I Is time really moving backwards?

[Joe30174]

TL;DR Summary

Let's say I am free falling off a skyscraper. Relative to me, earth is coming towards me and alluding that I am falling towards the earth.

Does the dimension of time follow the same logic? Is time moving backwards relative to me, resulting in me moving forward in time?

If so, is it simply just semantics to say wether time is moving forward or backward?

I don't have much knowledge on general and special relativity except what I watch on youtube and read, btw.

Edit: In addition, is traveling through a geodesic in spacetime relativistic between the object and spacetime itself? In other words, if I was traveling through a geodesic deep in space, relative to me am I moving through spacetime? Or is spacetime traveling around me?

 

[phinds]

Is time moving backwards relative to me

No.

 

[Ibix]

I don't think so.

The problem is that it isn't a spatial dimension that's moving in your first case - it's the Earth, an object in space. So it isn't analogous to ask if "the dimension of time" is moving backwards. You are correct to note that we are free to regard the Earth as coming to us or us as going to the Earth, but I don't think there's really any proper analogy with anything in a timelike sense. Geometrically, what we mean by "the Earth is moving relative to us" is that its worldline makes an angle with ours, and I can't see a way to make an analogy of the type you are looking for. The closest I can make is to observe that Monday morning comes at different times for frames in motion with respect to the Earth.

If you want to learn about relativity properly, it's in reach if you have high school level maths. Nothing tougher than Pythagoras' theorem is needed. Unfortunately many YouTube videos are wildly misleading. A good textbook will serve you much better - my personal favourite is Taylor and Wheeler's Spacetime Physics, which is free to download from Taylor's website.

 

[Joe30174]

I don't think so.

The problem is that it isn't a spatial dimension that's moving in your first case - it's the Earth, an object in space. So it isn't analogous to ask if "the dimension of time" is moving backwards. You are correct to note that we are free to regard the Earth as coming to us or us as going to the Earth, but I don't think there's really any proper analogy with anything in a timelike sense. Geometrically, what we mean by "the Earth is moving relative to us" is that its worldline makes an angle with ours, and I can't see a way to make an analogy of the type you are looking for. The closest I can make is to observe that Monday morning comes at different times for frames in motion with respect to the Earth.

If you want to learn about relativity properly, it's in reach if you have high school level maths. Nothing tougher than Pythagoras' theorem is needed. Unfortunately many YouTube videos are wildly misleading. A good textbook will serve you much better - my personal favourite is Taylor and Wheeler's Spacetime Physics, which is free to download from Taylor's website.

Perfect response because the entire point of my question, or what I was looking for, is wether time and space were analogous in that regard. Just trying to get a better comprehension on this whole spacetime thing lol. Thank you for the timely response.

 

[Ibix]

Edit: In addition, is traveling through a geodesic in spacetime relativistic between the object and spacetime itself? In other words, if I was traveling through a geodesic deep in space, relative to me am I moving through spacetime? Or is spacetime traveling around me?

This doesn't make much sense, I'm afraid. "Moving with respect to spacetime" isn't a thing you can do or not do. There's no way to peg something to spacetime so you can tell if it's moving or not - spacetime may not even be a real thing, but just something that appears in the concepts underpinning our mathematical model.

 

[etotheipi]

Edit: In addition, is traveling through a geodesic in spacetime relativistic between the object and spacetime itself? In other words, if I was traveling through a geodesic deep in space, relative to me am I moving through spacetime? Or is spacetime traveling around me?

Nothing moves in spacetime, the manifold is the entire history of the system. World lines are time like curves on the manifold, but particles do not 'move' along their world lines

 

[Joe30174]

This doesn't make much sense, I'm afraid. "Moving with respect to spacetime" isn't a thing you can do or not do. There's no way to peg something to spacetime so you can tell if it's moving or not - spacetime may not even be a real thing, but just something that appears in the concepts underpinning our mathematical model.

