Basic Questions on Special Theory of Relativity

[Sailark]

Hello everyone!

I've been studying the Special Theory of Relativity for a little while on my own, and I've had some difficulty understanding exactly what it is saying about the character of time. I would guess that these are very similar to the sorts of conceptual difficulties that a lot of people encounter in trying to grasp the theory, so I hope that a few of you might know the answer, and that these questions are of some general use or interest.

To just start by presenting what I believe that I understand, it seems like one of the major claims of the Special Theory of Relativity is that there is no such thing as absolute simultaneity. Now, this seems to mean that, for example, if I see two lightning-flashes at the same instant, while you see the one after the other, then it is meaningless to ask whether the two lightning-flashes are "really" simultaneous, or "really" sequential, since there is just no real answer to the question. The reason for that, so far as I can tell, is that there is no such thing as "absolute time," or no single and all-encompassing time, in which all beings and all events are situated, and in which they all have a certain determinate temporal relation to one another (i.e, in which both of the lightning-flashes would be, and in which each would have a certain relation to the other).

If there's anything wrong just in that part, let me know! But, just going forward from there, I find that I have a lot of difficulty in understanding what things really are, or how the two lightning-flashes are really constituted, if my ordinary sense of time is incorrect. For instance, are there two separate and distinct times, in the one of which the lightning-flashes are simultaneous, and in the other of which they're sequential - kind of like a Many Worlds theory, with a multiplicity of similar but distinctly ordered events? Or do the lightning flashes not actually exist in time at all, such that only the appearances of the lightning-flashes are in time, while the things themselves are not? Or, finally, do the lightning flashes exist in a single time, but without having any fixed relations to one another - such that both are "in" time, without being simultaneous or sequential? Or, finally, is there some possibility that I'm overlooking, which explains the character of things? (Or, I guess, is the theory neutral to these sorts of questions, and does it just deny that there is absolute simultaneity, without also saying what sorts of things really exist?)

Finally, just as a broader question, I've often found it difficult to figure out if the Special Theory of Relativity is a theory about what exists, or about what we can know exists? Some presentations seem to suggest that we just can't know that there's such a thing as absolute time, or which frame of reference is "really" at rest, or "really" in motion, since no experiment can prove it - even though one could be the one that's really at rest, and time could be absolute. Is that correct, or am I right in thinking that the theory does say that it's impossible for there to be absolute time, or a single frame of reference that's absolutely at rest or in motion?

I think that's everything that I'm uncertain about, though there may well be errors or assumptions in the questions themselves that I missed. In any event, thank you all for reading this, and hopefully someone knows the answer to these questions :) (and that they're clear enough to be capable of being answered!)

 

[bahamagreen]

The theory of relativity is a self consistent theory about measurements, neither existential nor ontological.

 

[Mister T]

For instance, are there two separate and distinct times, in the one of which the lightning-flashes are simultaneous, and in the other of which they're sequential

This depends on what you mean by sequential. If two events occur in a sequence at one location, then they will occur in that same sequence for all observers. If the two events are separated in space in such a way that a light beam has time to make it from one event to another, then again all observers will agree on their sequence and no one will observe them as simultaneous.

So if two events are simultaneous in one observer's frame, that means that a light beam wouldn't have time to leave one and arrive at the other. These events are said to be causally disconnected in the sense that neither one could have caused the other. Different observers will disagree on the sequence of these events.

Finally, just as a broader question, I've often found it difficult to figure out if the Special Theory of Relativity is a theory about what exists, or about what we can know exists? Some presentations seem to suggest that we just can't know that there's such a thing as absolute time, or which frame of reference is "really" at rest, or "really" in motion, since no experiment can prove it - even though one could be the one that's really at rest, and time could be absolute. Is that correct, or am I right in thinking that the theory does say that it's impossible for there to be absolute time, or a single frame of reference that's absolutely at rest or in motion?

The possibility is there that a preferred reference frame does exist. It's just that in the absence of any way, in principle, to distinguish between it and other frames, what grounds do we have to assume it exists? We may as well propose angels dancing on the heads of pins. One can do so, but with no way in principle to detect them their existence is not a scientific proposition.

