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

[ffp]

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.

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??

 

[Dale]

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.

 

[ffp]

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?

 

[Nugatory]

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]

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.

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.)

 

[A.T.]

if I forget worldline and geodesics

I would rather make sure that you get good intuition about geodesics. This might help:

- The video in post #9

- Chapter 2 of this:
http://www.relativitet.se/Webtheses/tes.pdf

- Chapter 10 of this:
https://archive.org/details/L.EpsteinRelativityVisualizedelemTxt1994Insight/page/n157/mode/2up

 

[Dale]

So the video is correct?

I didn’t watch the video, I just replied to that specific statement. Please do not take my reply as an endorsement of the video. I was just quickly commenting on the size of the effect that you seemed concerned about. It is small, not large.

 

[ffp]

Ok, I'd ike to know you guys opinion about the video, but it seems to be wrong, since it doesn't explain gravity using geodesics, but time gradient.

@Nugatory You made an excellent point. However, if we use a 3d space and a clock (or several clocks) to represent the flow of time wouldn't that work?

@PeterDonis Fair enough. But is the video explanation right or not?

@A.T. Thanks I will read them, but by getting a quick look at them I can see that the explanations are kinda the same as the video posted in post #9.

At this point I think I will have to just accept that time is not just the representation of causality, it's not just one moment after the other, but it is a dimension together with space and not only that, it can change the displacement of objects in our perception of space.

Two questions though: is that (the statement that gravity is caused by time as much as space distortion) a completely accepted fact among scientific community or it is just seen as a model, in a way that it works when used to calculate things that didn't with Newtonian gravity (like mercury orbit) but not necessarily what indeed happens in our physical universe (it's a tool or it's a fact)?
And the fact that relativity breaks down when used in quantum physics an indicative that it probably don't correspond with the reality of the universe? (bonus question, can anyone say more or less what breaks down when the two are used together? I read about that but can't remember right now)

 

[Dale]

Two questions though:

Don’t you think you should stick with your earlier question until you figure that one out first? Did you understand my description of how curved spacetime produces the observed gravitational effects?

 

[A.T.]

a completely accepted fact among scientific community or it is just seen as a model

All physics is models.

 

[Nugatory]

However, if we use a 3d space and a clock (or several clocks) to represent the flow of time wouldn't that work?

A clock can be used to represent the flow of time (the flow rate will always come out to be one second per second), but only at one point, the point where the clock is located. Everywhere else, we are making an assumption, called a “simultaneity convention”, about how the readings of a hypothetical clock at that remote point are related to our clock or equivalently how to synchronize the remote clock so that it reads the same as our clock. That convention is our definition of “at the same time”.

We define three-dimensional space by slicing four-dimensional spacetime along a plane of constant time, that is selecting all the “at the same time” points. This is somewhat analogous to the way that I can slice a three-dimensional sausage to expose a two-dimensional cross section; I make my slices along the “length” dimension and each slice spans the two “crosswise” dimensions. However, just as what is “length” and what is “crosswise” depends on the angle at which I hold the knife, the split of 4d spacetime into “time” and “3d space” depends on the definition of “at the same time”.

And as I said in the previous post…. That notion of “same time” is problematic in flat spacetime and hopeless in curved spacetime.
("Hopeless" applies to the problem at hand. There are some A-level subtleties about what meaning might be attached to the phrase "at the same time" that are covered in a digression below).

 

[anuttarasammyak]

Two questions though: is that (the statement that gravity is caused by time as much as space distortion) a completely accepted fact among scientific community or it is just seen as a model, in a way that it works when used to calculate things that didn't with Newtonian gravity (like mercury orbit) but not necessarily what indeed happens in our physical universe (it's a tool or it's a fact)?

I think facts are expressed and explained by good tools, models or theories. I do not think they are distinguishable if we are in success. We may regard
1+1=2
as a fact, a tool, a model and also a theory.

