step back and see the effects that bending spacetime has on space. What happens to the space around us when a planet like Earth bends spacetime? What's the difference between the space around you if you are on Earth and if you are in deep intergalactic space? What is the physically definition of bending space, since space is continuous and all around us?
Space is as much an arbitrary human invention as time. The physical thing is spacetime. I am not going to answer this question because you will just make the same complaints for the same reasons.

Time is not the same as space, as discussed above, but the division of spacetime into separate concepts of time and space is artificial.

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robphy, weirdoguy, vanhees71 and 3 others
First of all I want to thanks you all for your answers and even more for your patience. I know I am being very anoying, but that is something I wanted to understand for some time now.

@weirdoguy "Really happens" means something that is not an abstraction or something different from what is happening in our physical universe. Something that is not just a math tool or convention. For example, the direction of current flow in an electric circuit does not match reality, because in real circuits the electrons are the ones moving, so the direction is inverted. It's a simple example, but one that illutrates what I mean with "really happen".

@Ibix Ok, we can consider a ball not moving in space in relation to Earth in the initial instant. Suddenly it starts moving towards Earth. Without any force acting upon it...
About you tunnel example you mean C != 2xdxpi, right? d is the radius. Anyway, why C is different?

I have no trouble using coordinates. My trouble is when we use a coordinate for time and then bend it, because I can't understand bending a non-spatial dimension. We can, instead of using coordinates, use rulers and clocks. This way we can measure things exactly like we do on real life. Will that help?
Dale said:

I am sorry, I meant no harm and if you feel that I'm dismissing the answers, I'm not. I am just trying to direct them more into real world examples and less on abstract mathematical ones. I'll try to ask better questions now.

Dale said:
Frankly, this line of complaint is starting to irritate me. You asked a question and it was answered. Furthermore, I explained explicitly how the mathematical concepts in your question could be directly tied to real experimental result. As I already told you, curved time means that accelerometers which you have arbitrarily designated as being "at rest" read non-zero. If accelerometers at rest measure 0 then time is not curved, if accelerometers at rest measure non-zero then time is curved. I don't know how you can complain about "just the abstract math" when I already tied it into real physical measurements.

Ok, correct me if I'm wrong but accelerometers works with piezoelectricity, which means that a force must compress the component inside the accelerometer. I can't understand how a phenomena that affects time can have some effect on our universe other than altering the flow of time. From your post the answer is that there is no time, it's spacetime. Let's try to work with that.

If I am floating on space above Earth, at rest related to it, why would I be pulled towards it if there is no force acting upon me?
The answer that I got is because spacetime is curved by Earth's mass. Ok, why bending spacetime would pull me down to Earth? How can bending spacetime create a force-like interaction?

I can see that bending spacetime would affect our perception (and of our sensors/meters) about space and about time. Space would seem literally bent (gravitational lens) and time would literally flow slower/faster (GPS time differences). I just don't get the force-like feeling.

ffp said:
So, when I asked what does it means to bend time, I'm not asking to bend the axis representation of time. There is no axis in our universe. Axis are just a tool to measure some variable, like a rule.
For a physically realizable time axis, just consider a clock; its worldline is the time axis for some coordinate system. When someone says “time axis”, you can hear it as a convenient shorthand for “the timelike worldline of a (possibly hypothetical) clock that is at rest at the origin of the coordinate system for which this is the time axis”. Statements about the time axis being “bent” are statements about the worldline of this clock.

vanhees71 and Dale
Nugatory said:
For a physically realizable time axis, just consider a clock; its worldline is the time axis for some coordinate system. When someone says “time axis”, you can hear it as a convenient shorthand for “the timelike worldline of a (possibly hypothetical) clock that is at rest at the origin of the coordinate system for which this is the time axis”. Statements about the time axis being “bent” are statements about the worldline of this clock.

