Questions regarding traveling speed in time and gravity as a force

[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.

 

[Grasshopper]

I don’t understand how there CAN’T be time curvature since clocks do not tick at the same rate relative to altitude. I mean, when you look straight down at a curved surface, the only reason you know it’s curved is because points of perspective appear further away from each other or closer to each other than they would be if the surface were flat. Likewise, if you compare ticks of a clock where time curves to a clock where time doesn’t curve, I imagine the time between ticks on the curved time clock will be greater the closer you get to the surface, while a “flat time” clock would have the same interval between ticks (relative to the clocks you compare with, which are at different altitudes). Drawing little dots (ticks) that get further and further away from each other on one end and closer and closer to each other intuitively feels to me like an exact analogue of one dimensional curvature. If I wanted to draw a 1D curvature, that is exactly how I’d draw it. Like this:

If you are running holding a leaking bottle, the drops will be further apart when you’re running fast, and closer when you’re running slow. Which means there’s an acceleration, and if you plot that on a time vs space graph, you’re plotting a curve. The analogy only goes so far, but the plot points resemble a curve to me.
That’s kind of what curved spatial surfaces do when you look down at them: the distance between points you’d use to gauge how far away something is different than if the surface were flat. Since clocks in a gravitational field do something analogous to what a curved surface does, I don’t see what is wrong with saying time is curved.
And as for the spacetime thing, in SR it is already clear that one man’s time is another man’s spacetime (much like one man’s electric field is another man’s combination of a magnetic field and electric field). Since even in flat spacetime you have the mixing of space and time depending on reference frame, the notion of curved spacetime — including curved time for reasons above — doesn’t seem problematic to me.

 

[anuttarasammyak]

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.

Starting from comparison of IFRs in SR, you would share interest with me in observing rotating system that is like a merry-go-round. The larger the radius, the faster the piece moves tangent so #1 Slower time goes. the pieces go out if not bound toward the center. #2 Force (centrifugal force) appears. Perimeter rope of length $2\pi r$ is not enough due to Lorentz contraction of the parts. #3 Perimeter / radius > 2$\pi$. These amazing features in rotating system as function of radius are almost what you would expect in "bending of the axis", aren't they ?

Honestly saying, rotating system is a fake of bending spacetime because we can make it global IFR just by stopping rotation. Gravity does them in real way that we can cancel them only locally but not globally.

 

[A.T.]

I don’t understand how there CAN’T be time curvature since clocks do not tick at the same rate relative to altitude.

The problem lies with the term "curvature". It can mean different things. The cone surface in the video below has no intrinsic curvature (that's why we can roll it out flat without distortion). But it shows variable distances along the time dimension depending on altitude, which implies varying time dilation and gravity (apple falls down).

Of course if you draw the global picture, there will be intrinsic curvature (we cannot roll it out flat without distortion), because there is no way to connect the local cones without introducing it:

 

[ersmith]

@ersmith
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.

The line that "just counts seconds" in one coordinate system (e.g. that in which the clock is stationary) counts both seconds and meters in another coordinate system (e.g. one in which the same clock is considered "moving").

Now consider the case where a clock is considered to be "accelerating". In that case the relationship between space and time is continuously changing. For example, suppose an observer is inside an accelerating spaceship with two very accurate clocks. She drops one and uses the other to record the ticks of the falling clock (adjusting for light speed travel time, of course). Each tick of the falling clock is a microsecond, so if it takes 1 second to drop to the floor of the spaceship cabin then the observer will record a million ticks. These ticks all take place at different points in the cabin, so (relative to the observer's preferred reference frame, where she is considered stationary) they each have a different point in both space and time, whereas the clock the observer continues to hold only change in time (relative to the observer). If we plot a spacetime diagram in the observer's reference frame, the held clock follows a "straight" line in spacetime (along the observer's time axis) and the falling clock follows a "bent" or "curved" line as it continuously changes speed.

Now let's look at it from the perspective of the falling clock. In its preferred reference frame it remains stationary, and its time axis is straight, but the observer, rocket, and held clock are all accelerating relative to it and the held clock's spacetime diagram is a curved line. This is also the point of view that an outside observer would have.

So which one is "truly" accelerating? Well, we can attach an accelerometer to both clocks and see that it's the held one which is accelerating (the rocket is pushing on it) and the falling one is not. Put another way, the held clock is experiencing a force, the falling one is not.

