Clocks Vanishing into Thin Air - Gravitational Time Dilation

[Buckethead]

TL;DR Summary

Are we really looking into the past/future in both SR and GR?

With regard to relativity of simultaneity and the "block" universe and reflecting on the notion of skewed time slices associated with frames moving relative to each other, one observer sees one event a distance away (parallel to the direction of motion) occurring before another event a distance away in the opposite direction while another observer see them occurring simultaneously. In other words, one observer is witnessing an event before it occurs for the other observer and also after it occurs. If we are accepting a block universe, then we can say one observer is literally seeing into the past and into the future relative to the other observer.

I think from this one can say the two events actually occur at the same time for both observers, it's just that one observer is observing a past event and one a future event, therefore the events appear to take place at different times even if though they are not. Certainly the popular notion of skewed time slices indicate this. However, this is not the accepted conclusion. Instead it is accepted that the two events "actually" occur at different times. Why is this? Just convention?

My thoughts moved on to looking at this in a gravitational field. Looking at a clock at the base of a tall building from where we stand at the top floor, one sees a clock moving slowly relative to us. If GR is derived from SR, and adjusting for the time it takes for light to reach us, then is it correct to say the clock is being viewed (literally) as it was in the past, and is ever receding further and further into the past as time goes on due to the fact that it is simply moving through the block universe at a slower rate than we are? After all, the hands are moving slower, it must be moving through the "time slices" more slowly. Isn't this logical?

This being the case (if indeed it is), then there will never be a time in which the clock is in our present. The bizarre part then comes when we take the elevator down to the clock. When we get there, we are no longer seeing into the past as we are at the same gravitational potential as the clock, but the clock is still in the past! Afterall, the clock hands prove this. This means we should not even be able to see the clock. It should simply vanish into thin air. Clearly, it does not. Where am I going wrong? Thanks.

 

[PeroK]

There's nothing special about a clock: it's just a lump of matter like everything else. I'd be worried about what keeps the building standing, if the foundations have vanished into the past!

 

[PeterDonis]

one observer sees one event a distance away (parallel to the direction of motion) occurring before another event a distance away in the opposite direction while another observer see them occurring simultaneously.

You should not use the word "simultaneously" here. It is confusing you. What you should say is that one observer receives light signals from the two events at different events on their worldline, while the other observer receives light signals from the two events at the same event on their worldline.

In other words, one observer is witnessing an event before it occurs for the other observer and also after it occurs.

No. You have confused yourself into a wrong statement, and most of the rest of your post just compounds the error.

is it correct to say the clock is being viewed (literally) as it was in the past

Any light signal you receive from any object spatially separated from you is giving you information about how that object was in the past. That is an obvious consequence of the fact that the speed of light is finite.

and is ever receding further and further into the past as time goes on due to the fact that it is simply moving through the block universe at a slower rate than we are?

No. This is wrong. You have confused yourself again.

Where am I going wrong?

You appear to have an incorrect understanding of spacetime geometry. I suggest drawing some spacetime diagrams. That should help you at least to see that the things you are saying don't make sense, because you will find that it is impossible to describe consistently how the things you are saying would work in terms of a spacetime diagram.

 

[Buckethead]

You should not use the word "simultaneously" here. It is confusing you. What you should say is that one observer receives light signals from the two events at different events on their worldline, while the other observer receives light signals from the two events at the same event on their worldline.

"...at different events, ...at the same event" Was this a typo. I don't under stand what you mean here.

 

[Ibix]

I think that you are trying to wedge the "presentist" viewpoint, where things exist now and how they were in the past is gone and how they will exist in the future isn't yet written, into the 4d spacetime of relativity. That won't really work because "now" is so ill-defined in relativity. Relativity, in its usual interpretation, treats a clock (or anything else) as a 4d worldtube, and its past, present and future all "still" exist in some sense. In other words, we take those spacetime diagrams deadly seriously, as a slice through spacetime (or the best we can do on a Euclidean plane), whereas a similar diagram (a displacement-time graph) in Newtonian physics is typically regarded as a more abstract representation.

 

[Buckethead]

There's nothing special about a clock: it's just a lump of matter like everything else. I'd be worried about what keeps the building standing, if the foundations have vanished into the past!

