I Can time run backwards in an accelerating frame?

[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 :)

 

[Nugatory]

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

We're going to hijack this thread if we continue the discussion - but if I drop an object of mass $m$ into a black hole of mass $M$ we will end up with a black hole of mass $M+m$ in fairly short order.

New thread if you want to continue the discussion, please

 

[ergospherical]

Sure, but not in fairly short order (or at all) according to the guy watching the in-fall from infinity. It’s the same reason that distant observers can never actually see the formation of an event horizon of a collapsing star.

 

[PeroK]

Sure, but not in fairly short order (or at all) according to the guy watching the in-fall from infinity. It’s the same reason that distant observers can never actually see the formation of an event horizon of a collapsing star.

The OP's point, however, is that unless an observer sees an event it doesn't take place. Because there is only one valid coordinate system that the observer is allowed to use. This is the issue being challenged.

 

[Sagittarius A-Star]

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?

That is a definition of simultaneity. You could define it also differently.

 

[PeterDonis]

a rod has different lengths in different frames

No, different observers in different states of motion relative to the rod measure different invariants that, because of unfortunate limitations in ordinary language as compared to precise math, they both refer to as "length" of the rod. But nothing about the rod itself changes. All that changes is which invariant each observer measures.

a charged particle produces different magnetic fields in different frames.

No, a charged particle's field has different effects on another charged particle depending on the second particle's state of motion relative to the first. In other words, the effect of the first particle's field on the second particle is an invariant that depends on the invariant inner product of the 4-velocities of the two particles. And this invariant can be computed in any frame you like.

the relativistic Doppler shift includes the effect of time dilation, which depends on the frame.

No. As I've already said, you have this backwards. The relativistic Doppler shift is the invariant, and depends, like the charged particle effect above, on the invariant inner product of the 4-velocities of the emitter and the observer. (Actually, it's only that simple in flat spacetime; in curved spacetime you have to do a more complicated invariant computation for the shift. But it's still an invariant.) And you can compute that in any frame you like.

The "time dilation" is derived from the Doppler shift by allowing for "light travel time"--but the "light travel time" computation is not an invariant, it depends on your choice of frame, and the final result it gives you, "time dilation", is also not an invariant, it depends on your choice of frame. But that doesn't mean Doppler shift is frame-dependent; it means you are looking at everything backwards, as I've already said.

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.

There might not be any such unique frame that treats the observer as stationary. This has already been pointed out to you many times in this thread.

In any case, once more you are looking at things backwards. Invariants are the same in any frame. But among the invariants that are the same in any frame, some will be invariants that include the 4-velocity of an observer. Obviously which invariant is relevant to a particular observer will depend on that particular observer's 4-velocity, and changing observers means changing which invariant you look at. This doesn't make any invariant frame-dependent; it means that which invariant you care about will depend on which observer you care about. None of this requires any choice of frame. The choice of frame is a convenience for calculation. It is not necessary for any physics.

So wouldn't it make sense to say that's the frame of that observer?

No, because there is no requirement that an observer always adopt a frame in which they are at rest. What frame do you use when planning a trip to the grocery store? A frame in which you are at rest? Or a frame in which the Earth is at rest?

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?

It never makes sense to say that any quantity which is not an invariant is "true and physical". But it might make perfect sense to care about different invariants depending on which observer you are considering. No observer can say that they are stationary and everything else is moving in any absolute sense; no such statement can be "true and physical". But an observer can perfectly well say that they observe light signals from some source as having a particular Doppler shift (assuming they know the required properties of the source to be able to measure the Doppler shift), and (in flat spacetime) they can perfectly well attribute this Doppler shift to the relative velocity between them and the source. (In curved spacetime, as I've said, the computation has to be more complicated, because there is no invariant notion of "relative velocity" between spatially separated objects in curved spacetime. But there are more complicated invariants that correspond reasonably well to our intuitive notion of "Doppler shift".)

Per Wikipedia (emphasis added):

Wikipedia is not a valid reference. Find a textbook or peer-reviewed paper that takes the viewpoint you are advocating, and then we can talk.

 

[PeterDonis]

why does there appear to be unanimity to the contrary here?

It should be noted that the term "reference frame" is ambiguous. We have had some previous threads on this, which I can't find right now, but basically, there are at least three distinct concepts that can be referred to by the term "reference frame":

(1) A coordinate chart. (In many SR discussions, "inertial frame" means a particular kind of coordinate chart on flat spacetime, the one implied when the Minkowski metric is written as $ds^2 = - dt^2 + dx^2 + dy^2 + dz^2$.)

