# About the convention of simultaneity

1. Aug 17, 2013

### analyst5

Heys guys,

I asked a similar question in one of the previous threads and therefore I apologize if anybody is offended or thinks I'm asking too much. I just want to clear and define some concepts in my head.

So it is agreed that simultaneity is a convention and that in SR inertial frames have a standard convention or a set of rules which define what events are simultaneous relative to them. This part seems okay, but I really dont understand how we define simultaneous events relative to non inertial frames. It has been mentioned previously that non-inertial frames don't have a standard simultaneity convention, but what basically does that mean? Does it mean that there are no basic rules about simultaneity like in SR, but that we can still define a collectin of simultaneous events relative to a non inertial frame, of course if those events are trully simultaneous 'from a point of view' of a non inertial observer. I hope somebody can define this better to me.

Thanks in advance.

2. Aug 17, 2013

### ghwellsjr

It sounds like you've done a pretty good job yourself. I'm only concerned about your wording near the end where you say "if those events are trully simultaneous 'from a point of view' of a non inertial observer." If by that you merely mean, "if that non-inertial definition is consistent with itself and with observations" and that there are many different definitions that are all equally viable, then that's fine. But if you mean that there exists just one definition that is true while others are not, then I question whether you really understand the issue of simultaneity even for inertial frames.

Part of my concern is that you started out using the terms inertial frames and non-inertial frames and then at the end you switched to non inertial observer. The standard convention in SR can handle non inertial observers just fine, there is never any need or advantage to going that extra step to defining a non inertial frame just because there is a non inertial observer. Nothing is learned or gained by doing this, except for the mathematical exercise and satisfaction of doing so. No observer, inertial or non inertial, can tell that you are using any particular definition or convention, either the standard SR one or any other convention to establish simultaneity. Simultaneity is not intrinsic to nature, only our particular way of describing nature.

3. Aug 17, 2013

### bobc2

analyst5, there are two or three fundamentally different understandings of simultaneity. One understanding is consistent with the Lorentz Ether Theory (LET) interpretation of Special Relativity, another is consistent with the 4-dimensional space-time interpretation of Special Relativity (referred to as "Block Universe" by some), and a third model (a pure math model without any associated philosophical claims about physical reality--except that the idealism philosophy is sometimes asserted) may be taken for those who reject both LET and Block Universe. When discussing simultaneity, it is often useful to specify which of the three models provide the context for discussion.

Be aware that discussions of simultaneity on this forum is not particularly associated with any of the three, because those discussions would inevitably involve what the forum would consider as philosophical discussions. That is, establishing any of the three models as a context for discussion would immediately put the discussion in the philosophical arena (see forum rules). This forum is not for philosophical discussions of physical reality.

Your comments seem as though you are trying to understand simultaneity in the context of the pursuit of understanding of physical reality. This could lead to confusion for you when you read the responses to your questions. That is because the responders have no interest in pursuing an understanding of the "physical reality", rather the focus is, in this case, the mathematical "simultaneity convention."

Last edited: Aug 17, 2013
4. Aug 17, 2013

### ghwellsjr

The only sense in which LET asserts a fundamentally different understanding of simultaneity from Special Relativity is that it allows for only one preferred Inertial Reference Frame (IRF), that of the presumed rest state of the ether and so time is absolute with reference to that frame. But since no one can identify that state, it's a useless assertion to make. Otherwise, the simultaneity of that one preferred IRF is identical to the simultaneity of any other IRF. I don't know why you claim that simultaneity is any different for LET or why you bring it up as an issue to be considered.

I never thought that discussions of simultaneity in SR needed to have any additional association.

There is no "physical reality" to simultaneity apart from that which we arbitrarily supply by virtue of a convention. Are you asserting that there is?

5. Aug 17, 2013

### Staff: Mentor

It's worth noting that this "standard convention" has a physical basis, which Einstein first described in his early thought experiments on relativity. The idea is that, if you are an inertial observer, and two events are both at the same distance from you, then those two events are simultaneous for you if and only if light from both events reaches you at the same instant.