I understand that. Each dot in the axis represent a second in the future. But bending this axis should just mean altering the flow of time, since the axis represent the passing of time. How does that creates a "force" that pull every object with mass towards the planet?

ffp said:
I understand that. Each dot in the axis represent a second in the future. But bending this axis should just mean altering the flow of time, since the axis represent the passing of time. How does that creates a "force" that pull every object with mass towards the planet?
It’s not the “bending” of the axis (the scare-quotes are because bending is a very misleading way of thinking about intrinsic curvature) that does it, it’s that spacetime is curved in such a way that initially parallel timelike geodesics (the worldlines of free-falling clocks, which are a natural choice of time axis) will not remain parallel.

As for how this can create the effect of a force:
Suppose you and I are standing one meter apart at the equator, each holding one end of a relaxed one-meter coil spring. We both start walking due north, on paths that are initially parallel. As we proceed, we will become aware of a force that is shoving us towards one another and compressing the spring; if it weren’t for the spring we would collide at the North Pole. That’s spatial curvature at work.

The spacetime equivalent would be two objects suspended above the surface of the Earth at the two poles. When we release them they are in free fall, following straight-line geodesic worldlines that intersect the worldline of the center of the Earth - or would if the surface of the Earth wasn’t in the way. If you are standing on the surface of the Earth watching one of the objects heading towards you it’s natural to think in terms of a force pulling the object downwards, but we could as reasonably think of it as us getting in the way of the natural unperturbed free fall path of the object.

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cianfa72
ffp said:
I can't understand how a phenomena that affects time
That is because there isn’t a phenomenon that affects time involved here. The scientist chooses which objects they consider to be at rest. The accelerometers simply indicate if they chose a curved axis or not.

If a carpenter chooses to make a chair with a curved back then a straightedge can measure that. The straightedge doesn’t produce a phenomenon that curves the back, it just measures the choice that the carpenter made.

ffp said:
Ok, why bending spacetime would pull me down to Earth? How can bending spacetime create a force-like interaction?
This is a question that I think you will like the answers more.

First, an accelerometer is what measures a net force, so there is no net force acting on you. This means, by Newton’s first law, that your path in spacetime is a straight line (aka a geodesic). Also, initially you are at rest wrt the earth, meaning that your paths in spacetime started out parallel.

So geometrically, you have two straight lines that start out parallel but converge. In flat Euclidean geometry this is impossible. But consider the 2D surface of a sphere. On a sphere a geodesic is a great circle, like a longitude line. Two longitude lines are parallel at the equator but intersect at the pole. So longitude lines on a sphere have the behavior we need, they are straight lines that are initially parallel but converge.

This is what we mean by spacetime is curved. Worldlines do things that are impossible in flat spacetime. Triangles don’t add up to 180 degrees and straight parallel lines converge.

vanhees71 and PeterDonis
Nugatory said:
It’s not the “bending” of the axis (the scare-quotes are because bending is a very misleading way of thinking about intrinsic curvature) that does it, it’s that spacetime is curved in such a way that initially parallel timelike geodesics (the worldlines of free-falling clocks, which are a natural choice of time axis) will not remain parallel.

As for how this can create the effect of a force:
Suppose you and I are standing one meter apart at the equator, each holding one end of a relaxed one-meter coil spring. We both start walking due north, on paths that are initially parallel. As we proceed, we will become aware of a force that is shoving us towards one another and compressing the spring; if it weren’t for the spring we would collide at the North Pole. That’s spatial curvature at work.

I understand that. But as you said, this is spatial curvature at work. Also, in the example we are both moving, so what starts the movement is ourselves. My issue is what starts the movement in space when spacetime is bent. I can understand that two people still in space (relative to Earth) are "moving" through time, as of getting old. I can't understand how this passing of time can simulate a force.

Nugatory said:
The spacetime equivalent would be two objects suspended above the surface of the Earth at the two poles. When we release them they are in free fall, following straight-line geodesic worldlines that intersect the worldline of the center of the Earth - or would if the surface of the Earth wasn’t in the way. If you are standing on the surface of the Earth watching one of the objects heading towards you it’s natural to think in terms of a force pulling the object downwards, but we could as reasonably think of it as us getting in the way of the natural unperturbed free fall path of the object.

Ok, if I forget worldline and geodesics for a second and work with 3D space and instants of time as pictures (frames in a movie), we would have the first frame as the two objects suspended above the surface and the last frame the objects touching the surface of Earth. What caused this displacement of the objects in space?

