# Now plane moving to the past and future

When we accelerates in one direction, the now plane will slice the spacetime and move up in the direction of motion and move down behind us. That is, in the direction of motion, the further end, the time will be running faster as we accelerate and vice-versa. So now if we start to deaccelerate, will we see events in reverse order in the direction of motion, because the sliced now plane will start to move down from its present position.

Dale
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2021 Award
if we start to deaccelerate, will we see events in reverse order in the direction of motion
There is no valid reference frame where this is true.

PeterDonis
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the now plane

In relativity, "now" is just a convention; it doesn't correspond to any physical observable. This is a key difference between relativity and Newtonian physics (in the latter, "now" is absolute and has physical meaning). So you can't draw any physical conclusions from what the "now" plane as you have defined it does.

rajeshmarndi,

See if this helps... http://physics.unm.edu/Courses/Finley/p570/Handouts/accelObserv.pdf [Broken]

from page 5
"As the accelerated observer moves the lines of simultaneity rotate “upward” as (tau) increases from zero, and “downward” as it decreases."

from page 10
"c. Thirdly, for events in quadrant IV, as the value of t increases the associated value of (tau) would decrease, so that the normal ordering given by the progression of time is reversed. This suggests that we have already passed into an unacceptable region. Only I is correctly treated by these coordinates."

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rajeshmarndi,

[...]
from page 10
"c. Thirdly, for events in quadrant IV, as the value of t increases the associated value of (tau) would decrease, so that the normal ordering given by the progression of time is reversed. This suggests that we have already passed into an unacceptable region. Only I is correctly treated by these coordinates."

The idea that the co-moving-frames ("CMF") analysis can be allowable in some circumstances, but not allowable in other situations, seems inconsistent to me. For example, in the standard idealized twin "paradox" scenario with an instantaneous turnaround, right before the turnaround, the traveler (he) says that the home twin (she) is much younger than he is. He then accelerates toward her to reverse course, and the CMF analysis says that (from his perspective) during the turnaround she rapidly ages, and after the turnaround she is then much older than he is. This analysis is usually considered to be acceptable.

But what if he then immediately accelerates in the direction away from her (so as to immediately achieve his original velocity away from her)? The CMF then says that she rapidly gets younger, and after this second turnaround, she is much younger than he is ... she is again the same young age that she was before the first turnaround. This application of the CMF analysis (with his acceleration being AWAY from her) is often said to be invalid (because it produces a previous age for her).

But what if he then immediately reverses course a third time? The CMF then says that she rapidly ages, and after the third turnaround, she is again much older than he is. So the third turnaround produces the same state that existed right after the first turnaround. For the first and third turnarounds, the CMF analysis is considered "proper", but for the second turnaround, the CMF analysis is considered "improper". But, in order that the state after the third turnaround be the same state that existed after the first turnaround, it seems to me that we either need to believe that all three CMF results are "proper", or else none of them is "proper". Saying that it's OK to use the CMF when he accelerates toward her, but that it's not OK to use the CMF when he accelerates away from her, appears to me to produce an inconsistency.

ghwellsjr
Gold Member
...none of them is "proper"...
I tend to agree with this conclusion.

But if you realize as PeterDonis pointed out that we're talking about something that isn't a physical observable, then this is all nothing more than just different games played by different rules. It's only when a game has inconsistent rules that it no longer qualifies as a valid game.

By the way, none of these problems occur if you play the game according to the rules known as the radar method. But even then, it's important to realize that no additional knowledge or insight into a scenario is gained by playing these mind games. We do it just for the fun of it. (Or if you're lucky, like Brian Greene, you can also make a lot of money while playing these games.)

PeterDonis
Mentor
what if he then immediately accelerates in the direction away from her (so as to immediately achieve his original velocity away from her)? The CMF then says that she rapidly gets younger, and after this second turnaround, she is much younger than he is ... she is again the same young age that she was before the first turnaround. This application of the CMF analysis (with his acceleration being AWAY from her) is often said to be invalid (because it produces a previous age for her).

No, because it assigns multiple values of the time coordinate to single events on the home twin's worldline. That only happens if there is acceleration away from the home twin (and if you insist on constructing the CMF the way you are doing it); acceleration toward the home twin doesn't do that (at least, not on the home twin's worldline--it does assign multiple values of the time coordinate to single events elsewhere in spacetime, but we don't care about those events for this scenario). In other words, the CMF you are describing is not a valid frame; a valid frame has to be a one-to-one mapping between coordinate 4-tuples and events, at least for the region of spacetime you are concerned with.