 

[anuttarasammyak]

And the fact that relativity breaks down when used in quantum physics an indicative that it probably don't correspond with the reality of the universe? (bonus question, can anyone say more or less what breaks down when the two are used together? I read about that but can't remember right now)

You hit home of physics people. QM and GR have not married with yet.

 

[anorlunda]

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.

That's pretty narrow minded. Don't you acknowledge that there can be things in the universe beyond your real world experience?

Relativity and quantum mechanics are both things that can not be perceived by everyday real world experience on Earth. And both of them result in counter-intuitive results. That means things that contradict common sense.

Natural language has not evolved to describe things outside normal human experience. Why should it? That leave only mathematics as a valid way to describe some exotic things. Math is not an alternative, it is the only way to accurately describe some things. If you reject math, then you're doomed to never understand and if that is the case, what is the point of posting questions?

 

[robphy]

While the topic is quantum mechanics, the difficulty also applies to the understanding of (say) relativity
@7m05s

The difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, "But how can it be like that?" which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it.

[There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics.]

 

[ffp]

@Dale Yes, I agree. That was me kinda of giving up. I understand how curved spacetime could cause the effects of gravity. My issue is accepting the premises of the theory. For example, the relationship of time and space. I know they are related, because there is a maximum speed c and speed is space over time. So, space and time are bound in some way. Yet, they are very different things by definition, including how they are perceived. I can't grasp how time can affect anything other than the flow of time.

Time is the representation of causality. Is one thing happening after another. I can't see how this can create force effects, how it can change the trajectory of an object without just accepting that spacextime diagram presented in all explanations. However a diagram is a representation, which is contained in space. We are representing time in a spatial diagram and spatially bending it.

@A.T. and @anuttarasammyak Yes, but there are models that we know that are just tools and don't represent reality (they just work) and there are models that are true representation of reality as far as we know. An example is Newton's gravity. Today, it is a model that do not represent our reality, as relativity shows us. Yet, we still use it a lot because it works in some cases. So, my question would be more like: do the scientific community accept that there is no time and space, only spacetime and that time causes gravity?

A clock can be used to represent the flow of time (the flow rate will always come out to be one second per second), but only at one point, the point where the clock is located. Everywhere else, we are making an assumption, called a “simultaneity convention”, about how the readings of a hypothetical clock at that remote point are related to our clock or equivalently how to synchronize the remote clock so that it reads the same as our clock. That convention is our definition of “at the same time”.

We define three-dimensional space by slicing four-dimensional spacetime along a plane of constant time, that is selecting all the “at the same time” points. This is somewhat analogous to the way that I can slice a three-dimensional sausage to expose a two-dimensional cross section; I make my slices along the “length” dimension and each slice spans the two “crosswise” dimensions. However, just as what is “length” and what is “crosswise” depends on the angle at which I hold the knife, the split of 4d spacetime into “time” and “3d space” depends on the definition of “at the same time”.

And as I said in the previous post…. That notion of “same time” is problematic in flat spacetime and hopeless in curved spacetime.
("Hopeless" applies to the problem at hand. There are some A-level subtleties about what meaning might be attached to the phrase "at the same time" that are covered in a digression below).

That was a very good analogy. But can't we use several clocks like in the video I posted? We can place a clock for each point in space and compare them. I would like to know your opinion about the video explanation.

@anorlunda I didn't say my real world experience, because that is very, very limited. I said real world, which means that if people can somehow verify and demonstrate that is really what happens. While it is ok to use a mathematical tool to predict things in physics, it is still important to know how things work in reality.
What proof, what reason do we have to believe that time is indeed the cause of gravity, other than equations? We know math can work and still not be entirelly on par with reality as we know for now.
I can give you an example. The Ether. Physicists ditched that theory because there was no reason to believe the Ether really existed.

I don't want to really "see" any effect of relativity or quantum physics, that would be crazy unless I work in a lab that work with that. I would just want to understand the premisses they start the theory in an accpetabe way other than "if you say so". Yes, this is related to our intuity, which might get in place of understanding and I fear the only way to "understand" is to "if you say so" to time being able to affect trajectory of objects in space.