I can't grasp how time can affect anything other than the passing of events, like something passive.

This is a video of a channel that I like very much. I don't know how precise it is, would liketo know your opinion:

In this video, why does the object deslocates in spatial dimensions, since only time flows diferent for both of its ends? Shouldn't the right round part of the object just get "older" than the left one? Why are they treating time as a spatial dimension? Do we have any empyrical, real world proof that this is in fact what happens? How they come to this conclusion in the first place? I believe it was due to the mathematics, but is it possible to verify this experimentally or something?

Also, I see two issue in the example of the video: first, for a really small object (like a point in space) there would be no difference in time flowing because there is no left and right in a point. I guess that's part of the problem relativity has with quantum physics. Second, is this ridiculously small difference in time flow in each end of the object enough to make it "accelerate" at a rate as big as 9,8 m/s2??

ffp said:
is this ridiculously small difference in time flow in each end of the object enough to make it "accelerate" at a rate as big as 9,8 m/s2??
Yes. 1 g is a very small acceleration and it takes very little curvature to produce it. It is roughly a radius of curvature of 1 light year.

vanhees71
Dale said:
Yes. 1 g is a very small acceleration and it takes very little curvature to produce it. It is roughly a radius of curvature of 1 light year.

So the video is correct? And then, wouldn't the "force" of gravity depends on how big is the object being pulled, since the difference in time flow is related to its difference in distance from the Earth? I mean, a very, very long object perpendicular to Earth's surface would have a bigger time difference between its ends than a shorter one and hence time would flow even faster in the upper end and thus the object would be pulled with a stronger "force". But we know that objects "fall" at the same rate.

Still, why treat time as a dimension like we treat space (I mean using axis instead of clocks and frames)? I've seen another video saying that this is a tool that helps predict things that Newton's laws couldn't, but it isn't necessarily what really happens. This way, gravity "force "might not be caused by time flow differences. Is that true? I'm not asking about the effectiveness of relativity (that's definitely out of debate because it was proven several times), but its veracity regarding our real universe. How do you see the incompatibility of relativity and quantum physics and what this might say about its realism?

ffp said:
Ok, if I forget worldline and geodesics for a second….
That’s like saying we’re going to explain how a rowboat works, except that we’re going to forget water and oars and buoyancy for a moment. It’s not going to be effective.
….and work with 3D space and instants of time as pictures (frames in a movie),
That approach is guaranteed to mislead and confuse. The basic problem is that a frame in a movie purports to show things that are happening at the same time in different places in space (formally, “spacelike-separated events”) that that are happening at the same time. But even in flat spacetime the concept of “at the same time” is problematic (Google for “relativity of simultaneity” and “Einstein train simultaneity”); in curved spacetime it is completely undefined except within regions of space small enough to ignore the curvature the way I ignore the curvature of the Earth when I’m laying out the foundations of a house. Indeed, the reason we think in terms of four-dimensional spacetime is because there is no way of working with 3D space at a successive moments of time (except at speeds and distances small enough that relativistic effects can be approximated away and ignored).

PeterDonis
ffp said:
a very, very long object perpendicular to Earth's surface would have a bigger time difference between its ends than a shorter one and hence time would flow even faster in the upper end and thus the object would be pulled with a stronger "force".
You have this backwards. The strength of the "force" gets larger as the time flow gets slower, not faster. So the lower end of your long object would experience a larger "force" than the upper. This is just the Newtonian view of tidal gravity in the radial direction.

ffp said:
But we know that objects "fall" at the same rate.
We know that pointlike objects fall at the same rate. But you are now not considering a pointlike object. You are considering an object whose size is comparable to the distance scale over which tidal gravity is significant (or, to put it another way, over which the strength and/or direction of the "force" varies significantly). That requires a more complicated analysis since such an object, if each of its parts are allowed to free-fall, no longer has a single "rate of fall". (If, on the other hand, you want the object to remain rigid, so that all of its parts "fall" at the same rate, then the only point in the object that will be in free fall is its center of mass; every other point will experience a nonzero proper acceleration due to the internal forces within the object that are required to keep it rigid in the presence of tidal gravity.)