Just started reading a book by Brian greene and haven't gotten too far into it yet. But so far he seemed to point out that accelerated motion was relativistic to spacetime, according to Einstein. He may touch up on it more later and refute that point though, haven't gotten far enough into it.

 

[Ibix]

But so far he seemed to point out that accelerated motion was relativistic to spacetime, according to Einstein.

I would say you've misunderstood something - I very much doubt that Einstein said anything of the sort. I'd suggest a re-read of the passage, and if you still think it says what you say it says, post a quote and we'll see if we can make sense of it.

Note that Greene's popularisations are well known here for confusing people. We get a lot of questions from people saying "Greene says..." where we end up saying that what he's said is misleading.

 

[Joe30174]

I would say you've misunderstood something - I very much doubt that Einstein said anything of the sort. I'd suggest a re-read of the passage, and if you still think it says what you say it says, post a quote and we'll see if we can make sense of it.

Note that Greene's popularisations are well known here for confusing people. We get a lot of questions from people saying "Greene says..." where we end up saying that what he's said is misleading.

Yes I will have to look for that passage when I get a chance. What do most physicists tend to lean more towards as of today? Spacetime being a "thing" or not?

 

[etotheipi]

Spacetime is a pair $(M, g_{ab})$

 

[Dale]

If so, is it simply just semantics to say wether time is moving forward or backward?

Well, time doesn’t move, it just is. But we move, and you could certainly say that we move through time backwards. When you walk forwards you see where you are going and when you walk backwards you see where you have been. So with respect to time we only “see” the past which is where we have been.

So we move backwards through time in the same sense as we can walk backwards. No wonder we have so much trouble. Walking backwards is dangerous!

 

[Ibix]

Yes I will have to look for that passage when I get a chance. What do most physicists tend to lean more towards as of today? Spacetime being a "thing" or not?

I don't think most would take a position one way or the other. Most will talk about spacetime as a thing (a manifold and metric, as @etotheipi says) because talking about any physical model (not just in relativity) would be really clumsy if we had to caveat every last thing that's in the model but is not a direct observable with "...if it is more than a concept in the model". But if pressed on whether spacetime is really real, I think you'd find most would shrug. It's a useful concept that let's us make predictions that keep turning out to be accurate, so it's real enough for our purposes.

 

[Joe30174]

Nothing moves in spacetime, the manifold is the entire history of the system. World lines are time like curves on the manifold, but particles do not 'move' along their world line

Nothing moves in spacetime, the manifold is the entire history of the system. World lines are time like curves on the manifold, but particles do not 'move' along their world lines

Thank you, but I have no idea about world lines. So thank you for giving me something new to delve into lol

 

[Joe30174]

I don't think most would take a position one way or the other. Most will talk about spacetime as a thing (a manifold and metric, as @etotheipi says) because talking about any physical model (not just in relativity) would be really clumsy if we had to caveat every last thing that's in the model but is not a direct observable with "...if it is more than a concept in the model". But if pressed on whether spacetime is really real, I think you'd find most would shrug. It's a useful concept that let's us make predictions that keep turning out to be accurate, so it's real enough for our purposes.

Would be nice for people who teach this stuff to clarify that it is referred to as a something for helpful purpose it serves rather than implying it is determined.

Are there any answers to how it can curve and warp from mass such as planets, or how dark energy can make it expand if it's not a something? Wouldn't that be evident that it is a something? What are the supporting evidence to believe otherwise?

 

[phinds]

Are there any answers to how it can curve and warp from mass such as planets, or how dark energy can make it expand if it's not a something?

Spacetime is geometry. Mass affects the characteristics of the geometry. This is well understood, as is the expansion due to "dark energy". We don't know what dark energy IS but we know quite well what it DOES.

 

[Ibix]

Would be nice for people who teach this stuff to clarify that it is referred to as a something for helpful purpose it serves rather than implying it is determined.

