I Can time run backwards in an accelerating frame?

[Gumby The Green]

The issue then is to clearly specify what you mean by the Traveler’s frame...

I recommend the Dolby and Gull definition, but it is not mandatory.

I'll be able to look at the radar coordinates later today. In the meantime, can't I just say that the traveler's perspective is comprised of five different frames, two of which are inertial (Minkowski coordinates), three of which involve constant proper acceleration (Rindler coordinates), and all of which treat the traveling twin as stationary, stitched together so that the final position and velocity of the Earth in one frame is the initial position and velocity of the Earth in the next? Isn't this basically how the traveler's perspective in the twin paradox is usually analyzed (minus the accelerating frames at the beginning and end)? Would you say that this works with the basic twin paradox—but not with my variation of it—because it doesn't involve any time inversion?

 

[Nugatory]

What I care about is what answers you get when you assume that the traveler is stationary throughout the journey (that's what I mean when I say "what's true in the traveler's frame/perspective"—perhaps "perspective" is a better word).

The traveller’s perspective is going to be based on what they sees/experience, so let’s set up a strobe light on Earth that flashes once every second. Every time that the traveller sees a flash, they can say “OK, that’s another tick of the Earth twin’s clock” and they can look at their clock to see how much time has passed since the previous flash arrived.
On the outbound leg, the flashes arrive more than one second apart according to the traveler’s clock (which is measuring the traveler’s proper time). On the inbound leg, the flashes arrive less than one second apart according to the traveler’s clock. The total number of flashes received during the entire journey is greater than the number of seconds measured by the traveller’s clock during the journey - that is, the Earth clock ticked more often during the journey than the traveling clock so the Earth twin experienced more time and aged more between the departure and the return.

Note that there is no frame involved here. We’re just stating facts about the the time on the traveller’s clock when a flash of light reaches it. Everyone everywhere will agree about these statements of fact, no matter their state of motion and no matter what their clocks might be doing.

(You might want to take a moment to work out the Earth twin’s experience/perspective, assuming that the spaceship is also equipped with its own strobe light. The key difference will be when the flashes start arriving more rapidly - for the traveller it is halfway between departure and return, but for the Earth twin it will be closer to the return).

 

[PeroK]

Let's go back to your initial question:

Summary:: In the twin paradox, if the traveling twin keeps track of the proper time of a stationary observer who's farther away than the earthbound twin, how can he avoid concluding that the observer's time ran backwards at some points during the journey?

The proper time of an object never runs backwards, no matter what coordinates you choose. This is shown by considering a continuous emission of radio signals communicating the objects proper time. All the arbitrary changes in coordinate time that you make have no bearing on the matter. You can chop and change your simultaneity conventions as often as you please: that does not and cannot make an object's proper time run backwards.

Time to move on!

 

[Dale]

can't I just say that the traveler's perspective is comprised of five different frames, two of which are inertial (Minkowski coordinates), three of which involve constant proper acceleration (Rindler coordinates), and all of which treat the traveling twin as stationary, stitched together so that the final position and velocity of the Earth in one frame is the initial position and velocity of the Earth in the next?

I don’t believe so. The tricky part is that “stitching together” part. I don’t believe that there is a way to do that which satisfies the requirements.

Isn't this basically how the twin paradox is usually analyzed (minus the accelerating frames at the beginning and end)? Would you say that this works with the basic twin paradox—but not with my variation of it—because it doesn't involve any time inversion

I have never seen anyone actually do the analysis you propose. People worrying about the twin’s paradox almost universally refer to “the traveler’s frame” without ever even acknowledging the fact that there is no standard definition of such a frame

 

[Gumby The Green]

It is physically impossible, that the traveler can receive light from behind the Rindler horizon.

That's part of my point and I should've stated it more clearly: If the traveler, while accelerating away, can't even receive signals that the distant observer sends while behind the Rindler horizon, how can we say that he'll receive those signals in any particular order? Now the counterpoint would probably be, "But if he stops accelerating, then he'll receive all of those signals in forward order", to which I would respond, "That's because at that point, he's back in a frame whose time is not inverted relative to hers. The time inversion is relative, not absolute!"

 

[Ibix]

I understand all of that; I just haven't been using all the right words apparently.

One way to look at it is this. When you are moving inertially your worldline is straight. You can draw a unique grid on all of spacetime just by drawing lines orthogonal to or parallel to your worldline. But there is no suchgl grid in reality, any more than there are longitude and latitude lines marked on the Earth. So you aren't obliged to use the orthogonal grid you drew - you can just draw a different grid, possibly one that isn't even drawn with the parallel/perpendicular construction. It's usually unnecessarily complicated to do it, which is why people don't, but you can do it.