Dolby and Gull have generalized the above idea to non-inertial observers, in their paper on "radar time":

http://arxiv.org/abs/gr-qc/0104077

They use the idea here to analyze the "twin paradox" scenario, but it's applicable generally.

Fundamentally it means that, in relativity, "simultaneity" isn't a very useful concept for actually doing physics. The main reason we talk about it at all is our intuition: we are intuitively accustomed to a world in which there is some sort of "absolute time" that's the same for everyone. In relativity, this isn't true; more precisely, it is impossible to adopt a single, global simultaneity convention for all observers that has all of the intuitive properties we want it to have.

For example, the "radar time" simultaneity convention I mentioned above, the one that generalizes the Einstein convention to non-inertial observers, is still different for each observer; in other words, it's observer-dependent. But in relativity, all of the physics can be expressed purely in terms of invariants: things that are *not* observer-dependent. So simultaneity, since it is observer-dependent, will end up not appearing in a properly expressed relativistic description of physics.

6. Aug 17, 2013

### ghwellsjr

But don't you think that it's important to stress that "observer-dependent" doesn't mean it's just an observation or measurement made by an observer, it also requires the application of a convention and a calculation for the observer to create a set of coordinates for each event?

7. Aug 17, 2013

### WannabeNewton

You can say this all you want but the fact is that there are distinguished philosophers of physics out there still debating this so you can make blanket statements all you want but you should probably read the sea of literature on this first before trying to act authoritative. This doesn't even have to extend to simultaneity for non-inertial observers; the issue is there for Einstein synchronization itself.

8. Aug 17, 2013

### pervect

Staff Emeritus
In general non-inertial frames are accelerating, rotating, or both. If we ignore rotation for the time being, the standard simultaneity conventions make Newton's laws work. They are more or less a "required option" as far as Newton's laws go. Rather like a personal experience I had on an ancient computer system, you are perfectly free to not pick the "required option", it's just that if you do not pick the "required option" your application (in this case, Newton's laws) will fail to work.

IF this isn't obvious, imagine two identical masses, in a head on collision. There is only one clock synchronizing scheme that will make the measured velocities of the two identical masses that come to a dead stop when they collide have equal numerical values. This is the "isotropic" clock synchronization scheme of Einstein.

"Isotropic" is the textbook name for the required synchronization scheme, and the term used by Einstein. It seems to be abstract enough that people don't quite follow what it means :(. Hopefully the above example (with the head-on collision of two identical masses) will be a specific example of why we need the abstract concept of "isotropy".

Newton's laws don't actually work in non-inertial frames. One typically adds in "fictional forces". Then the usual convention for accelerated non-rotating frames becomes one that makes Newton's laws work with the additional fictional forces. Isotropy doesn't apply directly in an accelerating frame, the "up" and "down" directions act differently than the others.

Rotating frames cause a large amount of confusion - the solution is easy though, you simply use the underlying non-rotating frame and choose the non-rotating frame's simultaneity convention. To get into the whys and whatfors gets rather involved, more involved than I have time for. We live on a rotating planet, and this is the convention that we typically use to deal with it. One of the consequences of this standard choice is the so-called Sagnac effect.

Last edited: Aug 17, 2013
9. Aug 17, 2013

### Staff: Mentor

Well, the Dolby and Gull "radar time" is more or less a direct observable; you can certainly use it to set up coordinates, but you don't have to set up coordinates to make the observations that they use to define "radar time". I agree that the setting up coordinates part requires applying a convention, not just making observations.

Last edited: Aug 17, 2013
10. Aug 18, 2013

### ghwellsjr

The only direct observables are the Proper Time that the radar signal was sent and the Proper Time that the echo was received.

Then, the convention is applied that the amount of time it took for the radar signal to reach its target is the same as the amount of time it took for the echo to return to the observer and the calculation is performed to determine the average of the two observed Proper Times and assign it as the time when the radar signal reached the target.