Popularisations tend not to spend time on the fine philosophical distinction between observations, interpretations of observations, and models, and how they fit together. So you do tend to find things that are definitely true and real (in a model) stated without the qualifier, I'm afraid. It's an ongoing problem. I do wish that distinction were taught in schools, because understanding it is key to evaluating an awful lot of stuff beyond scientific topics.

Are there any answers to how it can curve and warp from mass such as planets,

No. The Einstein Field Equations describe how curvature is related to the distribution of stress-energy (which includes mass), but not why. A theory of quantum gravity may give you an answer, but it'll have it's own "just because" assumptions underlying it.

how dark energy can make it expand if it's not a something

That's not what dark energy does. Spacetime doesn't expand anyway - it's space that's said to expand, and that's a rather dubious description of the full picture (but probably as good as you can do without going into the maths). And dark energy doesn't make "space expand", just modifies the rate. Once again it's all governed by the Einstein Field Equations, so at the moment falls under "because that's the way the world works" with no deeper explanation that we're yet aware of (although quantum gravity theorists will happily tell you what their particular favourite theory says).

When we set up a manifold initially filled more-or-less uniformly with matter, the field equations say that two test particles initially at rest with respect to each other will start to move apart. Since neither of the particles feels any acceleration but they get further apart, it's not unreasonable to say that the space between them has expanded. But remember that spacetime is a four-dimensional manifold. That means that "space, now" is one 3d slice through the 4d whole and "space, in a minute" is a slice through a different part. So if you think of spacetime as a thing, nothing expanded. You just looked at different bits of it where stuff was different distances apart (everything was closer together in the earlier slice).

 

[etotheipi]

Landau referred to it as a "fictitious space".

It's useful to keep in mind that spacetime - a continuum of of "events" - isn't a concept inherent to relativity. For example, in classical mechanics, spacetime is a four-dimensional affine space $A^4$ over $\mathbf{R}$ equipped with a linear mapping $t: \mathbf{R}^4 \longrightarrow \mathbf{R}$ such that the time interval between $a, b \in A^4$ is $t(a-b)$. Thus Newtonian spacetime is foliated by hyperplanes $\Sigma_{\lambda}$ such that $A^4 = \bigcup_{\lambda \in \mathbf{R}} \Sigma_{\lambda}$. Each hyperplane is Newtonian absolute space at the instant $\lambda$ of absolute time.

But in the special theory, spacetime has a completely different causal structure. In the special theory spacetime is a tuple $(M, g_{ab}, \mathscr{J}^+, \epsilon_{abcd})$ where $M \cong \mathbf{R}^4$ is an affine space over $\mathbf{R}$, the metric $g_{ab}$ is is a symmetric non-degenerate bilinear form of Lorentzian signature, $\mathscr{J}^+$ is the future null cone of the metric which defines an arrow of time, and $\epsilon_{abcd}$ gives the spacetime an orientation. Given any event $p \in M$ one may still partition the spacetime into a causal past of $p$, causal future of $p$, past and future light cones of $p$ and events spacelike separated from $p$, however simultaneity is now well and truly observer-dependent.

It is more complicated still in the general theory, since rather than an affine space one now has a differentiable manifold which only locally is isomorphic to $\mathbf{R}^4$, and the spacetime metric is also no longer flat!

 

[Ibix]

...classical mechanics...
...in the special theory...
...in the general theory...

@Joe30174 - what etotheipi has written is a good example. There's quite a lot of "spacetime is xyz". That's fine because he's qualified it each time with the bits I've quoted - he's talking about components of our theoretical models and the bits of the models definitely really are bits of the models. But if you are not used to thinking in terms of formal models of reality you could easily miss those qualifiers (or not catch their importance, anyway) and read him as just saying "spacetime definitely is xyz in reality (and we know this because we're super brainy)".

So even when there are qualifiers they're easy to miss. And, to be honest, popularisations won't always be careful to put them there in the first place.