(2) A tetrad field. This is a more technical concept, but if you think of the four orthonormal coordinate basis vectors of an SR "inertial frame", in the sense described just above, i.e., the unit vectors in the $t$, $x$, $y$, and $z$ directions at every point, that is an example of a tetrad field. The general definition is an assignment of a tetrad--a set of four orthonormal vectors, one timelike and three spacelike--to every point in some region of spacetime.

(3) A physical apparatus for making measurements of time and length. In the simplest case, this will be a clock and a set of three mutually perpendicular rulers that are all at rest relative to the clock. Or, more comprehensively, a family of such clock-ruler setups spread at fixed intervals throughout your laboratory, all at rest relative to each other.

There are, of course, obvious correspondences between these definitions. For example, given a tetrad field covering a region of spacetime, one can always define a coordinate chart covering the same region. (The reverse is not necessarily true.) And given a clock-ruler setup of the kind described above in your laboratory, one can always define a tetrad field covering the region of spacetime corresponding to the "world tube" of the laboratory. So in some particular cases, such as the kinds of cases Einstein considered in his initial papers on SR, you can have a "reference frame" that defines all three of the above things at once, and in correspondence with each other (for example, Einstein's clock-and-ruler vision of an "inertial frame" in SR).

Because of such correspondences, one can, in some particular situations, get away with using the term "reference frame" without specifying which of the three above meanings is intended. But that is still a bad habit, and can easily bite you when you find yourself using the same term to mean different things which now no longer have a well-defined relationship with each other. Or when two people are using the same term to mean different things and are talking past each other.

And, of course, of the three things above, note that only #3 is an actual physical thing. The other two are mathematical abstractions. So if you're going to make claims about what is "true and physical", it's very important to be careful about how you use terms like "reference frame", which can refer both to things that are "true and physical" and things that aren't.

 

[Dale]

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

This is a subtle point that I wish to discuss a bit further.

Let's say that Bob, in a spaceship, is building a new bunk for his cabin. Bob measures the length of his cabin and the length of the bunk he is building.

Bob's measurement of the length of the bunk is invariant, as all measurements must be. Other invariant facts include Bob's measurement of the length of the cabin and whether or not the bunk will fit in the cabin. The relevant law of physics is that if Bob's measurement of the length of the bunk is smaller than Bob's measurement of the length of the cabin then the bunk will fit in the cabin. All frames will agree on Bob's actual measurements and whether or not it fits. Those are physical invariants.

The length of the bunk is frame-variant. In other words, all frames will agree on what number Bob obtains with his measurement device. Not all frames will agree that that number is the length. But the physics doesn't care about the frame-variant length. If some frame finds that, due to different orientations of the cabin and the bunk during its construction, the frame-variant length of the bunk is larger than the frame-variant length of the cabin, it will still fit if the invariant law says it will fit. Conversely, if some frame finds that the frame variant length of the bunk is smaller than the frame-variant length of the cabin, it will still not fit if the invariant law says it will not fit.

So the "measurable physical effect" is the actual number that Bob measures on his device. That is an invariant and it does not differ depending on the frame. The judgement about whether or not that number is the length does differ depending the frame, so it is a bit less "physical". Sometimes these less physical quantities, the frame-variant ones, are still super-useful, so you shouldn't hesitate to use them as needed. But it is important to pay attention to the context of a discussion so that you can pay attention to what quantities are invariant and which are not, and recognize that the invariant ones are the ones that drive physics.

 

[PeterDonis]

The judgement about whether or not that number is the length does differ depending the frame

Not that this judgment might be about other invariants, such as the invariant that Alice, who is moving relative to Bob, calls the "length" of the bunk, based on her measurements of the bunk (obviously done by a different process from Bob's). And if, as you say, the orientations of bunk and cabin were different during construction, Alice might have yet another invariant that she calls the "length" of the cabin, based on her measurements of that, and this invariant might be less than Alice's "length of the bunk" invariant. Alice's invariants are perfectly good invariants; they're just the wrong ones to look at if you want to know whether Bob's bunk will fit inside Bob's cabin.

 

[Dale]

Not that this judgment might be about other invariants, such as the invariant that Alice, who is moving relative to Bob, calls the "length" of the bunk, based on her measurements of the bunk (obviously done by a different process from Bob's). And if, as you say, the orientations of bunk and cabin were different during construction, Alice might have yet another invariant that she calls the "length" of the cabin, based on her measurements of that, and this invariant might be less than Alice's "length of the bunk" invariant. Alice's invariants are perfectly good invariants; they're just the wrong ones to look at if you want to know whether Bob's bunk will fit inside Bob's cabin.

