Friday, April 29, 2016

Relativity of simultaneity

I've been thinking about Einstein's nice argument for the relativity of simultaneity in his popular book. The argument starts with the assumption that the speed of light is the same in every inertial reference frame, and uses this to construct a method for determining whether two events are simultaneous. Basically, this method involves having an inertial observer spatially equidistant between the two events checking whether light reaches her simultaneously from the two events. Given the constancy of the speed of light and the equidistance assumption, it seems to follow that the two events are simultaneous if and only if light reaches the observer simultaneously from the two events. And then Einstein gives a very nice argument that applying this method gives different answers depending on the osberve, and concludes that simultaneity is relative to the reference frame.

But there is something that has been worrying me conceptually about Einstein's account of simultaneity. That account takes for granted that we know what it means for the observer to observe two events simultaneously. But isn't the task to define simultaneity?

I guess not. Einstein seems to presupposing that we already have the notion of simultaneity of events at the location of an observer. Moreover, the details of Einstein's argument assume this principle which I think he doesn't discuss:

  • Two events befalling the same observer occur simultaneously in the reference frame of the observer if and only if they occur at the same point in spacetime.
(Einstein also tacitly makes the simplifying assumption that observers are point-sized. I won't worry about that assumption in this post.) I am a little troubled by this principle. It's not clear that it's conceptually necessary (might we not think it's violated in cases of time travel?). Still, maybe the best way to take Einstein's account of simultaneity in the book is this. First, we define simultaneity for events befalling the observer who defines a reference frame by requiring sameness of spacetime location. Second, we use this and the equidistant-observer thought experiment to define simultaneity for events not both located at the observer. Third, we show that by this two-part definition of simultaneity, simultaneity is frame-relative.


Michael Gonzalez said...

Not sure how salient this is, but technically talking about "spacetime" (especially in a robust enough sense that time travel becomes a relevant factor) is anachronistic with regard to Einstein's STR. Einstein's view is of a 3-d space evolving dynamically through time. It was Minkowski who proposed the 4-d "spacetime" view.

Eintein seems to be talking about whether two events actually occur such that neither was earlier than or later than the other. And he is talking about how the constancy of the speed of light affects our relative perceptions of which things are simultaneous.

{Feel free to ignore the rest... it's a pet peeve of mine}
Of course, there could still be absolute simultaneity in an absolute or privileged reference frame. Einstein's only reason he gives for leaving that out is that Ernst Mach (a flaming logical positivist and verificationist, if ever there was one) says things which can't be empirically verified are meaningless. A privileged reference frame cannot even in principle be empirically verified. But, of course, we've since discovered that verificationism is self-refuting and obviously false, so we're actually back to the drawing board on Lorentz invariance... and I digress.

Alexander R Pruss said...

I agree that the positivist argument is bunk. But there is also a simplicity argument, actually two of them.

1. Positing an additional fact--which frame is privileged--when doing so is not needed to explain any phenomena goes against Ockham's razor.

2. The controversial assumption in Einstein's argument is that the speed of light is frame-invariant. That makes simultaneity relative. But the speed of light assumption makes for a very elegant set of fundamental axioms from which he can derive Lorentz transformations. I think--but I don't know--that the competing approach where the speed of light is non-frame-invariant requires a more complex set of axioms.

Michael Gonzalez said...

I completely agree. If the privileged frame were explanatorily otiose, then it would indeed be good practice to discard it. Of course, it turns out that that may not be the case. It should be suspicious from the outset when Relativity teaches that nothing actually has a speed... except light, and that speed is invariant in all reference frames. It's hard to understand what that could mean. Moreover, when we ask about things like "what if I were going 99.9% of the speed of light?" we seem to be ignoring the fact that in some perfectly good frame of reference we ARE going that fast! So, there are conceptual difficulties.

Lorentz himself had a favored way of deriving his own transformations, and it happened to involve an absolute frame plus dynamic effects of traveling at high speeds.