 

[Vanadium 50]

because understanding it is key to evaluating an awful lot of stuff beyond scientific topics

And in evaluating a lot of awful stuff beyond scientific topics.

 

[etotheipi]

Thank you, but I have no idea about world lines. So thank you for giving me something new to delve into lol

Whoops, I was going to reply to this too but forgot!

A particle with mass is defined by its entirety in spacetime as a piecewise twice continuously differentiable curve with everywhere timelike tangent vector. That's to say you have some $C^2$ function $\gamma: \mathbf{R} \longrightarrow M$, and the worldline you can just define in standard notation as $\gamma(\mathbf{R})$. This parameterisation is not unique, i.e. any bijective function $\zeta : \mathbf{R} \longrightarrow \mathbf{R}$ gives a new parameterisation $\tilde{\gamma} = \gamma \circ \zeta$, and in fact there's a "physical" parameterisation, proper time, corresponding to the time measured by an ideal clock along that worldline.

The point I was making is that in order to preserve the mixed character of spacetime it's meaningless to talk about "positions of a particle at a given instant", so it's very important to consider the entire curve in its entirety and not to think of the particle as somehow moving along its worldline!

 

[Dale]

Are there any answers to how it can curve and warp from mass such as planets, or how dark energy can make it expand if it's not a something?

What is the definition of “a something”? What is it about being “a something” that makes it a necessary condition for curvature?

The reason that people talk as though it were something is because it is easier. The reason they get wiggly if you ask them directly because “somethingness” is not a commonly defined term in science. If you define your key terms then you should get less evasion.

What are the supporting evidence to believe otherwise?

It isn’t a question of evidence. It is a question of definition.

Scientists don’t assert that it is something. We don’t assert that it is not something. That just isn’t part of the scientific discussion about it at all.

 

[PeterDonis]

Just started reading a book by Brian greene

I would not recommend his books if you are actually trying to learn how physics works in whatever area you are interested in. We have had many previous PF threads based on misunderstandings caused by something in one of his books. IMO he is more interested in producing sound bites that will sell books (sort of like click bait headlines on websites) than in actually describing the physics in a way that promotes real understanding.

 

[valenumr]

This doesn't make much sense, I'm afraid. "Moving with respect to spacetime" isn't a thing you can do or not do. There's no way to peg something to spacetime so you can tell if it's moving or not - spacetime may not even be a real thing, but just something that appears in the concepts underpinning our mathematical model.

Relativity is weird though. I would argue that an acceleration could be described as a deviation from the geodesic. But in any case, it seems fundamental to me that it still implies that a body that has had energy applied to it will be fundamentally different than one that has not. So any object in an *inertial* rest frame is indistinguishable from an object at rest, but a system that has a force applied is distinguishable.

 

[Dale]

it seems fundamental to me that it still implies that a body that has had energy applied to it

Acceleration does not imply energy has been applied. Uniform circular motion is a situation with continual application of a force but no transfer of energy. A force transfers momentum, and power transfers energy. If $\vec F \cdot \vec v=0$ then you have force but no power.

A non-inertial object is distinguishable from an inertial one, but not due to energy transfer

 

[valenumr]

Acceleration does not imply energy has been applied. Uniform circular motion is a situation with continual application of a force but no transfer of energy. A force transfers momentum, and power transfers energy. If $\vec F \cdot \vec v=0$ then you have force but no power.

A non-inertial object is distinguishable from an inertial one, but not due to energy transfer

But is not gravitational acceleration in GR a fictitious force? An object traveling along a geodesic is a rest frame? Or is that totally a misunderstanding on my part?

 

[jbriggs444]

But is not gravitational acceleration in GR a fictitious force? An object traveling along a geodesic is a rest frame? Or is that totally a misunderstanding on my part?

In general relativity, an object moving along a geodesic does not uniquely identify a frame of reference. You need more than than that.