And even if such a thing were discovered, it wouldn't negate the predictions of relativity. They have been overwhelmingly confirmed.

 

[Ibix]

Hello everyone!

Welcome to PF.

Now, this seems to mean that, for example, if I see two lightning-flashes at the same instant, while you see the one after the other, then it is meaningless to ask whether the two lightning-flashes are "really" simultaneous, or "really" sequential, since there is just no real answer to the question.

Two exceptions. Two things happening at the same time in the same place are genuinely simultaneous, and all observers will agree on that. Also, two events that are time-like or null separated (the spatial distance between them is less than or equal to c times the time separation) have an order that everyone will agree on.

But, just going forward from there, I find that I have a lot of difficulty in understanding what things really are, or how the two lightning-flashes are really constituted, if my ordinary sense of time is incorrect.

There is no real answer to your questions at our current level of understanding. Several interpretations are possible, so pick the one that is most convenient for understanding what you are trying to do.

The easiest way to visualise what's going on is to draw one space and one time dimension on a piece of paper. This is called a Minkowski diagram - typically time goes up the page and space across it. A lightning flash is an "event" - it happens at a place and a time, so is just a dot on this diagram. Two lightning flashes are two dots. If they are on the same horizontal line, they are simultaneous; if not they happened at different times.

The Lorentz transforms relate the diagrams that two people in relative motion would draw. It's analogous to rotating the grid on a map - everything gets different x and y coordinates, but nothing fundamental changes. You can see this happening here: http://www.ibises.org.uk/Minkowski.html (disclaimer: I wrote it). Click on the grid a couple of times to add events at the same time (on the same horizontal line) then set a boost velocity and click "Boost" to see how the diagram changes (it's not as simple as a rotation).

If you choose to take this picture literally (extended to three dimensions plus time), this is called the "block universe" model. The universe is a non-dynamic 4d solid. It suggests that all the frames are equally real (to address your last question). But you don't have to do so. You can see the universe exactly as we see it - a dynamic 3d object with time being "something else", just as in Newtonian theory. The only thing is, the universe is set up in such a way that you cannot determine whether the three spatial directions you are using match the "real" ones. This interpretation is the "Lorentz Ether Theory".

I personally prefer the block universe for thinking about relativity. But Lorentz Ether is the natural way to implement a numerical simulation. Neither model is right or wrong; neither makes predictions that can be tested. I gather that neither is totally satisfactory when one moves on to general relativity. But they are good ways to visualise what's going on in special relativity.

 

[Dale]

which frame of reference is "really" at rest, or "really" in motion

Usually the word "really" is an indication that the question is philosophical (ontology) rather than scientific. Generally, a scientific theory consists of some mathematical model and a mapping between the math and some experiments. Interpreting different parts of the model as "real" is called an interpretation, and primarily serves as a menmonic device.

I find that I have a lot of difficulty in understanding what things really are, or how the two lightning-flashes are really constituted, if my ordinary sense of time is incorrect.

My preferred approach is as follows: in classical physics we think of time being divided into future and past. In relativistic physics we add one more classification, which is sometimes called "elsewhere". So spacetime is divided up into the future (also called the interior of the future light cone), the past (also called the interior of the past light cone), and elsewhere (also called the exterior of the light cone). All causes are in the past, all effects are in the future, and events in elsewhere can neither be causes nor effects.

 

[Sailark]

Thank you all for your help! I think that I'm starting to get it, but I'll try to re-state my understanding now in my own words, just to see if any errors are still left over.

It sounds like the Special Theory is saying that one observer might see one sequence of events, while another observer might see another; but that, since there's no way to experimentally decide which sequence of events actually took place - or even whether the events did take place in a "temporal order," apart from the order of our observations - then no statement about the "absolute" temporal order of things should be science, except when there is a way to experimentally decide the order (i.e, when one event is the cause of the other, or when all observers would see the same things in the same sequence). Or, in other words, the theory is saying that two lightning-flashes which are separated at a distance really might be simultaneous - but it's just that we have no way of determining whether or not they are. (Or, the rejection of absolute time is "epistemological" or "methodological" in character, and not "ontological" - such that the old Newtonian absolute time and space could exist, but they are merely our beliefs about the world, and not scientifically verifiable hypotheses.)