Ha! crumbling foundations. I used a clock because it has hands that can be used to indicate its time dilation.

 

[Buckethead]

I think that you are trying to wedge the "presentist" viewpoint, where things exist now and how they were in the past is gone and how they will exist in the future isn't yet written, into the 4d spacetime of relativity. That won't really work because "now" is so ill-defined in relativity. Relativity, in its usual interpretation, treats a clock (or anything else) as a 4d worldtube, and its past, present and future all "still" exist in some sense. In other words, we take those spacetime diagrams deadly seriously, as a slice through spacetime (or the best we can do on a Euclidean plane), whereas a similar diagram (a displacement-time graph) in Newtonian physics is typically regarded as a more abstract representation.

Interesting. But I mentioned viewing into the past and into the future as if they existed. Isn't this eternalism? Are you saying that there is no present in eternalism?

 

[Ibix]

Interesting. But I mentioned viewing into the past and into the future as if they existed. Isn't this eternalism?

In that case, the same argument applies to the clock. Its past, present and future exist, so it won't be "not there yet" when you go down to the basement. So the problem you describe doesn't arise.

You don't seem to think that, though, which suggests to me that you are trying to wedge a presentist interpretation of the clock into an eternalist universe, which doesn't work.

 

[PeterDonis]

"...at different events, ...at the same event" Was this a typo. I don't under stand what you mean here.

Events are points in spacetime. Events on some observer's worldline are points that lie on a particular curve, the worldline.

This is very basic terminology in relativity. If you are not familiar with it, I would strongly suggest taking some time to improve your background in relativity.

 

[Buckethead]

In that case, the same argument applies to the clock. Its past, present and future exist, so it won't be "not there yet" when you go down to the basement. So the problem you describe doesn't arise.

Not exactly. The clock we see will be the clock from the past (its hands indicate this) and since we are in the same gravitational field strength, we should not be able to see this "past" clock anymore (like we could at the top of the building), but we do. We are not seeing the clock in the same time slice as we are currently in otherwise we would see its hands match those on our wrist watch as it would be in our present.

 

[Ibix]

Not exactly. The clock we see will be the clock from the past (its hands indicate this) and since we are in the same gravitational field strength, we should not be able to see this "past" clock anymore (like we could at the top of the building), but we do. We are not seeing the clock in the same time slice as we are currently in otherwise we would see its hands match those on our wrist watch as it would be in our present.

No. That's completely wrong. The scenario you describe is just a twin paradox with some gravitational complications. The clock and your wristwatch show different times because they took different "length" paths through spacetime. The time difference is just as real.

I can't illustrate this right now - will try to do so later.

 

[PeterDonis]

The clock we see will be the clock from the past (its hands indicate this)

I assume this is because (a) the clock is spatially separated from us, and (b) we synchronized our clock with this clock in the past?

since we are in the same gravitational field strength

We are? What scenario are you talking about? Weren't you talking about us being much higher up in the gravitational field than the clock?

We are not seeing the clock in the same time slice as we are currently in otherwise we would see its hands match those on our wrist watch as it would be in our present.

It is impossible to see any object that is spatially separated from you "in the same time slice" in this sense. Light travels at a finite speed. You do not appear to have grasped the implications of that simple fact.

 

[russ_watters]

Not exactly. The clock we see will be the clock from the past (its hands indicate this) and since we are in the same gravitational field strength, we should not be able to see this "past" clock anymore (like we could at the top of the building), but we do. We are not seeing the clock in the same time slice as we are currently in otherwise we would see its hands match those on our wrist watch as it would be in our present.

That's not how it works. What makes it a "present clock" is the fact that you are standing next to it. The time that it reads does not describe some location on a universal timeline (of which there is no such thing).

 

[Buckethead]

Events are points in spacetime. Events on some observer's worldline are points that lie on a particular curve, the worldline.

This is very basic terminology in relativity. If you are not familiar with it, I would strongly suggest taking some time to improve your background in relativity.

Got it. Yes, I'm familiar (sort of) with events being locations in spacetime. And I also get (sort of) that for moving observers, the coordinate system changes so that one observer sees simultaneous events while another does not. But it does not address the question of whether we are actually seeing something in the past or future when moving relatively. After all, changing coordinate systems does not change reality.