Once you accelerate, you can't just draw straight lines orthogonal to your worldline any more because they cross and you end up assigning the same event multiple coordinates. So we have to used curved lines. There is only one way to draw a straight line, but "draw a curved line" is a much less tightly specified instruction. And that's, basically, why there's no single answer to "what is the traveller's perspective" - it depends what curves you choose to draw. You need to add other constraints to get a unique answer, such as saying "I'll use Dolby and Gull's radar coordinates", to get an answer, but those constraints are your choice.

 

[Ibix]

"That's because at that point, he's back in a frame whose time is not inverted relative to hers. The time inversion is relative, not absolute!"

The problem if you try this is that your frames either overlap or are discontinuous - and we're back looking at a map with two copies of your house wondering if that means you've really got two houses.

 

[Gumby The Green]

The proper time of an object never runs backwards, no matter what coordinates you choose.

I think I've made it clear that I'm not talking about anyone's proper time running backwards. I'm only saying that the time of an inertial observer, as inferred from a non-inertial frame (i.e., a coordinate system or combination of them in which a non-inertial traveler is treated as stationary), can run backwards.

 

[Ibix]

I'm only saying that the time of an inertial observer, as inferred from a non-inertial frame (i.e., a coordinate system or combination of them in which a non-inertial traveler is treated as stationary), can run backwards.

It cannot, unless coordinate lines cross. If they cross then you don't have a coherent perspective - you have one where you claim that you have two houses because your house appears twice on your (bad) map.

 

[PeroK]

I don’t believe so. The tricky part is that “stitching together” part. I don’t believe that there is a way to do that which satisfies the requirements.

If we take a basic acceleration scenario we can see the problem immediately. In some IRF at time $t = 0$ we have:

Object $A$ at position $x = -L$; object $R$ at $x = 0$ and object $B$ at $x = L$.

Now $R$ is a rocket that accelerates very quickly to speed $v$ towards $B$. We can assume that the distance traveled and the time taken to accelerate are small compared with $L$. I.e. the rocket is still near the origin of the original frame.

Now, the new rest frame for $R$ at time $t' = 0$ has the time at $A$ of $+\gamma v L$ and the time at $B$ at $-\gamma vL$ (using the standard Einstein sync convention).

This, in the OP's terms, is $B$'s time running backwards from the original $t' = t = 0$ when the acceleration began. Moreover, as the rocket moves inertially, the time at $B$ (in the rocket frame) advances to $t' = 0$ again. We end up with two events that have $t' = 0$ in the rocket's changing inertial frames.

This is not a paradox because a) we can treat the coordinate time at $B$ going backwards as a change like the autumn clock changes; and b) we can use a different simultaneity convention to ensure that the coordinate time at $B$ never goes backwards.

In any case, it's only a technical problem with coordinates; and nothing more.

 

[PeroK]

PS in the above scenario if we imagine a clock at rest in the rocket's frame after acceleration, Einstein sync'd with the rocket clock, and colocated with $B$ then that clock shows a different local time from the clock at $B$. That clock does not show $B$'s proper time. That's the critical point.

Instead of $B$'s time having run backwards, $B$'s clock is ahead of the hypotehtical "rocket" clock at $B$.

 

[Gumby The Green]

Once you accelerate, you can't just draw straight lines orthogonal to your worldline any more... So we have to use curved lines... there's no single answer to "what is the traveller's perspective" - it depends what curves you choose to draw. You need to add other constraints to get a unique answer, such as saying "I'll use Dolby and Gull's radar coordinates"

That's why I proposed using Rindler coordinates during the acceleration phases of the journey (but those aren't defined behind the horizon where the distant stationary observer resides). Are (and Dale) you saying that there are other coordinates that would always 1) treat the traveler as stationary, 2) be defined where the distant observer resides, and 3) not show the distant observer's time as running backwards? If so, would the radar coordinates be an example?

 

[Dale]

"That's because at that point, he's back in a frame whose time is not inverted relative to hers

But aren’t you only interested in “the traveler’s frame”. What does it matter if they are momentarily at rest in some other frame?

 

[Dale]

In any case, it's only a technical problem with coordinates; and nothing more.

Yes. But it is a technical problem that must be resolved for anything that claims to be “the traveler’s frame”

 

[Dale]

Are (and Dale) you saying that there are other coordinates that would always 1) treat the traveler as stationary, 2) be defined where the distant observer resides, and 3) not show the distant observer's time as running backwards? If so, would the radar coordinates be an example?