It is only in the flat space-time of special relativity that there is a unique universe-spanning inertial rest frame for any given unaccelerated object. In curved space time there are no global inertial rest frames.

 

[valenumr]

In general relativity, an object moving along a geodesic does not uniquely identify a frame of reference. You need more than than that.

It is only in the flat space-time of special relativity that there is a unique universe-spanning inertial rest frame for any given unaccelerated object. In curved space time there are no global inertial rest frames.

I didn't mean to imply global, I just meat it could be treated as a local rest frame, as it would be in fee fall.

 

[Dale]

But is not gravitational acceleration in GR a fictitious force? An object traveling along a geodesic is a rest frame? Or is that totally a misunderstanding on my part?

That seems fine locally.

My objection was just to the idea that the difference (inertial vs non-inertial) is that “energy has been applied”.

 

[valenumr]

That seems fine locally.

My objection was just to the idea that the difference (inertial vs non-inertial) is that “energy has been applied”.

I'm just claiming, in my limited understanding, that energy (or work if we must) has to be applied to deviate a body from it's geodesic.

 

[Dale]

I'm just claiming, in my limited understanding, that energy (or work if we must) has to be applied to deviate a body from it's geodesic.

That is false, as I described previously. That is exactly what I was objecting to.

 

[jbriggs444]

I didn't mean to imply global, I just meat it could be treated as a local rest frame, as it would be in fee fall.

OK, fair enough. Let me try to flesh out this intuition a bit so that I can follow along.

We have this rest frame (inertial coordinate system) that is anchored on an object moving along a geodesic. We have to keep the frame small to try to keep curvature effects to a minimum. So it is something of a "world tube" around the object.

Of course, this will only be an approximately inertial frame. If one moves away from the center of the tube, one sees that small particles deflect from the inertial trajectories that we would naively predict.

Yes, those deflections are from "gravity". And yes, we could explain those deflections as "fictitious forces".

So yes, we are in agreement.

 

[valenumr]

That is false, as I described previously. That is exactly what I was objecting to.

So you've lost me... How is it possible for an object in free fall to do anything other than continue upon its path without a force applied? This is supposed to be true even in Newtonian physics.

 

[Dale]

So you've lost me... How is it possible for an object in free fall to do anything other than continue upon its path without a force applied? This is supposed to be true even in Newtonian physics.

A force is applied. That is not the same as energy. Forces transfer momentum, not energy. Energy is transferred by power, not force.

 

[valenumr]

A force is applied. That is not the same as energy. Forces transfer momentum, not energy. Energy is transferred by power, not force.

It's really not possible to apply a force to an object without applying energy... This is a fundamental principal of physics, is it not?

 

[valenumr]

It's really not possible to apply a force to an object without applying energy... This is a fundamental principal of physics, is it not?

Well, to be fair... Transferring energy, which is consevered.

 

[jbriggs444]

It's really not possible to apply a force to an object without applying energy... This is a fundamental principal of physics, is it not?

The same force can provide energy, can provide no energy or can extract energy from a moving object. It all depends on the reference frame you choose. There is no invariant fact of the matter.

Take a sack of concrete in the back of pick-up truck that is accelerating westward after the light turns green. Does the force of friction provide energy to the sack (because the truck is moving west) or subtract energy (because the road is rotating east)?

 

[jbriggs444]

Well, to be fair... Transferring energy, which is consevered.

Conserved but not invariant.

 

[valenumr]

OK, fair enough.
The same force can provide energy, can provide no energy or can extract energy from a moving object. It all depends on the reference frame you choose. There is no invariant fact of the matter.

Take a sack of concrete in the back of pick-up truck that is accelerating westward after the light turns green. Does the force of friction provide energy to the sack (because the truck is moving west) or subtract energy (because the road is rotating east)?

Let's not be pedantic here. You know what I mean. Without any impetus to the body, it will continue on its path. If it deviates, it will increase in "velocity", "momentum", and "energy", the latter two are conserved, so they must come from somewhere.