Now consider the same experiment on the surface of the Earth. Again, we would find that the falling clock experiences no forces, whereas a held clock is continuously experiencing a 1g acceleration. This is why gravity is considered a fictional force in GR; the clock that's "falling" is not actually experiencing any force (at least not so far as we can measure) whereas a clock that's supposedly "at rest" on the surface of the Earth is experiencing a force, and you can physically measure that with a scale or other force measuring device.

So saying that a dropped apple falls down to the Earth is not really accurate. It's more accurate to say that the Earth's surface accelerates upwards to meet it. This is where our intuition about space and time becomes difficult, because naturally we assume that if the Earth's surface is everywhere accelerating then the Earth must be growing (or shrinking). That would only be true if spacetime were flat around the Earth. The fact that the Earth isn't changing in size shows that spacetime around the Earth is curved.

 

[ffp]

@robphy Oh, sorry I wasn't talking about the worldline, but about the time axis.

No, it is not

I was talking about the light cone. While I don't know much about relativity, I know what a light cone is. And it doesn't exist in real world. You don't see cones for every object/particle around. It is just a tool to demonstrate what I said in the post you quoted. If you think I am wrong, please explain why. That might be a good game-changing information.

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.

Do you think there is much difference in stating that gravity comes from time or spacetime? I still find it an odd statement. I can understand space being curved. I can understand time being curved. I can understand both having a relation. I can't understand the dimension of time (even that it's spacetime, it still have differentiation of space and time, they are not the same) affecting the displacement of objects in space (I'm hitting that key because I saw that explanation several times, including in books that were recommended here!).

Yes, GR has passed all the tests. Those proved time dilation, curved space (or spacetime if you will), constant speed of light, etc. However nothing related to gravity and its origins, as far as I know. What you think about that?

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

That is very intersting! This more fundamental theory disregard gravity being a product of spacetime curvature? I will take a look at them and in the respective forums.
Also, this means that not all scientific community agree about the explanation of gravity provided by GR?

@Grasshopper Great post. I don't have an issue with "cruved time" either, as long as it works as you said, by having different flow of time rates, and not affecting objects in space.

@anuttarasammyak You said that time goes slower for points farther from the the center as they rotate faster. There is length contraction because of that speed difference. Centrifugal force appears. I don't get the perimeter/radius >2pi. Nor how this is analog to bending the axis.

@ersmith The "line that count seconds" I was talking about is the time axis.
The Earth surface going up thing is another issue of GR that I can't understand. Why having a spacetime curved around Earth stops its expansion? Also, about the accelerometer, they works similar to a spring inside the housing attached to a small part, it's the acceleration of the inside in relation to the housing that is measured. It reads 0 in freefall because the housing and the device inside are both accelerating equally, while on Earth you are holding the housing.

 

[jbriggs444]

I was talking about the light cone. While I don't know much about relativity, I know what a light cone is. And it doesn't exist in real world. You don't see cones for every object/particle around. It is just a tool to demonstrate what I said in the post you quoted. If you think I am wrong, please explain why. That might be a good game-changing information.

A light cone is "real" in the sense that many physicists would use the term. It is something that is "invariant". We call a thing invariant if it holds independent of the frame of reference or coordinate system that you adopt.

Whether event a is on the light-cone of event b is an invariant fact of the matter. It does not depend on one's point of view. This is enough to make it "real" in our eyes.

We can do physical measurements to determine where the light cone for a particular event is. Measurements that give the same result regardless of one's choice of reference frame. That is as real as it gets.

Contrast this with the question of whether two events occur at the same time. The answer to this question is not invariant. It depends on an arbitrary choice of synchronization convention. There is no "real" answer to this question.

 

[anuttarasammyak]

I don't get the perimeter/radius >2pi. Nor how this is analog to bending the axis.

Rotating system people measure the perimeter for r=1 m with measure and find perimeter is more than 2$\pi$ = 6.28.. m.

I tried to understand what you mean by saying "bending the axis". If your bending axis has nothing to do with phenomena of time pace change, emergent force or geometry change, I have nothing more to do for now, please forget what I said.

