B Is time a true variable in the scheme of things?

[Suppaman]

Whatever the process is that controls how time passes for an object (and there are no lines) the object is moving about and when it returns home and it compares clocks the moving objects clock has counted less time. Now, what makes it not possible to find some way to manipulate the clock and everything else in that object so it can do "something" and when done compares clocks and find that more time has passed for the object. I do not think we really know the mechanics of what makes time pass at a given rate. Must it be a gravitational field, motion through space, something else? Since we know things can experience slower time the universe allows that, does it allow faster time?

 

[Nugatory]

You are teaching me. So, it is a different path for the two separated clocks on earth, the higher clock travels a longer path, it is not the difference in gravity felt by the clocks? Is this correct?

You are right that gravitational time dilation is calculated from the gravitational potential, not the gravitational force. But look again at what I said in #27 above - the situation in which the two clocks start together, separate, then come together again later so that we can see which one has ticked off more time is completely different from the situation in which we have a higher clock and a lower clock and we say that the lower clock is running slower than the higher one. Which case are you asking about in the text I just quoted above?

 

[Suppaman]

I thought that it was the difference in gravity that explained the two clocks on Earth but just separated. I can see that the higher clock does cover more distance through spacetime. But my post is not to explain what we know, it is to ask about having a situation where we can make a clock go faster and if physics prohibits that.

 

[Nugatory]

Whatever the process is that controls how time passes for an object (and there are no lines)…

There is no such process because time always passes at the same rate, one second per second, just like the odometer of a car clicks over once every kilometer you drive. There’s nothing to control.
There are lines (called “worldlines” and it is essential that you learn what they are - drawing and understanding them in ordinary flat Minkowski space is a good exercise and you have to be able to do that before you can take on gravitational effects anyway so you might as well try it).

the object is moving about and when it returns home and it compares clocks the moving objects clock has counted less time. Now, what makes it not possible to find some way to manipulate the clock and everything else in that object so it can do "something" and when done compares clocks and find that more time has passed for the object.

You would have to send the object on a longer path through spacetime, so that its clock would tick off more time between departure and returning home (just as we could send a car on a long detour if we wanted to cover more kilometers on a trip between points A and B) . Here the two points are the events “clocks separate” and “clocks rejoin”. However, it turns out that the longest possible path between two points in spacetime is the path followed by an object that is in free fall between them - and that’s the path followed by the clock that isn’t moving about, just sitting still waiting for the other one to come back. You

In this regard spacetime is different from ordinary three-dimensional Euclidean space, the stuff we learn about in high-school geometry class. In Euclidean space, there is a shortest distance between two points, the straight line connecting them. In spacetime the geometry is non-Euclidean and instead of a shortest distance between two points there’s a longest distance and you can’t find any longer distance.

I do not think we really know the mechanics of what makes time pass at a given rate.

speak for yourself now...

 

[Herman Trivilino]

Whatever the process is that controls how time passes for an object (and there are no lines) the object is moving about and when it returns home and it compares clocks the moving objects clock has counted less time. Now, what makes it not possible to find some way to manipulate the clock and everything else in that object so it can do "something" and when done compares clocks and find that more time has passed for the object.

Because the clock that stayed at home shows the maximum possible elapsed time. Just as the shortest distance between two dots on a flat sheet of paper is a straight line. You seem to have trouble accepting the first claim, but you haven't responded to the validity of the second statement. Every thing you wonder about the validity of the first statement can be said of validity of the second statement.

For example, why is it not possible to make the distance between the dots on the flat sheet of paper less than the length of the straight line? Is there something wrong about the way we've defined length? Whatever the process that controls the length of the line, the straight line is always the shortest.

 

[cyboman]

This is a fascinating discussion. And much of it is over my head.

Perhaps, considering the fact that C is constant could be useful? Such that, it isn't so much that time is faster or slower. It's that when measuring velocity C is always C, so time and distance must change in order to account for the different states of frames. This is only noticeable as you approach C.

I think what the OP may be confusing, and I think this is suggested, is that it is not the passage of time that changes. As said, it always ticks. Think the film, Back to the Future (A personal fav), for the dog, nothing changed in his frame, the clock ticked the same. It's the difference between the two frames and the fact the velocity C is constant. So the others parameters of distance and time must dilate / contract.

Don't know if that is at all correct. I'm channeling my understanding of special and general I read from many years ago.

 

[cyboman]

Whatever the process that controls the length of the line, the straight line is always the shortest.

Right, I hope I'm not complicating the analogy by stating this: Note that the shortest path in space time is a curved line not a straight one. Since mass bends space-time.

 

[PeroK]

Right, I hope I'm not complicating the analogy by stating this: Note that the shortest path in space time is a curved line not a straight one. Since mass bends space-time.

In fact, in flat spacetime the straight line is the longest path between two points.

 

[cyboman]

In fact, in flat spacetime the straight line is the longest path between two points.