You should not use the word "simultaneously" here. It is confusing you. What you should say is that one observer receives light signals from the two events at different events on their worldline, while the other observer receives light signals from the two events at the same event on their worldline.

OK, I think I see what you are saying here. For one observer events happen at different times, right now, and for the other they occur at the same time, right now. No going into the past or future. But then it does not really say anything about the reality of a block universe does it?

No. You have confused yourself into a wrong statement, and most of the rest of your post just compounds the error.

It comes down to what the past and future really are. Do they exist or don't they? is the past and future instead just points on a timeline and have no real existence?

 

[Buckethead]

I assume this is because (a) the clock is spatially separated from us, and (b) we synchronized our clock with this clock in the past?

We are? What scenario are you talking about? Weren't you talking about us being much higher up in the gravitational field than the clock?

You missed the part about going down the elevator to match up spatially. So no to a) and yes to b)

It is impossible to see any object that is spatially separated from you "in the same time slice" in this sense. Light travels at a finite speed. You do not appear to have grasped the implications of that simple fact.

Distance is now zero (after the elevator ride) and the gravitation is the same for both the observer and the clock so the time slice should now be the same. I do have an understanding of the finite speed of time and mentioned that in italics when I was talking about the earlier time of when the observer was at the top of the building. But after the observer comes down to the clock, the clock indicates by its hands it is in the past.

The reason I say in the past just to be clear is because there is one clock, that exists from an earlier time slice to a later time slice. If you look at the time slices, you see the hands in different positions (clearly indicating what time slice they are in) So if you see a clock and the hands show a different time than that on your watch (assuming you synced to start) then this clock must be in the past.

 

[PeterDonis]

for moving observers, the coordinate system changes

"Moving" has no absolute meaning. A correct statement would be that, in flat spacetime, the "natural" coordinate system for an inertial observer depends on that observer's 4-velocity--heuristically, "which direction in spacetime" their worldline is pointing.

it does not address the question of whether we are actually seeing something in the past or future when moving relatively.

The question in itself is meaningless. You don't "see something in the past or future". You just see something. Light signals go from that something to you. Those light signals also have worldlines: there are particular curves in spacetime that describe the path through spacetime that those light signals take from the something to you. Those paths through spacetime are independent of any choice of coordinates, and you can describe them without ever having to even talk about "past" or "future" except in the simple and obvious sense of in which order the signals are emitted from the source and received by the receiver.

For one observer events happen at different times, right now, and for the other they occur at the same time, right now.

No. "Right now" is a meaningless phrase here. You'll notice that I did not use it at all. There is a reason for that.

It comes down to what the past and future really are. Do they exist or don't they?

These questions are meaningless without a clear definition of what the terms "past" and "future" refer to. There are multiple possible concepts that those words could refer to. You need to first clearly understand what those concepts are, and then clearly understand what the implications are of different claims about whether one or the other of those concepts "exist".

 

[Dale]

Summary:: Are we really looking into the past/future in both SR and GR?

In other words, one observer is witnessing an event before it occurs for the other observer and also after it occurs. If we are accepting a block universe, then we can say one observer is literally seeing into the past and into the future relative to the other observer.

For me, the words “witnessing” and “literally seeing” would refer to the past light cone. Not to simultaneity.

All frames in whatever state of motion agree on the past light cone. You can only literally see (meaning using your actual physical eyes) information from the past light cone.

As I look at my toes I do not literally see them as they are now. I see them as they were 6 ns ago. Now, if my toes are moving at a Chuck Norris snap-kick speed, roughly 0.9 c, then I will still literally see them as they were 6 ns ago.

Now, my toes and I may disagree about the order of my kick and Chuck’s punch. But I will never literally see the future, only the past. And all frames will agree.

 

[Buckethead]

That's not how it works. What makes it a "present clock" is the fact that you are standing next to it. The time that it reads does not describe some location on a universal timeline (of which there is no such thing).

The block universe description indicates that a clock (for example) will extend in the time dimension and at any given slice in that time dimension, the clock face will indicate different hand positions. If we are looking at a clock that has a different hand position from our watch, we are seeing the clock as it existed in the past, not as it exists in our time slice. A timeline (not universal) exists if the description of reality as being a block universe exists.