Yes, Alice and Bob will both agree about the value that the other person will get when doing the respective measurements. Both measurements are invariants, as they must be. Their disagreement is only in the labeling of that measurement as “length”. They each believe that their own number is the length and that the other number is not the length. And both agree which invariants determine if it fits.

 

[FactChecker]

The only thing I care about here is what's true in the frame of the traveling twin, i.e., what clock times for the stationary observers does he conclude are simultaneous to his at each point during his journey?

When the traveling twin is accelerating, he is changing any frame that he used to synchronize his clocks at a distance to maintain a constant speed of light. Whatever method he is using, the assumption that the speed of light is constant forces him to keep adjusting his "synchronized" clocks. He is the last one who can claim that the Earth's clocks ran backward.

PS. With the amazing sensitivity of current clocks and experiments, your hypothesis would be apparent in many of today's experiments.

 

[Gumby The Green]

He is the last one who can claim that the Earth's clocks ran backward...

PS. With the amazing sensitivity of current clocks and experiments, your hypothesis would be apparent in many of today's experiments.

I don't think you've understood what I was arguing for. I was saying that during his acceleration away from the Earth and the distant observer—who is farther away from him than the Earth is—he would believe that the time of that distant observer runs backwards relative to his own. But note that I'm not reasserting that hypothesis here (since I've promised to not do that yet). I'm just clarifying it and refuting what I see as a straw man of it...

To make it a little more clear, let's say that there's another observer who's only slightly farther from him than the Earth and let's say that the acceleration is finite. In this case, he would perceive that observer's time as slowing down relative to his own due to "gravitational" time dilation during his acceleration. The farther away that observer is, the slower the traveler will perceive her time to be. The question I've posed is essentially this: As we increase the distance between these two people, what happens when the observer's rate of time in the traveler's frame can't decrease any further?

If the answer is that beyond that distance, i.e., the Rindler horizon, it does begin to run backwards relative to his own in some sense, it would happen behind the horizon and thus he would have no way to directly measure it in real time (he could only measure the effects of it after he stops accelerating, which would be combined with the forward leaps in time he perceived to produce an end result that would be equal to any other mundane calculation of differential aging in an inertial frame). So no, the backwards time flow itself couldn't be directly measured by any experiment.

 

[Gumby The Green]

Bob's measurement of the length of the bunk is invariant, as all measurements must be.

The length of the bunk is frame-variant. In other words, all frames will agree on what number Bob obtains with his measurement device. Not all frames will agree that that number is the length.

This aligns with what I understand. It sounds similar to the concept of proper time. I was tempted to call it "proper length" but then realized that there's a subtle distinction: proper length is the length measured in the rod's rest frame, but you're saying that the measured length of the rod in any frame is invariant, which makes sense to me.

But the physics doesn't care about the frame-variant length.

So the "measurable physical effect" is the actual number that Bob measures on his device.

Let me make sure I understand this. You're saying that the physics in Bob's frame doesn't care about the frame-variant length (and only cares about the length that Bob measures), right? In another frame, which measures a different length, that length becomes the one that the physics in that frame care about, right?

Their disagreement is only in the labeling of that measurement as “length”. They each believe that their own number is the length and that the other number is not the length.

If they have disagreements on what the rod's length is, doesn't that effectively mean that they each occupy a particular frame (the frame whose length calculation aligns with what they measure)?

 

[Gumby The Green]

Alice's invariants are perfectly good invariants; they're just the wrong ones to look at if you want to know whether Bob's bunk will fit inside Bob's cabin.

True but they're the right ones to use if you want to know whether Bob's bunk will fit inside Alice's cabin for a brief moment while it flies through it (like in the ladder paradox), right?

 

[jbriggs444]

True but they're the right ones to use if you want to know whether Bob's bunk will fit inside Alice's cabin for a brief moment while it flies through it (like in the ladder paradox), right?

If the ladder flies through Alice's cabin then the invariant fact of the matter is that Alices cabin will be destroyed.

The ladder will not be in a very usable condition either.

However, if Alice opens her front and back windows at the right times, the ladder can pass through successfully whether it fits or not.

 

[Gumby The Green]

Because of such correspondences, one can, in some particular situations, get away with using the term "reference frame" without specifying which of the three above meanings is intended. But that is still a bad habit, and can easily bite you...

And, of course, of the three things above, note that only #3 is an actual physical thing. The other two are mathematical abstractions.

I see. Well I could use a term like "observational frame", like that Wikipedia article does, to specify that it's type #3. But isn't it just implied that that's the case when someone speaks of the frame as belonging to an observer?