Really, the whole thing about reference frames seems to me to start with Galileo, and Galileo had a subtly but importantly different view than what STR takes for granted. Galileo said that the ship at harbor and the ship that is traveling uniformly are identical ONLY because whatever changes that needed to happen in getting from actual stillness to actual uniform motion have indeed occurred. STR treats such a transition as a mere geometric "boost", which is just a coordinate transformation and shouldn't have physical consequences. But we know that acceleration does indeed have physical consequences; it isn't just a "boost". Indeed, John Bell was trying to help people understand this when he gave that "thread" thought experiment, and all the theoretical physicists said the thread wouldn't break until they did the calculations: it breaks. A real, dynamic, physical effect occurs to get you from one reference frame to another. And, since that is the case, the whole matter of things being relative to frames needs to be reframed (pun intended) in terms of a dynamics that takes this into account.

In short, yes, there may be more explanatory baggage, but it may be necessary for an accurate physics.

Moreover, I personally see Aspect-style experiments (violations of the Bell-inequalities) as evidence that superluminal causal interaction is possible, and the least ad hoc explanation is just to accept that (rather than concoct elaborate scenarios about infinite worlds or things that only actually have a state when they are being "observed", whatever that means). Quentin Smith has written a really amazing paper on the potential for a Neo-Lorentzian Relativity, coupled with a Neo-Bohmian approach to QM, to be the Unified Theory. He shows what he sees as clear superiority over GTR and the current approaches to Quantum Gravity.

Alexander R Pruss said...

Superluminal causal interaction doesn't violate relativity theory by itself. Of course, it has the consequence that in some reference frames there is backwards causation. But backwards causation is only problematic when it can generate causal loops or other paradoxes, and I don't think the kind of frame-relative backwards causation involved in the Bell inequalities leads to paradox.

Michael Gonzalez said...

You don't think backward causation is philosophically problematic? How does the PSR fare in such cases?

Besides, it is my understanding that Einstein's "contiguity" stipulation on physical theories required both an unbroken chain of causes if A is physically relevant to B, and also that no such chain exceed the speed of light. That was what defined the parameters of "local" vs. "non-local" effects on which Bell's paper was predicated.

Alexander R Pruss said...

The contiguity stipulation should be dropped, too. :-)

I don't see any difficulty for PSR in backwards causation. Those cases are just cases where an earlier state of affairs is explained by a later one, as when I do well on an exam because after the exam I will have prayed that I had done well.

Michael Gonzalez said...

LOL. Well, the difference between "local" and "non-local" is, at present, considered to be rather important in drawing the line between "relativistic" and "non-relativistic" interpretations of QM.

You're assuming a lot about the nature of time here. I won't pester you with my A-theoretical leanings yet again.... The reason I mentioned the PSR is because, in some reference frames, A is the explanation for B; in others, B is the explanation for A. So, which actually explains which? If they each explain each other, then there is a loop, which doesn't sit well with your account of modality, or with explanation in general.

William said...

In cosmology, there is a privileged reference frame, the one of the cosmic background, presumed to be originated somewhere near the center of the first few seconds of the big bang.

It's in many ways a useless reference frame since we can't use it for a precise location, so we cannot use it to measure anything local with any precision.

Alexander R Pruss said...

I don't think so. I think the cosmic background exhibits a lot of local variation, and only some kind of an arbitrary process of smoothing or local averaging will generate a unique frame.

William said...

Yes, true. It's the frame where on average the photons in the background are moving away in the same way in all directions (whereas by that frame we are moving at about 600 m/s away from that center). , 4th paragraph

Michael Gonzalez said...

William: Swinburne is with you in thinking of the cosmic frame as the absolute one, and he gives an argument for going with that (albeit averaged out) frame.

The truth is that GTR doesn't really have reference frames at all in the way STR does. And, given that GTR is the theory that actually describes our Universe, I am sometimes a little perplexed as to why STR jargon is used in these discussions.

As Tim Maudlin puts it, if STR just follows directly from the equivalence of all reference frames + the constancy of the speed of light, then, given that GTR is a different theory from STR... which of those two are we rejecting in moving from the one to the other?? That ought to unsettle us a little, until we dig deeper into what Galilean relativity (equivalence of frames) was supposed to mean historically.... But I digress again.

Alexander R Pruss said...

There is surely more than one way of defining the average, since it's a localized one (crude thought: average directions of photons in each 10 light year sphere; but why 10? Why not 15? Why a sphere? Etc.)

Alexander R Pruss said...

The special theory is trivially true given the general theory. All inertial frames are equivalent. There just aren't any inertial frames.

Michael Gonzalez said...