From what I understand. Spacetime is not flat.

 

[PeroK]

From what I understand. Spacetime is not flat.

It's locally flat and for many applications, e.g. high energy particle physics, only SR is required. The curved spacetime of GR is relevant to the solar system and galaxies etc.

In any case, in both flat and curved spacetime particles travel on paths, whether straight or not, that maximise the spacetime distance travelled.

 

[cyboman]

It's locally flat and for many applications, e.g. high energy particle physics, only SR is required. The curved spacetime of GR is relevant to the solar system and galaxies etc.

In any case, in both flat and curved spacetime particles travel on paths, whether straight or not, that maximise the spacetime distance travelled.

Right, but from my understanding, if you're ever think space-time is flat, it's because that perception has mathematical or visual cognitive advantages for thinking of it that way. In truth, it is curved.

Perhaps, it's only usefully considered flat because you are "zoomed" so far in.

 

[cyboman]

It's locally flat and for many applications, e.g. high energy particle physics, only SR is required. The curved spacetime of GR is relevant to the solar system and galaxies etc.

In any case, in both flat and curved spacetime particles travel on paths, whether straight or not, that maximise the spacetime distance travelled.

My intuition is that they are never traveling on straight paths. That may seem so in a localized frame. But ultimately, any particle traveling will follow a non-euclidean arc along curved space-time.

 

[weirdoguy]

Right, but from my understanding, if you're ever think space-time is flat, it's because that perception has mathematical or visual cognitive advantages for thinking of it that way. In truth, it is curved

No. Specetime of special relativity is flat in the mathematical sense, i.e. its curvature tensor vanishes globally.

 

[cyboman]

No. Specetime of special relativity is flat in the mathematical sense, i.e. its curvature tensor vanishes globally.

This is perhaps, over my head mathematically. But I would contend, the mathematics are not euclidean. Or flat. Einstein had to produce his own mathematics to deal with this space.

From an astronomical viewpoint, mass effects space-time, and the bodies that interact with that gravity / forces follow arcs, not straight lines. Because the space itself, is curved.

 

[PeroK]

My intuition is that they are never traveling on straight paths. That may seem so in a localized frame. But ultimately, any particle traveling will follow a non-euclidean arc along curved space-time.

Nature is under no obligation to follow your intuition.

If by non-Euclidean arc you mean a geodesic of the curved spacetime then, ironically, many people use that as the generalized definition of a straight line!

 

[cyboman]

[NQUOTE="cyboman, post: 6171798, member: 470031"]
My intuition is that they are never traveling on straight paths. That may seem so in a localized frame. But ultimately, any particle traveling will follow a non-euclidean arc along curved space-time.

Nature is under no obligation to follow your intuition.

If by non-Euclidean arc you mean a geodesic of the curved spacetime then, ironically, many people use that as the generalized definition of a straight line!
[/QUOTE]

OK, but that's not intrinsically, a straight line. It's actually curved. Mathematically, locally, straight perhaps, but to qualify it that way would not be accurate. It is perhaps, locally straight, but ultimately curved. Those of us that are not in the deep algebra of it all need to understand that difference.

 

[PeroK]

From an astronomical viewpoint, mass effects space-time, and the bodies that interact with that gravity / forces follow arcs, not straight lines. Because the space itself, is curved.

Before Einstein it was clear that the Earth traveled in a curved (almost circular) orbit through space around the sun.

Ironically, Einstein found that, in a way, the Earth follows a straight line through curved spacetime.

 

[PeroK]

From an astronomical viewpoint, mass effects space-time, and the bodies that interact with that gravity / forces follow arcs, not straight lines. Because the space itself, is curved.

Before Einstein it was clear that the Earth traveled in a curved (almost circular) orbit through space around the sun.

Ironically, Einstein found that, in a way, the Earth follows a straight line through curved spacetime.

 

[cyboman]

Before Einstein it was clear that the Earth traveled in a curved (almost circular) orbit through space around the sun.

Ironically, Einstein found that, in a way, the Earth follows a straight line through curved spacetime.

I disagree, it's semantic I think. But the path is not straight unless you are taking into account the space being curved. And for most analysis that would look like an arc not a straight line. But I admit, perhaps you understand it more than me and to you it looks straight. I simply don't see it that way. I see your perspective as a localized perspective.

I think it may be a mathematical visualization vs an intuitive one. We could argue forever which is more correct. I think perhaps they both are.

And it is a matter of relativity.

 

[cyboman]

Before Einstein it was clear that the Earth traveled in a curved (almost circular) orbit through space around the sun.

Ironically, Einstein found that, in a way, the Earth follows a straight line through curved spacetime.

A straight line through curved space time is an arc.

 

[PeroK]

From an astronomical viewpoint, mass effects space-time, and the bodies that interact with that gravity / forces follow arcs, not straight lines. Because the space itself, is curved.

Before Einstein it was clear that the Earth traveled in a curved (almost circular) orbit through space around the sun.