 

[Dale]

I can't grasp how time can affect anything other than the flow of time. … time causes gravity

I think you have spent too much time reading pop-sci sources and will have to unlearn some stuff.

Relativity isn’t about time causing things. I think the phrase “time causes X” is generally either wrong or misleading.

Relativity is about geometry. The geometry of the universe is more interesting than a piece of paper, it includes time and it is curved (in a real sense, not just an axis). Triangles don’t always add up to 180 degrees in reality. And parallel straight lines can converge. And a straight line is the longest path between some events.

If you take the geometry seriously, then relativity is more interesting and much less confusing. But if you keep in dismissing the geometry out of hand like you have been doing then you will be left trying to memorize a bunch of separate facts that really belong together.

Time is the representation of causality.

Well, not really. In the actual world A caused B implies more than just B occurred at a later time than A. It also means that B was close enough to A that light could have gone from one to the other. This causal structure is built into spacetime, and it is the single most important geometric feature of spacetime.

However a diagram is a representation, which is contained in space. We are representing time in a spatial diagram and spatially bending it.

We draw diagrams on flat pages and flat screens because that is what we have for drawing diagrams. It is inherently limited because the metric on a flat piece of paper is $ds^2=dx^2+dy^2+dz^2$ while the metric of flat spacetime is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$. So you will have to remember that the diagrams represent the geometry, they don’t duplicate it. To actually calculate the geometry requires using the metric, not just drawing carefully.

Your complaint is true but a little unfair. Our drawings are the best that we can do to show you an easy to understand picture. Particularly since you seem to avoid the math. If you want to stick to the math you can, but if you don’t want to stick to the math then I am afraid you have little right to complain about the drawings. How else are we supposed to show you the geometry if not with the math and not with drawings?

 

[Nugatory]

But can't we use several clocks like in the video I posted? We can place a clock for each point in space and compare them. I would like to know your opinion about the video explanation.

How do we compare two clocks not at the same place? That is not a rhetorical question, and it is tricky enough that you should distrust any easy/obvious answer that comes to mind. One hint: if you have not already tried googling for "Einstein clock synchronization", now is the time... and note that this technique doesn't do what you think it does if there is curvature.

 

[anuttarasammyak]

So, my question would be more like: do the scientific community accept that there is no time and space, only spacetime and that time causes gravity?

In the case of xy plane there is x and y. After we find Rotation we can say "There is no (independent) x and y, only xy". We don't deny specific features of x and y but observe their transformable nature. Similarly we find Lorentz transformation, we could say "There is no (independent) t and x, only tx". We don't deny specific features of time and space but observe their transformable nature.

There is curvature in space even without time. Say surface area of sphere $S_1$ and $S_2$ around Origin are shown as
S_1=4\pi r_1^2,S_2=4\pi r_2^2
$r_1$ and $r_2$ are radii of spheres in our common sense but if there exists mass on Origin, They are slightly different from radius due to space curvature by Gravity. Euclid geometry does not stand any more.

 

[ffp]

I think you have spent too much time reading pop-sci sources and will have to unlearn some stuff.

Relativity isn’t about time causing things. I think the phrase “time causes X” is generally either wrong or misleading.

Relativity is about geometry. The geometry of the universe is more interesting than a piece of paper, it includes time and it is curved (in a real sense, not just an axis). Triangles don’t always add up to 180 degrees in reality. And parallel straight lines can converge. And a straight line is the longest path between some events.

If you take the geometry seriously, then relativity is more interesting and much less confusing. But if you keep in dismissing the geometry out of hand like you have been doing then you will be left trying to memorize a bunch of separate facts that really belong together.