The special theory is described entirely in terms of reference frames. For the general theory to totally lack them ought to give us pause (even if a total lack of frames is a trivial sort of equivalence...).

Unknown said...
This comment has been removed by the author.
Unknown said...

Does anyone know of an essay that gives a perspicuous summary and discussion of the arguments for and against the existence of a privileged reference frame?

Michael Gonzalez said...

Richard: I HIGHLY recommend the anthology called "Einstein, Relativity, and Absolute Simultaneity", edited by William Lane Craig and Quentin Smith.

Johannes said...

The "troubling" principle is just a particular instance of the definition of simultaneity from the viewpoint of an observer: two events occur simultaneously in the reference frame of the observer if and only if they occur at the same time.

A point in spacetime is defined as (t, x, y, z) if using cartesian coordinates, where x, y and z are measured from the position of the observer and t is time marked by a clock at the position of the observer. In the case of "two events befalling the same observer", x, y and z = 0 by definition. If the events are simultaneous, t is the same by definition. Therefore both events "occur at the same point in spacetime" by definition.

Now, IMV the most relevant aspect of the relativity of simultaneity is that the possible relation of causality is the same for ALL observers. This is clear by considering the invariant interval between two events, which in the case of the Minkowsi spacetime of Special Relativity is:

ds^2 = -c^2 dt^2 + dL^2

where dL is the spatial distance between the events, expressed in cartesian coordinates (x, y, z) as: dL^2 = dx^2 + dy^2 + dz^2.

Let's examine the tree possible cases:

a. ds^2 < 0, meaning (c^2 dt^2) > dL^2. The distance travelled by light in dt es GREATER than dL. Therefore, there CAN be a relation of causality between the two events.

b. ds^2 = 0, meaning c^2 dt^2 = dL^2. The distance travelled by light in dt is exactly dL. Therefore, the events are two points in the world line of a photon.

c. ds^2 > 0, meaning (c^2 dt^2) < dL^2. The distance travelled by light in dt is LESS than dL Therefore, there CANNOT be a relation of causality between the two events.

Since the invariant interval ds between the events is the same for all observers (which is why it is called "invariant"), the possibility or impossibility of a relation of causality between the events is the same for all observers. If the events can be causally connected for one observer, then they can be causally connected for all observers.

Unknown said...
This comment has been removed by the author.
Unknown said...

Thank you, Michael. Just what I was needing!


Special Relativity(SR)itself does not point to absolutes. That includes the exclusion of absolute simultaneity. Meanwhile, many say that they absolutely understand SR, yet this is an absurd statement, since SR does not extend far enough to reach absolutes.

However, if you analyze "motion", then things change. You find that if you have "absolute" motion that is ongoing within an "absolute" 4 dimensional Space-Time environment, the outcome of this setting, is Special Relativity.

An absolute frame is discovered. This absolute frame is what SR resides within.

Unknown said...

Michael Gonzalez, I want to ask you a question about relativity and spacetime. I am a physics student and currently studying Special and General relativity. In all of my textbooks they take the spacetime Minkowskian interpretation for granted. Now in a recent answer to a question about how he views General relativity Dr Craig said that it is possible to be a spacetime realist and still be a neo-Lorentzian if we allow for proper slicing of spacetime into proper temporal slices. Now is it compatible with the A Theory needed for Kalam argument if I hold on to the flat spacetime of SR and curved spacetime of GR?

Alexander R Pruss said...

I'm not Michael, but let me say a little. Some, but not all, GR spacetimes have a foliation by maximal spacelike hypersurfaces. If it turns out that our spacetime has such a foliation, then we can always privilege one of the hypersurfaces in the foliation as The Objective Present, and have an eternalist A-theory (= moving spotlight). Or we can add to this that all the hypersurfaces that intersect the forward lightcone of The Objective Present are mere mathematical abstractions, and then have growing block theory. Or we can more radically say that all the hypersurfaces other than The Objective Present are mere mathematical abstractions, and then have presentism.

I think in the literature, people like add further conditions on the privileged foliation, like constant mean curvature. But the philosophical application doesn't need any further conditions.

Given flat spacetime, the existence of a foliation is trivial (just foliate with parallel spacelike hyperplanes).

Of course, all this adds cost by adding degrees of freedom to the theory that are not empirically constrained.