Furthermore, the convention that light propagates at c is applied along with the calculation of the difference between the observed Proper Times divided by two to determine the distance away that the target was at the moment the radar signal reflected off of it.

By repeatedly emitting radar signals at targets and keeping track of the corresponding sent and received Proper Times by using signatures, the non inertial observer can construct a non inertial coordinate system. This is exactly what Dolby and Gull describe in their paper.

Now if the observer only cares about the simultaneity of distant events, he doesn't have to do the calculation for the distance and he doesn't have to construct a non inertial coordinate system but he still has to repeatedly send out and keep track of the Proper Times and the signatures of all radar signals and their returned echoes and he still has to apply the convention that I described for determining the time of the events. And for simultaneous events that are different distances away from him, he will have sent the radar signals at two different Proper Times and received them at two other different Proper Times and he can't know ahead of time which pairs will go with which events so I don't know why you would say that "is more or less a direct observable".

11. Aug 18, 2013

### Staff: Mentor

Yes that is exactly what it means. If I say the phrase "Events A and B are simultaneous wrt inertial observer O" then people know exactly what that means. It means that events A and B have the same time coordinate in an inertial reference frame where O is at rest.

However, if you say the phrase "Events A and B are simultaneous wrt non-inertial observer O" then nobody knows exactly what that means without some additional definitions.

There are some common definitions of simultaneity for specific types of non-inertial observers. For example, Rindler coordinates define a common meaning of simultaneity for a uniformly accelerating observer. Born coordinates are a common convention for observers in uniform circular motion. Dolby and Gull's radar coordinates are a well-known convention for arbitrarily moving observers.

So, you could say "Events A and B are simultaneous wrt non-inertial observer O using radar coordinates" and then people would know exactly what that means.

12. Aug 18, 2013

### Staff: Mentor

Yes.

Yes, but all of these are direct observables. The fact that there are a lot of them doesn't make them any less direct.

Yes, that's true; this convention is basically the analogue of the Einstein synchronization convention for a non-inertial observer. But if all he's interested in is defining simultaneity, he can make it even simpler; see below.

Yes, but the observations themselves will tell him; see below.

For any two (emission, reception) pairs (each pair being the proper time of emission and proper time of reception of the same radar signal), the test for whether they are simultaneous is simple: are both pairs "centered" on the same proper time? (That is, is the "halfway point" of each emission, reception interval the same?) Technically, this is not a "direct observable" since there is a calculation that has to be done, but the calculation is so simple that I think it qualifies as "more or less a direct observable". And computing this observable does not require actually assigning a "time" to events; if all the observer cares about is simultaneity, he can apply this test directly to his observations without doing any other calculations or constructions.

13. Aug 20, 2013

### ghwellsjr

As far as I can tell, calling them "centered" or at the same "halfway point" means exactly the same as what I called the average of the emission and reception times. Are you suggesting some other way to make the determination than actually taking the average?

If you don't assign times to the events, then it is a pointless exercise which I think you will see after you actually do an exercise which I will present to you.

Which is what I said (except that I claim he must also correlate the times and the events).

Here's an exercise that I'd like you to do:

A non-inertial observer emits a signatured radar signal every unit of his Proper Time, that is, each radar signal includes the Proper Time that it was sent. There are two targets of unknown acceleration that start off colocated with him and end up colocated with him after 32 units of his Proper Time. The observer and two targets remain in line. The observer keeps a list of the Proper Times of the signatures of the reflections (I've grouped them according to the two targets) but to make the list more manageable, I've only included the reflections that are coincident with increments of the Proper Time unit.

Can you please show how the observer determines whatever it is you claim "is more or less a direct observable"?
Code (Text):

Proper    Sig for     Sig for
Time      Target 1    Target 2

0           0           0
1
2
3
4           1
5
6
7
8           2
9
10
11
12           3
13
14
15
16           4           1
17           5
18           6
19           7
20           8           2
21           9
22          10
23          11
24          12           3
25          13
26          14
27          15
28          16           4
29          20           8
30          24          12
31          28          16
32          32          32

14. Aug 20, 2013

### Staff: Mentor

I think that's right, yes.