Yes, and yes.

 

[Gumby The Green]

But aren’t you only interested in “the traveler’s frame”. What does it matter if they are momentarily at rest in some other frame?

Yes but (if I understand your question) what I'm saying is that when the traveler stops accelerating and then receives the backlog of signals from the distant observer in the forward order, that wouldn't prove to him that her time was never running backward in his frame; it would only prove that it's not doing so anymore.

 

[PeroK]

Yes but (if I understand your question) what I'm saying is that when the traveler stops accelerating and then receives the backlog of signals from the distant observer in the forward order, that wouldn't prove to him that her time was never running backward in his frame; it would only prove that it's not doing so anymore.

Because if time ran backwards, then you'd get, for example, two signals with "my time is $t_0$". That's what time running backwards would mean. The time would go something like: $t_0$, $t_0 - 1$, $t_0 - 2$. Then, running forwards again you would further get $t_0 -1$, $t_0$, $t_0 + 1$.

You would receive signals $t_0, t_0 - 1, t_0 - 2, t_0 -1, t_0, t_0 + 1$.

What you could get are signals where those were your coordinate times, calculated by the distant observer and communicated to you. In full, you could see messages something like:

"My clock reads $0$, your coordinate time at my location is $0$."

"My clock reads $1$, your coordinate time at my location is $-2.0$.

"My clock reads $2$, your coordinate time at my location is $-4.0$."

"My clock reads $3$, your coordinate time at my location is $-2.0$."

"My clock reads $4$, your coordinate time at my location is $0$.

My clock reads $5$, your coordinate time at my location is $+2.0$.

The distant observer could calculate your coordinate time at their location just as easily as you can. This exposes that although your coordinate time at their location is going backwards and forwards as you change your simultaneity convention, their proper time is behaving normally.

 

[Dale]

when the traveler stops accelerating and then receives the backlog of signals from the distant observer in the forward order, that wouldn't prove to him that her time was never running backward in his frame; it would only prove that it's not doing so anymore

Yes, which is an indication that the question about time running backwards is not a physical question, it is a question about coordinates.

Nothing can be proven about coordinates from any physical measurement.

 

[Ibix]

I've been making analogies with topographic maps quite a lot - thought it might be worth illustrating it a bit. Here's a map (public domain, taken from https://commons.wikimedia.org/wiki/File:Topographic_map_example.png) on which I've added a red line representing a simplified version of someone following the road through Lower Village and Stowe (it's in Vermont, if anyone's curious). There's only one corner in this trajectory, so it consists of just two straight line segments (just like the traveling twin's worldline in the idealised twin paradox).

Now, let's do what the OP wants to do. In the spacetime diagram, he takes the regions swept out by a perpendicular to each line segment (that is, the regions that are "next to" some part of the path), and glues them together so that the path is straightened out. Let's do that same thing on the map:

Note that in this version some parts of Cady Hill (left of the path) are missing while some parts of Stowe and Taber Hill (right of the path) are duplicated. A fair criticism of my demonstration of this approach is that the missing parts of Cady Hill arise because of the instantaneous nature of the corner. A more realistic smooth corner would include a distorted representation of those missing parts, but that's too hard to draw, and it doesn't change anything important about this argument, which is about what happens on the other side of the path. The duplication of Stowe and Taber Hill on the right of the path is unavoidable (well, to be precise you could corner slow enough not to duplicate those specific features, but there'd always be some feature on the right that was duplicated).

The question is: is this image the perspective of someone following that red route? Well, if you claim that it is, you claim that there is a perspective where Taber Hill exists in two places. So I'd say no.

What does this second image actually show? Imagine slicing the image into a stack of narrow slivers:

Like this, you can see that each horizontal slice shows you an accurate map of the part of the world that lies on a line perpendicular to the path's current direction, so the glued-together version of these is just that: everything that's directly to the side of you at some point, glued together. That's why Taber Hill appears twice - because your perpendicular direction changed when you took the corner so it genuinely was directly abeam of you twice. But do the slices of the world that are currently next to you combine together to make an accurate picture of the world? Something that could reasonably be called a perspective? No, not really, because nobody's perspective has Taber Hill doubled up. So the lesson you should take away is that simply stitching together the bits of the world that are directly to your left or right does not yield a good map (unless you always travel in a straight line).