Just to make an analogy, it sounds it's like saying that, since there is no way to experimentally decide which religion is true (if any at all), then no article of faith should be admitted into science - even though, for all of that, one of those articles might be true (i.e, we aren't positively asserting that no religious belief is correct - just that none of them are verifiable by the scientific method.)

Is that correct, and does that seem to be the right way to think about the character of Special Relativity? If it is, then that would definitely explain a number of my confusions, since I had thought the theory was a lot more "ontological" than "epistemological" in nature!

But, I'll try playing around now with some of the Minkowski space-time diagrams, and the app you wrote, and think some more about how exactly one set of observations or measurements would be translated from one frame of reference into the next. Again though, thank you for all of your help :)

 

[Dale]

I had thought the theory was a lot more "ontological" than "epistemological" in nature!

That is a pretty good way to characterize it, in my opinion. In that same vein, most scientific theories are "epistemological" and the "ontological" parts are primarily in the interpretations.

 

[Mister T]

Or, in other words, the theory is saying that two lightning-flashes which are separated at a distance really might be simultaneous - but it's just that we have no way of determining whether or not they are.

If they are simultaneous to an observer then there is definitely a way to make that determination scientifically. They really are simultaneous. But to other observers there is an equally valid way of determining that they are not simultaneous. So it's the notion of absolute simultaneity that must be abandoned.

(Or, the rejection of absolute time is "epistemological" or "methodological" in character, and not "ontological" - such that the old Newtonian absolute time and space could exist, but they are merely our beliefs about the world, and not scientifically verifiable hypotheses.)

There is no way to resurrect the Newtonian notion of absolute time. There is an overwhelming amount of experimental evidence that tells us it's just plain wrong. Einstein got it right.

 

[Sailark]

There is no way to resurrect the Newtonian notion of absolute time. There is an overwhelming amount of experimental evidence that tells us it's just plain wrong. Einstein got it right.

Do you mean that it's impossible for there to be a single time in which all events and all things have a place, or that it's impossible to know that such a thing exists, and that it is necessary to avoid reference to it, if we are to speak with scientific precision? I had thought that you and earlier posters had been expressing the latter thought - for instance, when you had suggested that there might be a preferred frame of reference, which I had taken to be equivalent to saying that there might be an absolute time and space (i.e, the time or space of that frame of reference) - but this post seems to suggest the latter.

I am also probably not quite clear on what "absolute time" or "absolute space" means (I've never seen them defined), so that might be part of my confusion :) I've been taken each just to mean "a single time or space, in which all things are members, and in which all things have a relation to one another" as contrasted with no time or space, or with many times and spaces, or with a single time or space in which all things belong, but in which not all of the members have some relation.

 

[Mister T]

Do you mean that it's impossible for there to be a single time in which all events and all things have a place,

Correct. Such a thing is clearly not a possibility in Nature.

I had thought that you and earlier posters had been expressing the latter thought - for instance, when you had suggested that there might be a preferred frame of reference,

It makes no difference to any experiment that's ever been done. That doesn't mean that someone might find a way to do such a thing in the future. But if someone does accomplish that, our current understanding of relativity will not be overturned. It will just reveal to us more about its limits of validity.

I am also probably not quite clear on what "absolute time" or "absolute space" means (I've never seen them defined), so that might be part of my confusion :)

In my experience you have to understand what relativity tells us about the nature of space and time before those notions can even make sense.

Perhaps the most dramatic example is what, in an unfortunate choice of terminology, has come to be known as the twin paradox. Two entities are at the same place at the same time, something that's absolute in the sense that all observers will agree upon it. Then they are at the same place at the same time again, later. This is an example of a pair of events that have a definite sequence that all observers will agree upon. The amount of time that elapses between the two events is different for the two entities. Also something that all observers will agree upon. This is an effect that must be considered, for example, every time a GPS satellite makes an orbit around Earth, or a subatomic particle completes a lap in a particle accelerator. These are events that occur thousands of times every day.

 

[pervect]

If there's anything wrong just in that part, let me know!