(Of course, as ghwellsjr pointed out, coordinates are just conventions anyway; you do not need them to describe physics. They are a great convenience, but that's all. But if you're going to use them, you have to use them correctly.)

Nugatory
Mentor
For example, in the standard idealized twin "paradox" scenario with an instantaneous turnaround, right before the turnaround, the traveler (he) says that the home twin (she) is much younger than he is. He then accelerates toward her to reverse course, and the CMF analysis says that (from his perspective) during the turnaround she rapidly ages, and after the turnaround she is then much older than he is. This analysis is usually considered to be acceptable

That's not what the comoving frame analysis says, at least not if we're talking about the analysis in terms of inertial and momentarily comovng frames (if instead you mean the single egregiously non-inertial comoving frame in which the traveller is always at rest, I disagree that this analysis is "usually" considered to be acceptable). Instead, it says that the traveller's pre-turnaround and post-turnaround frames are different and therefore we can expect to find a discontinuity of no physical significance when we compare coordinate time values across them.

Th most intuitive way of seeing this is to imagine that instead of turning his spaceship around, the traveller jumps from his outbound ship onto a ship that conveniently just happens to be travelling in the opposite (inbound) direction at the appropriate speed. When he compares his notes with the logbooks of the second ship and discusses his and twin's past history with the crew of the second ship, he will find a completely consistent story in which he was ageing less quickly than the stay-at-home twin the whole time. The fact that the traveller's diary doesn't line up well with the ship's logbook just tells us that the two logs were maintained using a different standard of time.

Dale
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2021 Award
The idea that the co-moving-frames ("CMF") analysis can be allowable in some circumstances, but not allowable in other situations, seems inconsistent to me.
I am not certain exactly what you mean by "the CMF analysis" (as Nugatory mentioned, you could mean analysis in a MCIF or you could mean a non-inertial frame constructed by using the simultaneity convention defined in each MCIF). However, the rule which is applied is perfectly consistent. The rule is:

"A chart or coordinate system consists of a subset U of a set M, along with a one-to-one map φ : U → Rn, such that the image φ(U) is open in R."
http://preposterousuniverse.com/grnotes/grnotes-two.pdf [Broken]

If a mapping is not one-to-one, such as when you have "time run backwards", then it is not a valid coordinate system according to the above rule defining coordinate systems. You may dislike that rule, but it is the accepted rule and there is nothing inconsistent with applying to all circumstances and finding that some are allowed and some are disallowed.

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But the still unanswered question is this:

Does an immediate back-to-back (matched) pair of instantaneous course-reversals leave all ages the same as before? I.e., if the traveler instantaneously changes his velocity (wrt the home twin) from +V (away from her) to -V (toward her), but then immediately instantaneously changes his velocity from -V to +V, is the net effect the same as if there had been no reversals at all?

If the answer to that question is "yes", then it seems to me that the following is implied:

IF he is allowed to use the co-moving-frames (CMF) analysis for the first course-reversal, then he will say that her age suddenly increases during that first reversal. But if her age is the same before and after the matched pair of reversals, it is necessary that her age must decrease during the second reversal, by the same amount that her age increased during the first reversal. And this decrease in her age during the second reversal is exactly what the CMF says will happen.

PeterDonis
Mentor
Does an immediate back-to-back (matched) pair of instantaneous course-reversals leave all ages the same as before?

You still have not grasped the fundamental point: for the traveler, the "age" of anything or anyone not spatially co-located with him is a matter of convention. There is no one unique answer to the questions you are asking; it depends on the simultaneity convention the traveler adopts. It is just a convention because no actual physical observable is affected by it.

Nugatory
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IF he is allowed to use the co-moving-frames (CMF) analysis for the first course-reversal, then he will say that her age suddenly increases during that first reversal. But if her age is the same before and after the matched pair of reversals, it is necessary that her age must decrease during the second reversal, by the same amount that her age increased during the first reversal. And this decrease in her age during the second reversal is exactly what the CMF says will happen.

That is not what the comoving frame analysis says - it's how you are misunderstanding the comoving frame analysis.

We have our two twins, A and B. The question "Is A older than B, younger than B, or the same age?" is inherently ill-formed; the problem will be more apparent if we phrase the question more carefully: "At the same time that the age of A is X, is the age of B greater than X, less than X, or the same as X?" or "Did B reach his nth birthday before, after, or at the same time as A?"