 

[PeterDonis]

I don’t understand how there CAN’T be time curvature

Time isn't a surface (or more generally a manifold), so "time curvature" makes no sense. Spacetime is what is curved in the presence of gravitating masses.

 

[PeterDonis]

I was talking about the light cone.

Doesn't change my response at all.

And it doesn't exist in real world.

"Exist in the real world" is not a scientific concept to begin with, so it's off topic here. This is a physics forum, not a philosophy forum.

Our model of spacetime, including light cones, makes very accurate predictions that have passed thousands of experimental tests. That's the most you can ask of a scientific model.

Do you think there is much difference in stating that gravity comes from time or spacetime?

Nobody has said either of those things. What we have said is that gravity comes from curvature of spacetime.

I can understand space being curved.

Spacetime being curved is the same kind of thing. Spacetime is a geometric manifold, just like the "space" you are imagining, and the same geometric concepts apply to it.

I can understand time being curved.

I don't see how, since, as I said in post #68 just now, time isn't a surface (or more generally a manifold), so saying it is curved makes no sense.

(even that it's spacetime, it still have differentiation of space and time, they are not the same)

It is true that spacelike and timelike vectors are different kinds of things in spacetime; but those are not the same as "space" and "time". "Space" and "time" are coordinate-dependent, and as you have already been told, coordinate-dependent concepts are the wrong thing to focus on if you want to understand physics. The right things to focus on are invariants; whether a particular vector is spacelike or timelike (or null, aka lightlike) is an invariant.

GR has passed all the tests. Those proved time dilation, curved space (or spacetime if you will), constant speed of light, etc. However nothing related to gravity and its origins, as far as I know.

I have no idea what you're talking about. GR is a theory of gravity. All of the experimental tests of GR involve gravity.

This more fundamental theory disregard gravity being a product of spacetime curvature?

No. It says that gravity being a product of spacetime curvature is an approximation valid in a particular range of circumstances (roughly, when spacetime curvature is small enough that quantum gravity effects can be ignored--which turns out to be a pretty wide range; our current best guess is that quantum gravity effects don't become significant until spacetime curvature reaches the Planck scale, which corresponds to an energy density about 94 orders of magnitude larger than the energy densities in our solar system). This is no different from Newtonian gravity being an approximation to General Relativity valid in a particular range of circumstances (when gravity is weak and all speeds are slow compared to the speed of light).

this means that not all scientific community agree about the explanation of gravity provided by GR?

No. It just means that the scientific community is considering the possibility that GR might not be a fundamental theory. GR will still be a valid approximation within its domain no matter how that comes out, which means that within that domain, GR's explanation of gravity using spacetime curvature will still be valid, since it will still make accurate predictions. Just as the Newtonian model of gravity as a force still works just fine if you're trying to predict the trajectory of a baseball, let's say, here on Earth.

 

[ersmith]

The "line that count seconds" I was talking about is the time axis.

There is no unique time axis. There are infinitely many possible choices for a time axis. There's no point in talking about "time" as a thing independent of "space", because one observer's time axis is skewed into space in another observer's coordinate system. This is really important: you won't understand relativity if you don't get that space and time are not independent. That's why saying something like "gravity is caused by curvature of time" is nonsense: "time" isn't a well defined thing, you always have to consider space along with it. It's also why light cones are so important: all observers, regardless of how they divide spacetime into "space" and "time", can agree on the contents of light cones and hence on what things are "past", "future", and "elsewhere". Note my choice of words: "present" does not have a unique meaning in relativity (due to the relativity of simultaneity) and "past" and "future" are only defined relative to a light cone.

The Earth surface going up thing is another issue of GR that I can't understand. Why having a spacetime curved around Earth stops its expansion?

OK, this one is hard. At some level this question is like "why in Newtonian physics do things move in a straight line unless acted on by a force"? The answer is, that's just the way things work. Similarly, in GR objects not acted on by a force move in a "straight line" in curved spacetime. In the absence of any forces everything on the Earth's surface would follow geodesics in spacetime, i.e. would keep falling towards the center of the Earth (forming a black hole).

Similarly for a "falling" apple. It's just following the nearest thing to a straight line that exists in local spacetime, namely a path that leads towards the center of the Earth in the future. It'll follow that path until acted upon by a force, e.g. contact forces from the surface of the Earth (or from your hand, if you catch it). Note that its path goes through both space and time.