Fair enough. However "In simple terms, geometry is the study of shapes. More specifically, geometry is a branch of mathematics that deals with space, the shapes that inhabit space, and a range of properties that apply to these shapes"
When you deal with time, which is not a spatial dimension, with geometry you haveto choose one: this is just a representation of the mathematics so we can at least understand things quantitatively or time as we know/feel it is completely an illusion, there is nothing as time itself only spacetime, however we don't know exactly what it is in nature.

Again, what experiment were made to prove that the aspect of time of spacetime is responsible for gravity?

Well, not really. In the actual world A caused B implies more than just B occurred at a later time than A. It also means that B was close enough to A that light could have gone from one to the other. This causal structure is built into spacetime, and it is the single most important geometric feature of spacetime.

I'm not wrong, but your answer is much more detailed than mine. And you are correct. I wouldn't call it geometric, though. We can draw two axis (TimexSpace) and have the hypotenuse fixed as c and work with that. However, that is a mathematical tool.

We draw diagrams on flat pages and flat screens because that is what we have for drawing diagrams. It is inherently limited because the metric on a flat piece of paper is $ds^2=dx^2+dy^2+dz^2$ while the metric of flat spacetime is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$. So you will have to remember that the diagrams represent the geometry, they don’t duplicate it. To actually calculate the geometry requires using the metric, not just drawing carefully.

Your complaint is true but a little unfair. Our drawings are the best that we can do to show you an easy to understand picture. Particularly since you seem to avoid the math. If you want to stick to the math you can, but if you don’t want to stick to the math then I am afraid you have little right to complain about the drawings. How else are we supposed to show you the geometry if not with the math and not with drawings?

Yes. I know I'm not being much fair here. As you said, we only have space to work and represent things, so it is very, very difficlt to represent spacetime. I don't want to avoid math entirely. I know how important it is. It's just that when it comes to visualizing the concept in our real world, math does not help much. In those cases, images/words/description might work better. The video I posted tried to do that, but I don't know if their explanation is indeed true.

We agree that diagrams are a representation and not a duplication. Knowing that, do you think that it is possible to try to explain, through any means possible, what is really happening? Maybe our brains and perceptions are incapable of that?@Nugatory Can't we represent the differece in time flow as the video does by showing clocks ticking at different speeds? I took a quick look at Einstein's synchronization and it's more about literally syncing clocks not about representing time everywhere.

@anuttarasammyak , Exactly. I don't deny specific features of time and space but observe their transformable nature. The transformable nature is the speed relation v=s/t. Since we fixed speed (c), then we can transform time into space (light-years) and vice-versa. However, this relation says nothing abot how time can affect things in space. How time can simulate a force acting upo objects inside space...

 

[Nugatory]

Can't we represent the differece in time flow as the video does by showing clocks ticking at different speeds? I took a quick look at Einstein's synchronization and it's more about literally syncing clocks not about representing time everywhere.

Clock synchronization is the essence of showing that clocks are "ticking at different speeds"; any statement about the relative rate of two clocks is actually a statement about clock synchronization and how we're defining "at the same time".

Think about what it means to say that time is passing more slowly for clock B than for clock A:
Initially clock A reads some time $T_{A}$ and clock B reads some time $T_{B}$. (There's no reason why $T_{A}$ and $T_{B}$ have to be the same - for example the two clocks might be in different time zones).
Later we see that clock A has advanced by amount $\Delta A$ so it now reads $T_A+\Delta A$ while clock B has also advanced, but not to $T_B+\Delta A$ - instead it reads something else, $T_B+\Delta B$.
When $\Delta B\lt\Delta A$ we conclude that time is passing more slowly for B, and when $\Delta B\gt\Delta A$ we conclude that time is passing more quickly for B.

But there's a catch here. When I said "Initially clock A reads some time $T_{A}$ and clock B reads some time $T_{B}$" I was really saying that clock B reads $T_B$ at the same time that clock A reads $T_A$, and likewise the "later we see..." is really a statement about what clock B reads at the same time that clock A reads $T_A+\Delta A$. Without some synchronization procedure that allows us to relate the readings of the two clocks all we know is that time is passing at the rate of one second per second at each clock.