One thing I want to stress is that if the block universe is a good description of reality, then a clockface indicates the exact position in time in that block universe. If it differs from what your hand watch says (after syncing of course), then it is in a different time slice. But if we are standing next to it, it can't be otherwise the clock face would match ours.

I think the part I'm missing is the idea that "events" as indicated on a worldline, are not related to actual time as in past and future (as defined by a block universe), but are just part of a eternal "present". But I can't really make sense of that.

 

[PeterDonis]

You missed the part about going down the elevator to match up spatially.

Ok, then if we are now at the same spatial location as the clock, and moving along with it, then our clock is ticking at the same rate as that clock. So what is the problem?

Here is what you said in the OP:

The bizarre part then comes when we take the elevator down to the clock. When we get there, we are no longer seeing into the past as we are at the same gravitational potential as the clock, but the clock is still in the past! Afterall, the clock hands prove this. This means we should not even be able to see the clock. It should simply vanish into thin air. Clearly, it does not. Where am I going wrong?

Your mistake here is thinking that the clock's hands tell you it is "in the past" in some absolute sense, even when you are standing right next to it. That's wrong.

As I have said several times now, the reason why light signals you see from a distant object show you how that object was "in the past" is that light travels with a finite speed. But if you are right next to the object, that issue goes away: the light is not traveling any distance (or at any rate a negligible distance), so you are seeing the object in your present, not "in the past". There is no such thing as an object "staying in the past" when you move right next to it.

What the clock's hands are telling you is how much proper time has elapsed along the clock's worldline. The fact that the clock's hands read an earlier time than your wristwatch when you take the elevator down to be right next to the clock just means less proper time elapsed along the clock's worldline than along yours. In geometric terms, the arc length along the clock's worldline was shorter than the arc length along yours. This is just geometry. There's no mystery or inconsistency about it at all. You just have to understand that there is no absolute time, so the clock's hands aren't telling you "where it is in time" in any absolute sense. They are just telling you how much arc length there was along its worldline.

 

[PeterDonis]

The block universe description indicates that a clock (for example) will extend in the time dimension and at any given slice in that time dimension, the clock face will indicate different hand positions.

No. The clock's extension "in the time dimension" is just a single curve. There are no "slices". There are just points along the curve. At each point on the curve, the clock indicates a different time. (To really do this right, the clock should have a date indicated on its face as well as the hands, so its indicated time never repeats.)

If we are looking at a clock that has a different hand position from our watch, we are seeing the clock as it existed in the past, not as it exists in our time slice.

No. There are no time slices. If we are looking at a clock that is distant from us, we are seeing its hands as they were at the point on the clock's worldline at which the light signals we are receiving were emitted. The time on our own wristwatch when we see the distant clock is whatever our wristwatch reads at the point on our own worldline when we receive the light signals. There are no "time slices" anywhere. There are just worldlines, points, and light signals. "Time slices" are an artifact of particular coordinate systems, and, as you have already agreed, such coordinate artifacts have no physical meaning. So any reasoning that uses "time slices" is simply wrong as a matter of physics.

One thing I want to stress is that if the block universe is a good description of reality, then a clockface indicates the exact position in time in that block universe.

Wrong. There is no such thing as "position in time" in the block universe (or in any interpretation of SR).

If it differs from what your hand watch says (after syncing of course), then it is in a different time slice.

Wrong. There are no "time slices". See above.

But if we are standing next to it, it can't be otherwise the clock face would match ours.

Wrong. See above.

I think the part I'm missing is the idea that "events" as indicated on a worldline, are not related to actual time as in past and future (as defined by a block universe), but are just part of a eternal "present".

Wrong.

But I can't really make sense of that.

And you shouldn't, because it is wrong.

Basically, I think you need to unlearn everything you think you know about SR and start from scratch. Pretty much everything you are saying is wrong.

 

[Buckethead]

Your mistake here is thinking that the clock's hands tell you it is "in the past" in some absolute sense, even when you are standing right next to it. That's wrong.