I didn't spot anythign obviously wrong, it looks good so far.

But, just going forward from there, I find that I have a lot of difficulty in understanding what things really are, or how the two lightning-flashes are really constituted, if my ordinary sense of time is incorrect.

"Real" is a philosophical concept. You have a lot of freedom in what you regard as "real", as long as your notion of "reality" matches observation. So if you understand the notion of observers and their coordinates, then as long as you can calculate their observations, you don't need to know what "really" hapens. If you don't understand the notion of observers and coordinates, the discussion tends to get rather vague and unfocussed, I'm afraid I can't say much except that it would be best to resolve those issues first, then go back to relativity when there is enough shared understanding of the framework of coordinates.

One of the issues here is the observer dependence - you have to specify a lot of facts about observer A and observer B to state what they measure. While it doesn't necessarily answer the question of what "really" happens, one might ask if it's possible to express what "really" happens in terms that don't depend so much on the observer. That can be done.

What's independent of the observer in special relativity is the Lorentz interval. It's a combination of spatial distances and temporal intervals, the square of the Lorentz interval is the difference between the square of the spatial interval between two events, and the temporal interval between two events multipled by the speed of light squared. Typically this will be written as $c^2 dt^2 - dx^2 - dy^2 - dz^2$ or $dx^2 + dy^2 + dz^2 - c^2 dt^2$, depending on the sign convention. The first form

This is rather similar to the pythagorean theorem, except for a change in sign.

Now there is one tricky point here. If you have two events, A and B, and the Lorentz interval between them, that's the only observer-independent thing that you can say. And if a light beam travels between event A and event B, the Lorentz interval is zero.

This is all well and good, but one might well ask - "If I see two three light flashes, A, B, and C, where A is co-located with me, and B and C are distant events, I don't know anything about whether B is near or far, nor C. One of the events might be next door, the other might be a supernova in the Andromeda galaxy.

A single simple obervation of single light flashes just won't tell you which event is near and which event is distant. You can't tell from that informationm all you can say is that the light flashes occurred at the same proper time. You'll need multiple observations at distant points to be able to figure out via various methods (triangulation, differential propagation delays, etc) which event was distant and which event was near. The usual way of computing all this needs a fairly elaborate framework, the framework of space and time and their coordinates that I mentioned earier, one that each observer creates. And this framework is observer dependent.

While knowing the Lorentz interval between any two events doesn't fully describe "reality", the interesting point is that knowing the Lorentz interval between ALL events (any pair that you specify) does fullly describe everything you can calculate or observe, which we'll regard as "reality". So knowing the Lorentz interval is really sufficient, but if you know all the Lorentz intervals you can get a complete picture.

It's helpful to actually go through and figure out how you would measure the distance from yourself to a distant light flash if you know the Lorentz interval between all possible points. You start by creating a chain of observers on the route between you and the light flash, and imagining thee observers are at rest relative to one anotyher. Operationally, you can tell that they are at rest because when they are, the round-trip time of light flashes between each pair of observers is constant. So you can define this notion of "at rest" and this chain of observers by known all the Lorentz intervals, because the round-trip light time is just the sum of the Lorentz interval "there" and the interval "back".

Once you have this chain of observers, the basic approach to computing the distance is that when you specify a particular notion of simultaneity to "synchronize the clocks" of all the observers in the chain, you can determine the distance by adding up the observer-independent Lorentz intervals along the chain that all happen "at the same time" by your notion of simultaneity. By the way the notion of "at rest" was specified, these Lorentz intervals will not vary with time. You can regard this process as a radar measurement of distance between each pair of observers in the chain if you like.

But you do need a notion of simultaneity to accomplish this. Without it, you have a chain of observers, but you need a way of reducing the Lorentz interval between two observers into a distance, and this process requires adopting a simultaneity convention.

 

[PAllen]

Correct. Such a thing is clearly not a possibility in Nature.

Not quite. It is easy to posit that there exists absolute time and simultaneity in SR as long as you also posit that they are intrinsically undetectable. You can neither prove nor disprove the belief that Nature has an absolute time and simultaneity, only that it is undetectable. I may find such a concept superfluous, and inelegant, but it is possible.