 

[Dale]

When you deal with time, which is not a spatial dimension, with geometry you haveto choose one: this is just a representation of the mathematics so we can at least understand things quantitatively or time as we know/feel it is completely an illusion, there is nothing as time itself only spacetime, however we don't know exactly what it is in nature.

Perhaps you should learn the material first before making pronouncements about what people who have already learned it must choose between. The specific branch of geometry is pseudo-Riemannian geometry which is itself a branch of differential geometry.

Again, what experiment were made to prove that the aspect of time of spacetime is responsible for gravity?

I am not sure what you are asking for here. I have already told you that I don’t think statements of the type “time causes X” are usually right. So I am not sure how you think “time is responsible for X” differs.

So I am not sure that I even agree with the claim “the aspect of time of spacetime is responsible for gravity” let alone have evidence for it. Can you explain more what you are asking for, because I agree in principle that experimental evidence is essential to have.

I wouldn't call it geometric, though.

You should. It is called a light cone, and it is a standard part of pseudo Riemannian geometry

Causes are always in the past light cone of effects and effects are always in the future light cone of causes. That is geometry, and it is geometry which constrains physical causality.

Knowing that, do you think that it is possible to try to explain, through any means possible, what is really happening? Maybe our brains and perceptions are incapable of that?

Yes, it is possible and many people’s brains are fully capable of it (including mine and most of the regulars on this forum). I cannot see what is in your head, but from what you write it seems that your difficulty stems more from a lack of willingness to accept the premises than any particular challenge of the material itself.

 

[Nugatory]

Again, what experiment were made to prove that the aspect of time of spacetime is responsible for gravity?

Well... The GPS system works, and it wouldn't work if General Relativity were wrong. Then we have the anomalous precession of Mercury, Pound-Rebka's demonstration of gravitational time dilation, more stuff linked in the sticky at the top this forum about experimental proof of relativity, gravitationa lensing and the measured deflection of light... People have been doing this stuff for more than a century now and that's long enough to build up a pretty huge body of support.

Now strictly speaking none of the experiments do exactly what you say: "prove" that the theory is correct. Instead, what they have done is agree with GR at every opportunty while also disproving all competing theories. However that is the way that all experiments work: they don't (and can't) prove the theory correct, they confirm that the theory has always been right so far.

 

[timmdeeg]

Again, what experiment were made to prove that the aspect of time of spacetime is responsible for gravity?

At fixed time you have two points. Let time flow then you have two neighboring geodesics which show (search geodesic deviation) whether or not if there is gravity. It's not that "the aspect of time of spacetime" is responsible for gravity.

 

[anuttarasammyak]

The transformable nature is the speed relation v=s/t. Since we fixed speed (c), then we can transform time into space (light-years) and vice-versa.

Familiar Galilean transformation is
x'=x-vt
t'=t
where primed is new spacetime coordinate after transformation. In the last century we find it incomplete to know the exact one is
x'=\cosh\theta \ x - \sinh\theta \ ct
ct'=\cosh\theta \ ct- \sinh\theta \ x
where
\cosh\theta=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}
\sinh\theta=\frac{\frac{v}{c}}{\sqrt{1-\frac{v^2}{c^2}}}
satisfying the relation
\cosh^2\theta-\sinh^2\theta=1
You perceive ct is introduced to match x as you stated as "speed relation".

This is much similar to the transformation by Rotation of angle $\theta$, i.e.
x'=\cos\theta \ x - \sin\theta \ y
y'=\cos\theta \ y+ \sin\theta \ x
satisfying the relation
\cos^2\theta+\sin^2\theta=1
This resemblance impress us spacetime rather than space and time.

How time can simulate a force acting upo objects inside space...

The above relation might be complex enough but still under absence of gravity. Gravity make spacetime structure much more complicated and thus generate observed force.