Ironically, Einstein found that, in a way, the Earth follows a straight line through curved spacetime.

 

[PeroK]

A straight line through curved space time is an arc.

You ought to research the term "geodesic".

In any case, the geodesics of spacetime, which are the paths that particles and planets naturally take, are paths of maximal spacetime distance.

 

[cyboman]

You ought to research the term "geodesic".

In any case, the geodesics of spacetime, which are the paths that particles and planets naturally take, are paths of maximal spacetime distance.

So from an objective frame, does the particle follow a straight line, or does it follow a geodesic arc along space-time? What is your frame of reference?

 

[PeroK]

So from an objective frame, does the particle follow a straight line, or does it follow a geodesic arc along space-time? What is your frame of reference?

Geodesics are independent of frame of reference.
As I said, many people consider a geodesic as the definition of a straight line.

Personally, I reserve straight line for Euclidean geometry and simply use geodesic.

But, there is no other possible definition of a straight line in curved spacetime. It's either a geodesic or left undefined. An arc is likewise an undefined term.

One problem with the question is that descriptions like straight line and arc depend on your coordinates. Unless you give them some coordinate free description, like shortest distance between two points, or maximal spacetime distance between two points.

You can define a straight line in these ways in classical mechanics and SR. And you can extend the latter definition to curved spacetime if you wish. But unless you do that straight line has no meaning in curved spacetime.

 

[cyboman]

Geodesics are independent of frame of reference.
As I said, many people consider a geodesic as the definition of a straight line.

Personally, I reserve straight line for Euclidean geometry and simply use geodesic.

But, there is no other possible definition of a straight line in curved spacetime. It's either a geodesic or left undefined. An arc is likewise an undefined term.

One problem with the question is that descriptions like straight line and arc depend on your coordinates. Unless you give them some coordinate free description, like shortest distance between two points, or maximal spacetime distance between two points.

You can define a straight line in these ways in classical mechanics and SR. And you can extend the latter definition to curved spacetime if you wish. But unless you do that straight line has no meaning in curved spacetime.

Fascinating.

I guess I was thinking that the conventional Newtonian idea of a straight line, in a curved space-time is actually an arc. This is what I come to understand of SR. The shortest distant turns out to be a curve, not a line, because the space itself is bent and non-euclidean due to gravity.

 

[PeroK]

Fascinating.

I guess I was thinking that the conventional Newtonian idea of a straight line, in a curved space-time is actually an arc. This is what I come to understand of SR. The shortest distant turns out to be a curve, not a line, because the space itself is bent and non-euclidean due to gravity.

If you take an example from Newtonian physics. A ball falls straight down under gravity. That is spatially a straight line in the Earth's reference frame. But if you plot height against time, then as the ball is accelerating it's path in Newtonian spacetime is curved.

Whereas a ball moving at constant velocity would follow a straight line through Newtonian spacetime.

This is also true in the flat spacetime of SR.

But, in GR the ball falling under gravity is not accelerating. In the sense that it feels no force and has no intrinsic or "proper" acceleration.

Whereas the ball rolling along a table does feel an upward force from the table, so is accelerating.

The situation in GR is somewhat reversed. And, it is not just semantics to say that the ball in free fall - or a planet in orbit - is following a natural, geodesic "straight" path through spacetime. And the ball rolling at constant velocity is not following a geodesic path but being accelerated in a "curved" path.

 

[Herman Trivilino]

But I would contend, the mathematics are not euclidean. Or flat.

The spacetime of special relativity is flat, but it is not Euclidean.

 

[Herman Trivilino]

Note that the shortest path in space time is a curved line not a straight one.

There is no shortest path through spacetime for objects with mass. However short a path you choose, a shorter one can always be found.

Just as, on that flat sheet of paper I was talking about, there is no longest path between the two dots. However long a path you choose, a longer one can always be found.

 

[cyboman]

Thanks for the examples!

That is spatially a straight line in the Earth's reference frame.

But isn't it true that that's because it locally only appears that way. Because you are in effect zoomed in so far. It looks like it's straight, but if you go far enough out it's actually happening in curved space-time. So like everything else, the ball exists in curved space-time due to the mass of the Earth.

This is also true in the flat spacetime of SR.

But when you say flat spacetime, are you not assuming there is no gravity. Empty spacetime is flat where no masses are curving it.

And the ball rolling at constant velocity is not following a geodesic path but being accelerated in a "curved" path.

Is a geodesic path not curved? Zoomed in locally it appears straight. It's as close to straight as you can get, but it's still a curve. So, there are no straight lines in curved space-time. Isn't that correct? If there is no Earth then the space-time is flat and you could say there are straight lines right.

 

[cyboman]

The spacetime of special relativity is flat, but it is not Euclidean.

It's only flat if there is no masses curving it though right? In the context here the Earth is curving space-time.

I'm wondering, could one argue that everywhere in the universe space-time has some curvature?