 

[jbriggs444]

Let's not be pedantic here. You know what I mean. Without any impetus to the body, it will continue on its path. If it deviates, it will increase in "velocity", "momentum", and "energy", the latter two are conserved, so they must come from somewhere.

Let us please be pedantic here.

This is general relativity. This is complicated stuff. Tiny implicit assumptions can trip you up. Energy is not necessarily conserved or even well defined. If we are in a space-time where energy is conserved, deflection from a path due to a real force can provide kinetic energy, remove kinetic energy or be energy-neutral.

 

[valenumr]

Let us please be pedantic here.

This is general relativity. This is complicated stuff. Tiny implicit assumptions can trip you up.

I still don't see your argument. The energy of said system is still conserved in GR, is it not? If you can explain how a body in free fall could accelerate WRT it's local geodesic with no energy transferred to said body, I would be very willing to digest that.

 

[jbriggs444]

I still don't see your argument. The energy of said system is still conserved in GR, is it not? If you can explain how a body in free fall could accelerate WRT it's local geodesic with no energy transferred to said body, I would be very willing to digest that.

Pebble strikes lump of clay. Kinetic energy decreases.

If you are going to conserve energy, you need to close your system. The lump of clay is in the system.

There is another prejudice that you are imposing on the system -- you are trying to account for the energy of your object using a frame of reference that is tied to the object before the force (from God's hand) was applied. It would be equally valid to use a frame of reference that is tied to the object after the force was applied. Then one could argue that forces (from God's hand) always reduce kinetic energy.

 

[valenumr]

A force is applied. That is not the same as energy. Forces transfer momentum, not energy. Energy is transferred by power, not force.

Dale, would you agree that a change in momentum also results in an increase in energy, and that both are conserved? One cannot come without the other.

 

[valenumr]

Dale, would you agree that a change in momentum also results in an increase in energy, and that both are conserved? One cannot come without the other.

Edit: sorry, change in energy, not increase.

 

[A.T.]

would you agree that a change in momentum also results in an increase in energy,..

Not in uniform circular motion, for example.

 

[Ibix]

Dale, would you agree that a change in momentum also results in an increase in energy, and that both are conserved? One cannot come without the other.

No he wouldn't. Circular motion is an (already stated) example with an applied force that causes acceleration but no energy change.

 

[jbriggs444]

Dale, would you agree that a change in momentum also results in an increase in energy, and that both are conserved? One cannot come without the other.

It is well known that momentum can change without an accompanying change in energy.

For point-like particles with no internal degrees of freedom, energy indeed cannot change without there also being an accompanying change in momentum.

I think, however, that you are angling for the special case of a [point-like] particle at rest at the origin and wanting confirmation that there can then be no change in either energy or momentum without an accompanying change in the other.

Yes, if the system is closed then both energy and momentum are conserved.

 

[Dale]

would you agree that a change in momentum also results in an increase in energy

No, I already gave a counter example: uniform circular motion.

both are conserved?

Yes, both are conserved locally

 

[valenumr]

No he wouldn't. Circular motion is an (already stated) example with an applied force that causes acceleration but no energy chan

No he wouldn't. Circular motion is an (already stated) example with an applied force that causes acceleration but no energy change.

In what sense? Angular momentum? If we are talking gravitational circular motion, than there is no "force" per se. If you are spinning a sling around, it definitely has increased energy.

 

[Dale]

If you are spinning a sling around, it definitely has increased energy.

Not if you are spinning it in uniform circular motion.

 

[jbriggs444]

In what sense? Angular momentum? If we are talking gravitational circular motion, than there is no "force" per se.

With Newtonian gravity there is a force.

With gravity in General Relativity, the trajectory is only circular in space, not in space-time. But yes, under this model, there is no force.

If you are spinning a sling around, it definitely has increased energy.

An ideal (no air resistance) sling spinning at a constant rate has constant energy despite the presence of a continuing force.