This is also true in relativity. Literally the only difference in the argument is that we use Lorentz notions of orthogonality when thinking about Minkowski space rather than Euclidean notions in Euclidean space. It is certainly true that the traveling twin can draw two (or more) lines orthogonal to his worldline that pass through one event (that line is spacelike, so he can't actually see the same event more than once). But the lesson you should take from this is not that "time runs backwards", but rather that naively combining the sets of events on the lines orthogonal to your worldline does not produce anything resembling anyone's perspective. The only exception is if your worldline is always purely inertial, and it's this fact that makes inertial frames so easy to use (and so easy to conflate with "an observer"), and makes it so easy to think that naively applying the same approach to more complicated circumstances will produce a helpful result.

 

[PeterDonis]

What is that based on though?

The fact that what each observer sees in the Doppler shifted light signals they receive is a direct observable and is invariant. There's no calculation involved; there's no "correction" because of some choice of coordinates. There's just what each observer directly sees, and they directly see all other observers' clocks running forward.

If the signals don't accurately depict the exact speed of the distant clock's "flow"

No signal can possibly "accurately depict the exact speed of the distant clock's flow" if the distant clock is in motion relative to the observer.

how are you sure that they accurately depict its direction in the traveler's frame at all times

Because the ordering of the light signals between emitter and detector is invariant. That is a simple physical fact about how light propagates. All of the light signals are moving in the same direction and at the same speed.

(even while its behind the traveler's Rindler horizon)?

If the distant object is behind the traveler's Rindler horizon, the traveler can't see it at all; no light signals are received. And the "accelerating frame" you are implicitly using for the traveler won't even cover the region of spacetime behind the Rindler horizon; it only covers the portion of spacetime that the traveler can actually see, i.e., receive light signals from. So objects behind the traveler's Rindler horizon are simply not included at all in the entire scenario you are talking about.

I'm not making any claims about what's actually happening to the distant observer in their own frame. All I care about is what's true in the Traveler's frame.

There is no such thing as "what's actually happening to the distant observer in their own frame" as contrasted with "what's true in the Traveler's frame". Coordinates and frames don't tell you what's "true". They are conveniences for calculation. They are not physical things and they do not tel you physical things.

"What's true" is contained in invariants: things that are independent of any choice of coordinates. In other words, "what is true" must be the same in all frames. The time an observer reads on their own clock at a particular event, such as emitting a particular light signal, is an invariant. What an observer actually sees in a Doppler shifted light signal arriving from a distant object is an invariant. But "what time is it for a distant object at a given event for the traveler" is not an invariant. It depends on your choice of coordinates and is a convenience for calculation; it doesn't tell you anything about "what is true".

Unless and until you are able to properly grasp the above, you will continue to make mistakes and you will continue to say wrong things that we have to correct.

I'm not applying any correction to the Doppler shift.

Yes, you are: in order to calculate what you are calling "what's true in the traveler's frame", you have to apply corrections to the Doppler shifted information in the light signals the traveler receives. If you just take the Doppler shifted information as it is, you are working with invariants that aren't "in" any frame, they are just invariants. But you refuse to do that; you insist on talking about "what is true in the traveler's frame" as thought it had physical meaning. It doesn't.

I don't care about the Doppler shift or about anything the traveler sees.

And you should. That's the point. What the traveler actually sees is invariant. What you are calling "what's true in the traveler's frame" is not, and has no physical meaning. So you're focusing on the wrong thing.

My argument is all about what can be logically deduced at the end of the journey from the most basic principles.

You might think it is, but you are wrong. What you are doing is not based on any physical principles. It is based on incorrectly treating coordinate-dependent quantities as though they had physical meaning. They don't.

 

[PeterDonis]

Are you implying that differential aging is 0% physical throughout the entire journey until the moment that the twins are standing in the exact same place (which is technically impossible), at which point it becomes 100% physical?

Not at all. In the standard twin paradox, each twin can view the Doppler shifted light signals arriving from the other twin throughout the journey and correctly add up the differential aging between them all through the journey, and come up with the correct answer as to what their respective clock readings will be when they meet up again.

See, for example, here:

https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html

The whole article is worth reading, but the specific page I linked to discusses the Doppler shift analysis I described above.

 

[Dale]

Because the ordering of the light signals between emitter and detector is invariant.

I can’t believe that this fact never occurred to me. It is super-obvious once you stated it. For a series of light cones from any timelike worldline every later light cone is entirely inside every earlier one. And that is frame invariant

It is based on incorrectly treating coordinate-dependent quantities as though they had physical meaning.