It should be clear that neither question is well-formed if we cannot agree about what is meant by "at the same time" - and that is only possible when they are colocated. Thus, the comoving frames analysis doesn't tell us when one or the other twin is aging differently, it just gives us a way of reconciling the calculation done on the outbound leg and the inbound leg.

ghwellsjr
Gold Member
But the still unanswered question is this:

Does an immediate back-to-back (matched) pair of instantaneous course-reversals leave all ages the same as before?
It depends on how you want to play the game. In the game I play based on the radar method the answer is yes.

I.e., if the traveler instantaneously changes his velocity (wrt the home twin) from +V (away from her) to -V (toward her), but then immediately instantaneously changes his velocity from -V to +V, is the net effect the same as if there had been no reversals at all?
In the game I play, all the ages stay the same even in between the two instantaneous velocity changes. You don't have to play a game that creates discontinuities of age in remote objects under any circumstances.

If the answer to that question is "yes", then it seems to me that the following is implied:

IF he is allowed to use the co-moving-frames (CMF) analysis for the first course-reversal, then he will say that her age suddenly increases during that first reversal. But if her age is the same before and after the matched pair of reversals, it is necessary that her age must decrease during the second reversal, by the same amount that her age increased during the first reversal. And this decrease in her age during the second reversal is exactly what the CMF says will happen.
A good reason not to play the game according to CMF rules and to switch to radar rules.

Dale
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2021 Award
Does an immediate back-to-back (matched) pair of instantaneous course-reversals leave all ages the same as before?
As others have mentioned, this depends entirely on your convention for non-inertial reference frames. In the radar time convention they would be left the same.

The type of convention that you seem to favor cannot be applied in all of spacetime. Specifically, it cannot be applied in any region where it violates the one-to-one condition I listed above. That means that the only place you can use it is in regions where it does not cause time to go backwards. A pair of back to back accelerations (using your convention) would result in a pair of regions of spacetime which were not covered by the chart.

And this decrease in her age during the second reversal is exactly what the CMF says will happen.
You have already been told that this is wrong by multiple people in multiple different ways and with multiple references to the professional literature. There is no excuse for you to continue with these disproven assertions.

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If simultaneity at a distance is as meaningless in special relativity as the prevailing opinions on this forum seem to indicate, it's odd that Einstein put so much emphasis on the Lorentz equations, which fundamentally are about simultaneity at a distance. I understand that coordinates are basically meaningless in general relativity, but I don't think that need be the case in special relativity, which assumes a flat universe of infinite extent, with no gravitational fields.

PeterDonis
Mentor
the Lorentz equations, which fundamentally are about simultaneity at a distance.

They're fundamentally about transforming between inertial frames, which all use a particular simultaneity convention, yes. Back when Einstein and others were discussing all this, they all believed that that particular simultaneity convention was physically "privileged", because in an inertial frame in flat spacetime, it's the one that arises from Einstein clock synchronization and the Einstein definition of simultaneity, which was a foundational concept in Einstein's development of SR.

However, today we understand that, however important those concepts were in the development of SR, they are not necessary for the modern formulation of the theory. The modern formulation of SR is based on flat Minkowski spacetime, independent of any particular system of coordinates. See further comments below.

I understand that coordinates are basically meaningless in general relativity, but I don't think that need be the case in special relativity, which assumes a flat universe of infinite extent, with no gravitational fields.

When Einstein developed SR, he (and others) viewed coordinates as always being derived from particular physical constructions, such as the systems of rods and clocks that are ubiquitous in Einstein's thought experiments and which ground his construction of inertial frames in SR.

However, today we understand that, while coordinates can be derived this way, they do not have to be, even in SR. (And conversely, you can, if you want, construct coordinates that have physical interpretations in GR as well--you just are more limited in what physical interpretations you can pick.) You can describe flat Minkowski spacetime in any arbitrary system of coordinates, and still write down all the laws of SR in covariant form, valid in any coordinate chart, even one where the coordinates have no physical meaning.

Bottom line: saying "Einstein said this..." or "Einstein thought this..." is not a valid argument about physics, however interesting it may be as a study in the history of physics.

Dale
Dale
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2021 Award
I understand that coordinates are basically meaningless in general relativity, but I don't think that need be the case in special relativity
It isn't that they are meaningless. It is that they are conventional. You can pick meaningful conventions, but they are still conventions.

This is not peculiar to relativity (either special or general), but it applies to coordinates in classical physics as well. In fact, the whole of Lagrangian mechanics was developed precisely in order to take full advantage of the fact that coordinates are conventional in classical physics. By picking conventions that are meaningful for a particular problem you can solve problems that would be intractable otherwise.

ghwellsjr