 

[ersmith]

... 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.

You seem to be assuming that there is a single universal "time", or at least a single direction in spacetime which is uniquely picked out as the direction of time. This is not the case. In fact time and space can and do get mixed up together, which is why we talk about "spacetime" in the first place rather than separate space and time.

For example, consider a clock, and label the spacetime event where it starts to tick one second as A, and the event where it starts to tick the next second as B. In the reference frame where the clock is stationary, the vector from A to B is pointing directly along the time axis and has no spatial component at all. However, in a different coordinate system where the clock is moving, there is a difference in spatial components: the clock has moved in space between A and B, and so the vector from A to B is not aligned with the time axis in these coordinates. The events are the same, it is just the coordinate systems which differ. Both coordinate systems are perfectly valid. (Note too that the interval, or spacetime distance, ||B-A||, must be the same in all inertial coordinate systems, so if it contains some spatial component in a "moving" frame then the temporal component must change; this is why time dilation exists.)

So it is perfectly reasonable to talk about "bending" a time axis, and in this case it really does mean mixing time and space coordinates. There is a limit to how much time and space can be mixed, and that limit is the speed of light (or the speed of causality).

 

[ffp]

@Nugatory Fair enough. But you are treating an hypothesis where we would do an experiment. The video I posted don't go this way. Think of it as if some external observer that could see everywhere clocks. I get your point though. Would you mind to give an analysis of the video?

I am not sure what you are asking for here. I have already told you that I don’t think statements of the type “time causes X” are usually right. So I am not sure how you think “time is responsible for X” differs.

So I am not sure that I even agree with the claim “the aspect of time of spacetime is responsible for gravity” let alone have evidence for it. Can you explain more what you are asking for, because I agree in principle that experimental evidence is essential to have.

That's good to read. What I'm asking is experimental proof for the statements, which I see often when reading/watching about relativity, that gravity is not a fundamental force the way the other 3 are and that is, instead, caused by the curvature of time. I've seen this more than once.

But, I think you didn't say that. In this case, let's take a step back and I ask you: Is gravity a fundamental force like electromagnetism, and nuclear weak and strong forces? And what is the cause of gravity?

You should. It is called a light cone, and it is a standard part of pseudo Riemannian geometry

Causes are always in the past light cone of effects and effects are always in the future light cone of causes. That is geometry, and it is geometry which constrains physical causality.

No. Geometry is used to represent the passing of time versus space. It's a representation to show that information cannot go beyond the past/future cones because its speed is limited by c. There is no light cone in our universe, it's just a way of explaining how it works. You can getrid of the cones by just explaining that nothing (including information) can travel faster than c, so if something is farther than 1 light-second away from you, you can't get any kind of contact/interaction with it in less than 1 second.

That's a very nice example of how you can explain something in our real world without using the math/geometry. And it's also an example of how the geometry is just a drawing that, sometimes, might help visualize or calculate things.

Yes, it is possible and many people’s brains are fully capable of it (including mine and most of the regulars on this forum). I cannot see what is in your head, but from what you write it seems that your difficulty stems more from a lack of willingness to accept the premises than any particular challenge of the material itself.

You are completely right. I was not asking if our brains were capable of understanding the theory of relativity, that is obvious. I was talking about we being able to trully comprehend and grasp what it means to live in a 4 dimensional universe, what exactly is spacetime and, of course, to understand (not accept) the premises and why they are true. Unless they are experimentally proven (that's why I asked before), in which case there is nothing more to understand than "we experimentally saw universe works this way", there must be a reason to believe it works that way.

@Nugatory , answering your second post, didn't want to make several quotes. I am not doubting the theory of relativity at all. I know about GPS, mercury orbit, etc. (even wrote those as examples in my posts). I'm specifically asking about the experiments about time and gravity. We can have the theory of relativity without having time to be responsibe for gravity.

@timmdeeg You answered with geodesics, which is related to the geometry of spacetime. My issue is the premisse that time can be treated as a spatial dimensional and curving it can do more than affecting the flow of time.