Also, in this case the coordinates are not even valid. I don’t mind talking about coordinate-dependent things (e.g. energy), but you really need to have valid coordinates

 

[PeterDonis]

But then he'd be pretending to be in a frame other than the one he's actually in, which wouldn't be truthful, would it?

There is no such thing as being "in" one frame but not another. Everything in a given region of spacetime is "in" every frame that covers that region of spacetime.

Everything I've ever read about SR says that each observer should conclude that they're stationary and that anything that moves relative to them is actually moving. If someone wants to know what's true in their own frame, isn't that what they need to do?

Where have you read all this? Please give specific references.

Every textbook I have read on SR says it's perfectly fine to use whatever frame you like; there is no requirement that every observer can only use a frame in which he is at rest. That's part of the impact of the principle of relativity: since the laws of physics are the same in all frames, you can use whatever frame you like to analyze a given scenario and, if you do the analysis correctly, you will get the same answer as you would get doing the analysis in any other frame.

 

[Gumby The Green]

Because if time ran backwards, then you'd get, for example, two signals with "my time is $t_0$"...

You would receive signals $t_0, t_0 - 1, t_0 - 2, t_0 -1, t_0, t_0 + 1$.

Thanks for giving a concrete example but I see a hole in it. When the traveler starts accelerating and the distant observer is suddenly behind his Rindler horizon, the traveler won't receive duplicate signals from any events whose signals hadn't yet crossed the location of the horizon when it formed. In fact, he obviously won't receive any signals at all from such events (until he stops accelerating and the observer's time thus stops moving backward in his frame). And if the degree of the backward time movement (in years) of the observer's time is limited to her distance behind the Rindler horizon (in light years)—as I strongly suspect it is—then the only events that can be reversed in the traveler's frame are those whose signals can't ever reach him (until he stops accelerating). This aligns with what I said earlier that, just like time dilation, time inversion can't be directly observed; it can only be inferred.

This exposes that... their proper time is behaving normally.

I might be misunderstanding your point, but again, I'm not saying that anyone's proper time is affected here; that would be absurd on its face and I don't know what it would even mean to claim such a thing.

 

[PeroK]

When the traveler starts accelerating and the distant observer is suddenly behind his Rindler horizon, the traveler won't receive duplicate signals from any events whose signals hadn't yet crossed the location of the horizon when it formed.

The Rindler horizon is irrelevant here.

I might be misunderstanding your point, but again, I'm not saying that anyone's proper time is affected here; that would be absurd on its face and I don't know what it would even mean to claim such a thing.

Then you are saying precisely nothing.

You really, really do not understand the arbitrariness of coordinate systems and frames of reference.

 

[Dale]

then the only events that can be reversed in the traveler's frame are those whose signals can't ever reach him (until he stops accelerating). This aligns with what I said earlier that, just like time dilation, time inversion can't be directly observed; it can only be inferred.

But again, it cannot be inferred either since such a coordinate system is not a valid coordinate system. There are very few restrictions on coordinates, but that inference fails. As I have explained many many times already.

 

[ergospherical]

Every textbook I have read on SR says it's perfectly fine to use whatever frame you like; there is no requirement that every observer can only use a frame in which he is at rest. That's part of the impact of the principle of relativity: since the laws of physics are the same in all frames, you can use whatever frame you like to analyze a given scenario and, if you do the analysis correctly, you will get the same answer as you would get doing the analysis in any other frame.

To be fair to Mr Gumby, the term ‘observer’ has various precise definitions. For Sachs and Wu it is a future pointing timelike curve (for others it includes a tetrad field along said curve). With this in mind, it risks confusion to entertain ‘observers using frames in which they are not at rest’ (viz: just introduce a different observer…).

 

[PeroK]

To be fair to Mr Gumby, the term ‘observer’ has various precise definitions. For Sachs and Wu it is a future pointing timelike curve (for others it includes a tetrad field along said curve). With this in mind, it risks confusion to entertain ‘observers using frames in which they are not at rest’ (viz: just introduce a different observer…).

That said, if you took the approach to physics promoted in many SR introductions too literally, then you wouldn't be able to take a physics exam sitting in an exam hall, but would have to continualy get out into a moving train or accelerating elevator in order to "be in the right frame"!

 

[ergospherical]

And then there are engineering considerations. The Victoria line is quite fast but a little bit off $0.6c$. (I am very jealous of Alice and Bob’s commute.)