No.

If I'm reading this right, then the observer would make calculations like the following ($\tau$ is the observer's proper time):

Signal emitted $\tau = 1$, received reflection from target 1 at $\tau = 4$: the "average" is therefore $(1 + 4)/2 = 2.5$.

Signal emitted $\tau = 1$, received reflection from target 2 at $\tau = 16$: the "average" is therefore $(1 + 16)/2 = 8.5$.

The observer can therefore tabulate the "averages" for all the signals whose reflections he receives from each target. Any "averages" that are the same for both targets indicate pairs of events, one on each target's worldline, which are simultaneous according to the observer. [Edit: An example of such a pair would be the signal emitted at $\tau = 5$, with a reflection from Target 1 received at $\tau = 17$; and the signal emitted at $\tau = 2$, with a reflection from Target 2 received at $\tau = 20$. Both of these average to 11.]

Last edited: Aug 20, 2013
15. Aug 20, 2013

### ghwellsjr

Yes, you are doing it just like I said.

But how is this "more or less a direct observable"? Can you look at the list that I gave you and see a pattern (or anything else) that would allow you to see the pairs of simultaneous events without actually doing the calculation on "all the signals", as you say?

Also, you said that you don't have to assign a time to the simultaneous events, and yet you did this for your one example. So what did you mean by that statement?

16. Aug 20, 2013

### Staff: Mentor

I can't just stare at the list and read off the simultaneous pairs, no. But it would be very simple to program a computer to process the data as it comes in and spit out the simultaneous pairs. We routinely do much more complicated processing on signals in scientific experiments and still call the results "direct observables".

No, I didn't. I never claimed that the "average" I calculated was the "time" of the simultaneous events. That is an additional interpretation--an obvious one to make, of course, but still an interpretation. My point is that you do not have to adopt that interpretation in order to say that any pairs of events with the same average are simultaneous; the average could just be a number with no other physical meaning besides serving as a label for events that lets you pick out the simultaneous pairs.

All of this is really a question of terminology, though. We appear to agree on the point I was really trying to stress, which is that simultaneity is observer-dependent, and therefore will not appear in the laws of physics when they are written in proper relativistically invariant form. Whether simultaneity is a "direct observable" or not, or whether it requires assigning a "time" to events, seem like minor issues to me in comparison.

17. Aug 20, 2013

### ghwellsjr

And what does the computer spit out for the example you worked out above?

Then what calculations are considered indirect observables (or whatever you call things that are not "direct observables")?

Why did you exclude the third simultaneous event for the observer? It is determined in exactly the same way as the pair for the two targets. I don't see it as an interpretation at all, it's truly a direct observable.

I don't think its a minor point when most people read about all the so-called observations that are made by observers and think that the observers can actually see what you are calling a direct observable.

18. Aug 20, 2013

### Staff: Mentor

Code (Text):

Average  0  Target 1: sent  0 received  0  Target 2: sent  0 received  0
Average 11  Target 1: sent  5 received 17  Target 2: sent  2 received 20
Average 16  Target 1: sent 10 received 22  Target 2: sent  4 received 28
Average 21  Target 1: sent 15 received 27  Target 2: sent 12 received 30
Average 32  Target 1: sent 32 received 32  Target 2: sent 32 received 32

Python code available on request.

I don't think there is a single term for "things that aren't direct observables", because that's a very heterogeneous category of things. But, for example, we run particle physics experiments and say that the results count as observations of things like the Higgs particle, even though there is a lot of post-processing of data that has to occur for such an "observation"; but we calculate things like the various interaction coupling constants that appear in the Standard Model, and we don't call those direct observables.