@anuttarasammyak Ok, what I understood from that is that space and time are related as if one can be a function of the other. I don't understand why you made that point in your last sentence.

@ersmith Great post. You had me until the last paragraph: "So it is perfectly reasonable to talk about "bending" a time axis, and in this case it really does mean mixing time and space coordinates. There is a limit to how much time and space can be mixed, and that limit is the speed of light (or the speed of causality)."

You painted two examples: one with a stationary clock, where it only moves throught the time axis (parallel to the time axis, perpendicular to space axis) and the other with a moving clock, having an angle between both axis. So, the moving clock will tick slower than the stationary clock, because part of that spacetime limit is now into the spatial axis and not only in the time axis.
I understand "mixing time and space" as being displaced in the spatial axis, which means changing the coordinates of both time and space. But not the bending of the axis. The axis are there just to measure the passing of time and distance. I don't understand what the heck it means to bend the line that is just used to count seconds.

 

[robphy]

I don't understand what the heck it means to bend the line that is just used to count seconds.

First of all,
the line (more completely, the worldline) is
the position-vs-time graph of the particle moving in this frame of reference.
In PHY 101, that line is drawn the same way.

What's different in Special Relativity is that we are not making the
incorrect Galilean approximation that the elapsed time along all worldlines
is given by the vertical displacement on the graph (assuming time runs upwards),
which you can think of as the worldline of Big Ben ticking as a master clock for the universe.

Instead, the elapsed time is given by a measure along that line,
ticked off by the particle's wristwatch,
akin to the way it is in Euclidean geometry (where distance is marked off by an odometer).

This may help...

Taken from a figure from a chapter of mine about to appear in print,
with time running to the right (like the usual position-vs-time graph)

when the blue worldline (describing a particle with velocity 3 m/s in this frame)
meets the t="1 s" vertical line,
the elapsed time along the blue segment from the origin to that t="1 s"-line
is not 1s, but 1-(5\times10^{-17})\rm\ s,
which may be measured by high-precision wristwatches soon,
but which we (for practical purposes) treat as "1s".

The problem is that this approximation is terrible when the particle speed is comparable to the speed of light. Since most of our lives, we deal with low relative-speeds,
our "common sense" approximation is so ingrained that we have trouble letting go of the approximation.

 

[PeterDonis]

No. Geometry is used to represent the passing of time versus space.

No, it is not.

It has already been pointed out to you more than once in this thread that, since you have admitted you are not knowledgeable about relativity, you should not be making claims about it; you should be thinking carefully about the answers you are getting to your questions.

If you are unable to do that, there will be no point in continuing this thread and it will be closed. It looks to me like you are getting close to that point now.

 

[PeterDonis]

What I'm asking is experimental proof for the statements, which I see often when reading/watching about relativity, that gravity is not a fundamental force the way the other 3 are and that is, instead, caused by the curvature of time.

Not time. Spacetime. You have been told this more than once already.

You have also already been told that asking for experimental "proof" of a theory is pointless. Theories are models. It is impossible to prove a model correct. The best you can do is to subject it to more and more stringent experimental tests, and see if it continues passing those tests. So far, GR has passed every experimental test that has been done.

Is gravity a fundamental force like electromagnetism, and nuclear weak and strong forces?

Not in the theoretical model of GR, no.

Many physicists believe that GR might not be a fundamental theory, and that some more fundamental theory of gravity (the usual term is "quantum gravity") might treat gravity as a "fundamental force" like the other three interactions in our current Standard Model of particle physics. Usually such theories are assumed to be a theory that somehow unifies all of the fundamental interactions. But no such theory has yet passed any experimental tests. And if you want to discuss such theories, the place to do it is in the Beyond the Standard Model forum, not the relativity forum.

what is the cause of gravity?

In GR, the spacetime geometry is caused by the distribution of matter and energy in the universe.