 

[Dale]

To be fair to Mr Gumby, the term ‘observer’ has various precise definitions. For Sachs and Wu it is a future pointing timelike curve (for others it includes a tetrad field along said curve). With this in mind, it risks confusion to entertain ‘observers using frames in which they are not at rest’ (viz: just introduce a different observer…).

I disagree with this. The principle of relativity is about frames, not observers. So indeed, regardless of the precision of your definition of “observer”, there is no requirement that an observer must only use the frame where they are at rest. The principle of relativity guarantees that you will get the correct outcome when analyzing any experimental measurement from any frame.

 

[ergospherical]

@PeroK also a good thing it’s a special theory paper, because I’m not sure I’d want to try out one of those infalling geodesics into a black hole for myself. For starters, the characteristic time scale of Hawking radiation might make it a bit difficult to submit my solutions (and that is assuming the string-theoretical viewpoint that the radiation would even contain some information about what I’d been writing)!

 

[Gumby The Green]

Coordinates and frames don't tell you what's "true". They are conveniences for calculation. They are not physical things and they do not tell you physical things...

"What's true" is contained in invariants: things that are independent of any choice of coordinates. In other words, "what is true" must be the same in all frames...

What you are calling "what's true in the traveler's frame" is not, and has no physical meaning.

Ok, here's what I'm not understanding about that: Relative motion causes relativistic effects that can include measurable physical effects that differ depending on the frame. For example, a rod has different lengths in different frames, and a charged particle produces different magnetic fields in different frames. And the relativistic Doppler shift includes the effect of time dilation, which depends on the frame. And it turns out that the magnitudes of these effects that are measured by an observer equate to their magnitude in the frame that treats that observer as stationary. So wouldn't it make sense to say that's the frame of that observer? And wouldn't it make sense to say that those effects—as well as the claim that that observer is stationary and everything else is moving—are true and physical in that frame and for that observer? If not, what am I missing?

Per Wikipedia (emphasis added):

An observational frame of reference, often referred to as a physical frame of reference, a frame of reference, or simply a frame, is a physical concept related to an observer and the observer's state of motion. Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized only by its state of motion. However, there is lack of unanimity on this point.

In light of this, why does there appear to be unanimity to the contrary here?

 

[Gumby The Green]

But again, it cannot be inferred either since such a coordinate system is not a valid coordinate system. There are very few restrictions on coordinates, but that inference fails. As I have explained many many times already.

I'm not ignoring your points Dale; I'm thinking through them. In a number of my comments, I'm just clarifying points I've made or showing why I think that someone's refutation of one of those points fails regardless of whether the point is true. So my rebuttals to attempted refutations of my points aren't necessarily intended to reassert the points. (And now I've said "point(s)" too many times and the word has lost all meaning.)

 

[PeroK]

Ok, here's what I'm not understanding about that: Relative motion causes relativistic effects that can include measurable physical effects that differ depending on the frame. For example, a rod has different lengths in different frames, and a charged particle produces different magnetic fields in different frames. And the relativistic Doppler shift includes the effect of time dilation, which depends on the frame. And it turns out that the magnitudes of these effects that are measured by an observer equate to their magnitude in the frame that treats that observer as stationary. So wouldn't it make sense to say that's the frame of that observer?

This is potentially a subtle point and one where we have to be careful about language.

Let's take an example of an object in space. You might want to argue whether it is upside-down or not. But, that's completely arbitrary. There is no sense, "truth" or physical concept of upside-down in physics.

If we have a gravitational field, then the concept of upside-down relative to that field is important.

Most of your ideas are based on taking something like this and imbuing it with a physical significance that does not in fact apply.

E.g. an object's state of motion, its measured length, the wavelength of a light pulse. All of these appear to the novice student as elements of physical reality. But, in the language of physics they are frame dependent quantities and there's no contradiction if different observers obtain different measurements.

A photon does not have an absolute wavelength. It's true that the wavelength relative to the source is important in some sense. But, that does not mean that other measurements are contradictory.

Your example of the EM field was a key motivation for Einstein's SR in the first place. You can read the opening of the 1905 paper where he says something like:

Although in one frame we have a magnetic field and a current and in the other an electric field and a moving magnet, this asymmetry is not reflected in the observed physical phenomena.

In other words, the same physics results whatever your frame of reference. And the things that you currently accept as critical measurements ( e.g. the magnetic field) do not in themselves represent a "physical reality".

Digesting this is a key aspect to fully understanding modern physics.

 

[Dale]

I'm not ignoring your points Dale; I'm thinking through them

Ok, but at this point you have had more than enough time to think through this specific point: a coordinate system is a one-to-one mapping between events in spacetime and points in R4.