Sure, you could calculate an "average" for an event on the observer's worldline the same way, and you would, of course, notice that this "average" is just the observer's proper time at that event. I did say that the interpretation of the "average" as the "time" of all events that are part of the "simultaneous set" with that average was an obvious interpretation.

In my experience, this kind of issue usually comes up when someone (and I admit I've been guilty of this) uses a term like "see" in reference to something like time dilation, which I agree is certainly *not* a direct observable. This use of language certainly does cause confusion, sometimes to the point that readers think of something like time dilation as more fundamental than something like Doppler shift, which *is* a direct observable by just about any reasonable definition.

19. Aug 21, 2013

### ghwellsjr

And since you agreed that the observer's own Proper Times are also events that are simultaneous with calculated events for the two targets, you could modify your Python code to spit out events that were simultaneous between the observer and Target 1 and between the observer and Target 2, couldn't you?

Furthermore, if I had included all the reflections in my list on post #13 (I can do that if you want), then the lists of simultaneous events would be much larger, wouldn't it? And, in fact, if the observer had sent out many more radar signals, even continuously, then the list would be longer, even infinitely long and it would be better if the computer would instead present the results as a function. We don't want anyone to jump to the conclusion that just because in my example there were only five "hits", that simultaneity is not a continuous function.

And since we have established that simultaneity is a continuous function, what is that point of doing the limited exercise of calculating and presenting the data as only sets of events that are simultaneous without also presenting the locations of the targets when those simultaneous events occurred? Aren't they just as much "more or less direct observables" according to your criterion that a computer program can derive the results from the data?

If we include observations made from Doppler shifts, namely the Proper Times of the two targets, then our computer program can actually calculate time dilation just as easily as simultaneous events. So why do you claim that time dilation is not a direct observable if simultaneity is a direct observable?

20. Aug 21, 2013

### Staff: Mentor

Huh? Simultaneity is a binary property of pairs (or, more generally, n-tuples) of events--either a given pair (or n-tuple) of events are simultaneous, or they're not. It's not a "function" of anything.

The function you are trying to construct here is a time coordinate; you're basically setting up a coordinate chart using the Dolby & Gull method.

We haven't. See above.

This amounts to adding the space coordinates to the time coordinate to form a chart. See above. (Also, converting the time observations to distance observations requires additional "conventions", like assuming that the round-trip speed of light is constant.)

That's not what I said. I said we sometimes call things "direct observables" even though they require computer programs to post-process the data. I even gave the example of particle physics experiments. I did not say that anything that a computer can calculate from the data is a direct observable; I even gave another example, relating to the particle physics experiments, of something that is calculated from the data but isn't called a direct observable.

Your own position appears to be that, as you said in an earlier post, the only "direct observables" are the proper times of emission and reception of the signals. But your table was a table of numbers: how were those numbers obtained? Suppose we read them off an ordinary analog clock face. Then the actual "direct observables" were the positions of the clock hands relative to numbers on the clock face; we have to adopt an "interpretation" to equate those positions with "proper times".

So we could get into an endless, pointless argument about what's a "direct observable" and what isn't. But the argument would be about terminology, not physics; the physics, meaning the laws as written in terms of invariants, is the same whether we call simultaneity, or anything else, a "direct observable" or not.

Strictly speaking, that's not what the Doppler shift observable is. It's a redshift/blueshift of the light signals coming from the targets.

But you could use a very powerful telescope to actually see an image of each "Target", so that you can watch their clocks; then you could say things like "when this particular light signal was emitted from Target X, that target's clock was reading such and such". Then you could notice that, while the target is moving away from you, the clock readings in the images seem to "run slow" compared to your own proper time, but when the target is moving towards you, the clock readings in the images seem to "run fast" compared to your own, and these observations correlate with the Doppler redshift/blueshift observed, for example, by a spectrometer.

I personally don't like using the term "Doppler shift" unqualified to refer to the latter type of observation, but I agree it's often used that way (for example, in the Usenet Physics FAQ on the twin paradox).

With some other "conventions" adopted (as with the spatial coordinates, above), yes.

See above.

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