Can time run backwards in an accelerating frame?

[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.

 

[DrGreg]

light from an event E must reach observer O.

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

In fact it's worse than that. Even in flat spacetime, an accelerating observer can outrun light and therefore never see E.

 

[Gumby The Green]

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.

I realize that. I just made the events “equidistant” from me in my example for simplicity.

 

[PeroK]

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?

https://www.imeko.org/publications/tc4-2014/IMEKO-TC4-2014-362.pdf

 

[Nugatory]

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

No. The distant observer observes that the black hole has absorbed the infalling object in a finite time.

The "never reaches the horizon" thing is a good example of a coordinate-dependent statement that is devoid of physical meaning; it would be more accurate to say that if we try to describe the situation using Schwarzschild coordinates we will be unable to explain how the object reaches the horizon

This has been discussed in many many other threads here, but a black hole is a sufficiently complicated object that you will be better off working on the more easily analyzed special relativity examples.

 

[ergospherical]

No. The distant observer observes that the black hole has absorbed the infalling object in a finite time.

I bet you a tenner that they would observe no such thing :)