This is a straightforward concept, it is simply part of the definition of a coordinate system (the other part being that it is continuous). Is there anything unclear about that? If so, ask directly and specifically about that definition. Otherwise please make your future arguments consistent with it.

We need to make progress here. This is the simplest issue in the thread since it is just a definition, so let’s start with it. Please focus, ask direct clarifying questions, and only move on once you are clear.

If you are unwilling to focus, then at least make sure that none of your posts on other topics violate this point while you cogitate. If you cannot make an argument without violating it then your argument is wrong a priori.

 

[ergospherical]

So indeed, regardless of the precision of your definition of “observer”, there is no requirement that an observer must only use the frame where they are at rest.

What I mean is that multiple authors take the term ‘observer’ as synonymous with a local frame (tetras field). In which case what you say doesn’t make sense (in a way you’re overly anthropomorphising the term).

 

[PeroK]

What I mean is that multiple authors take the term ‘observer’ as synonymous with a local frame (tetras field). In which case what you say doesn’t make sense (in a way you’re overly anthropomorphising the term).

https://www.physicsforums.com/threa...o-communication-theorem.1013630/#post-6613520

 

[Gumby The Green]

E.g. an object's state of motion, its measured length, the wavelength of a light pulse. All of these appear to the novice student as elements of physical reality. But, in the language of physics they are frame dependent quantities and there's no contradiction if different observers obtain different measurements.

A photon does not have an absolute wavelength. It's true that the wavelength relative to the source is important in some sense. But, that does not mean that other measurements are contradictory...

And the things that you currently accept as critical measurements ( e.g. the magnetic field) do not in themselves represent a "physical reality".

I completely realize that they're frame dependent quantities and that there's no contradiction in the fact that they're measured differently in different frames. That's exactly what I was just explaining in detail. When I say that an effect is physically real in a given frame, I'm just saying that it has measurable effects in that frame. I'm acknowledging that it's frame dependent, i.e., relative. I'm not saying that it's true in every frame, i.e., absolute. Now that that's clear, I'd like to repeat my questions because I think they get to the heart of one of my main sources of confusion:

And it turns out that the magnitudes of these effects that are measured by an observer equate to their magnitude in the frame that treats that observer as stationary. So wouldn't it make sense to say that's the frame of that observer? And wouldn't it make sense to say that those effects—as well as the claim that that observer is stationary and everything else is moving—are true and physical in that frame and for that observer? If not, what am I missing?

 

[jbriggs444]

I completely realize that they're frame dependent quantities and that there's no contradiction in the fact that they're measured differently in different frames.

Yes, it is a physically real fact that I weigh a svelte 150 pounds when I adjust my bathroom scale to make it so.

 

[Gumby The Green]

Is there anything unclear about that? If so, ask directly and specifically about that definition. Otherwise please make your future arguments consistent with it...

at least make sure that none of your posts on other topics violate this point while you cogitate.

I think I understand what constitutes a valid coordinate system, and I won't mention backwards time again until we iron out the issues that are keeping us from talking about it constructively.

 

[PeroK]

Now that that's clear, I'd like to repeat my questions because I think they get to the heart of one of my main sources of confusion:

I can't see any purpose to that question. If you understand what you've said, then the question becomes pointless.

When you study GR it becomes more apparent that we do physics abstractly in a chosen coordinate system (which generally cannot be associated with a single observer) and then predict local measurements made by relevant observers.

For example, your insistence on there being "no choice" and a given frame being "the one true reference frame" for a given observer leads to fundamental problems in GR. For example: the issue of an object taking "infinite time" to fall into a black hole "according to a distant observer".

There are several threads on here where posters can't accept that the Schwarzschild coordinates are arbitrary and do not constitute the "one true frame" that you would like to cling to. And, that if we change to appropriate coordinates, then the object crosses the event horizon after finite time.

It is important to understand that your question is ultimately pointless and the more physics you learn the more you'll see this.

 

[Gumby The Green]

Yes, it is a physically real fact that I weigh a svelte 150 pounds when I adjust my bathroom scale to make it so.

I don't see what that has to do with frame dependent quantities. I don't have to adjust the length of my ruler in order to measure different lengths for a rod in different frames.

 

[Gumby The Green]

For example: the issue of an object taking "infinite time" to fall into a black hole "according to a distant observer"...

if we change to appropriate coordinates, then the object crosses the event horizon after finite time.

But isn't it true that it does take infinite time in the frame that treats the distant observer as stationary—which I'll simply call the frame of that observer for brevity—and finite time in the frame of the observer who's falling in? And aren't these effects measurable for each observer, e.g., the distant observer can see the other forever slowing down and becoming more red shifted as they approach the event horizon (ignoring other effects like destructive tidal forces)?

 

[ergospherical]

That's true, if you are interested I did the calculation some time ago in a previous post:
https://www.physicsforums.com/threads/mathematical-treatment-of-approaching-event-horizon.1007653/

 

[PeroK]

But isn't it true that it does take infinite time in the frame that treats the distant observer as stationary

No, it's not true. There is no single "true" frame of reference for the distant observer. There is no unique definition of global simultaneity.

This is critical and fundamental. Although you claim to understand the theory of relativity, the fact is that you do not. You need a fundamental rethink of what it means for spacetime to be a 4D continuum and not as independent space and time.

 

[jbriggs444]

I don't see what that has to do with frame dependent quantities. I don't have to adjust the length of my ruler in order to measure different lengths for a rod in different frames.

Coordinates. The scale lays out a coordinate scale from 0 lbs on up. If I re-scale those coordinates, it does not change my weight. It just changes the number that the scale reads.

When you measure a moving object with a ruler, you have the problem of where the two ends of the object are when you make the measurement. That involves the relativity of simultaneity. Which frame you use to judge simultaneity affects whether the object's length matches the ruler's length or fails to do so.

 

[Gumby The Green]

No, it's not true. It's as wrong as anything can be! There is no single "true" frame of reference for the distant observer. There is no unique definition of global simultaneity.

But again, can’t the distant observer see the falling observer forever slowing down and becoming more red shifted as they approach the event horizon? I’m not talking about global simultaneity; I’m only talking about simultaneity for a distant observer that’s stationary relative to the black hole.

you claim to understand the theory of relativity

I don’t think I’ve claimed that. I’m asking a lot of questions here, so hopefully it’s clear that I’m trying to learn.

 

[Gumby The Green]

Which frame you use to judge simultaneity affects whether the object's length matches the ruler's length or fails to do so.

If light from two equidistant events reaches my eyes at the same time, I say those events are simultaneous for me. How would it make sense for me to judge simultaneity any other way?

Regardless of the answer to that question, if I apply that method consistently in every frame I find myself in (i.e., every frame that treats me as stationary) as I change my speed, I find that the object’s length is different in every frame in a way that can have physical effects on me, do I not?

 

[PeroK]

But again, can’t the distant observer see the falling observer forever slowing down and becoming more red shifted as they approach the event horizon?

That's not the issue. It's not necessary for a light signal from an event to reach an observer for the event to take place. The red-shift is a local measurement, which is dependent on the nature of the spacetime around a black hole. There's nothing in the laws of physics that says that light from an event E must reach observer O.

In flat spacetime that is true, but not in general spacetimes.

I’m not talking about global simultaneity

You are, although you don't recognise it. The fact that you do not recognise that you are adopting a specific simultaneity convention does not mean that you are not. This is the problem in a nutshell. You don't know it, but you are still effectively thinking in terms of Newtonian absolute space and absolute time - with a few relativistic effects thrown in.

I’m only talking about simultaneity for a distant observer that’s stationary relative to the black hole.

It's that observer's global simultaneity convention I'm talking about. To be precise, Suppose an object is at some point in space "half way" to the black hole. Your position is:

That event has a true, unique time (according to the distant observer). He or she has no choice. And there is no time, and can be no time, at which the object crosses the event horizon. That is one of your "truths" that we are challenging.

I'm saying they have a choice of simultaneity conventions. We may use Schwarzschild coordinates (which are singular at the event horizon). Or we could switch to Eddington-Finkelstein coordinates, for example, whereby the distant observer could specify a time at which the object crosses the horizon. And a different time coordinate for the half way point. And these are just as valid as your Schwarzschild coordinates.

I’m asking a lot of questions here, so hopefully it’s clear that I’m trying to learn.

Yes, but you're thinking is set deeply in Newtonian physics. But, you don't see it yet.

 

[ergospherical]

If light from two equidistant events reaches my eyes at the same time, I say those events are simultaneous for me. How would it make sense for me to judge simultaneity any other way?

True for this specific example but in the general case, say: two people are stationed at the start and finish line respectively of a running track of length $d$ and they both clap their hands. If you're also at the start line, then you'll conclude the claps were simultaneous if you hear the second one $d / v_{\mathrm{sound}}$ after the first, yes? Same principle for light in relativity; you have to subtract off the light travel time first.