This assumption on my part comes directly from the idea that the block universe shows that a clock existing for some stretch of time will have its hands in different positions at different time slices. If a clock and my wristwatch agree on the time, we are in the same timeslice. If for whatever reason our clocks do not match as is the case if I go up an elevator, then back down to meet up with the clock, this indicates I am looking at the clock as it existed at an earlier time slice. Now clearly it seems the block universe as depicted in popular media is NOT an accurate representation of reality otherwise the clock I am observing when meeting up again would have to be in the past. Therefore, I need a better picture of what a "block universe" actually is.

As I have said several times now, the reason why light signals you see from a distant object show you how that object was "in the past" is that light travels with a finite speed. But if you are right next to the object, that issue goes away: the light is not traveling any distance (or at any rate a negligible distance), so you are seeing the object in your present, not "in the past". There is no such thing as an object "staying in the past" when you move right next to it.

Of course I understand the concept of seeing a distant object as it was in the past due to light speed, so you can leave that out of the discussion. The issue I am addressing is strictly why the clock that is next to you that has a different reading than your watch is not in the past if according to the block universe depiction, that clock matches up with a clock at an earlier time slice, not the current time slice. Just to be clear, I am not saying the clock is in the past, (otherwise it would have vanished as per my OP), I'm just asking why is the block universe represented as showing definite times at definite slices on the one hand, when clearly we can have a clock showing an earlier time than our watch when we are standing next to it.

What the clock's hands are telling you is how much proper time has elapsed along the clock's worldline. The fact that the clock's hands read an earlier time than your wristwatch when you take the elevator down to be right next to the clock just means less proper time elapsed along the clock's worldline than along yours. In geometric terms, the arc length along the clock's worldline was shorter than the arc length along yours. This is just geometry. There's no mystery or inconsistency about it at all. You just have to understand that there is no absolute time, so the clock's hands aren't telling you "where it is in time" in any absolute sense. They are just telling you how much arc length there was along its worldline.

Well put. And I subscribe to it. But this does contridict the block universe theory as depicted in popular press. So what does the block universe actually look like? How can it be shown so that it doesn't contridict what you just said?

 

[Ibix]

If a clock and my wristwatch agree on the time, we are in the same timeslice.

No. Forget this. It is wrong and nonsensical.

 

[Dale]

But this does contridict the block universe theory as depicted in popular press.

No it certainly doesn’t.

If you have some threads embedded in a block of amber there is absolutely no contradiction in the fact that some threads may have different lengths than others. The claim that the different lengths contradict the block is absurd.

 

[Buckethead]

No it certainly doesn’t.

If you have some threads embedded in a block of amber there is absolutely no contradiction in the fact that some threads may have different lengths than others. The claim that the different lengths contradict the block is absurd.

OK, I'll dump the time slice depiction and give some thought to the threads idea. I need to think about what this means.

 

[PeterDonis]

This assumption on my part comes directly from the idea that the block universe shows that a clock existing for some stretch of time will have its hands in different positions at different time slices.

You are not reading carefully. There is no such thing as time slices. You will continue to draw mistaken conclusions until you banish the term "time slices" from your understanding.

Of course I understand the concept of seeing a distant object as it was in the past due to light speed, so you can leave that out of the discussion.

No, we can't leave it out of the discussion, because it is an essential part of forming a correct understanding of how spacetime in SR works. And if you don't have a correct understanding of how spacetime in SR works, you cannot possibly have a correct understanding of how the block universe, or any other interpretation of SR, works.

this does contridict the block universe theory as depicted in popular press.

I don't know what you mean by "the popular press", but you have been here long enough now to know that you should be learning science from textbooks and peer-reviewed papers, not pop science books, articles, videos, or whatever, and that "popular press" is not a valid reference to be giving in any PF discussion.

 

[PeterDonis]

what does the block universe actually look like?

A four-dimensional spacetime geometry. This geometry has timelike curves in it that are the worldlines of observers, and null curves in it that are the worldlines of light signals. These curves intersect at particular points (events) which mark the emission or reception of light signals by objects or observers. The geometric relationships between all of these curves and events are invariant, just as they are in ordinary Euclidean geometry; the only difference in spacetime is that the geometry is Minkowskian.

 

[Dale]

OK, I'll dump the time slice depiction and give some thought to the threads idea. I need to think about what this means.

Think of threads embedded in amber. Some threads are straight, which we call inertial, some threads are not. The length along any thread is marked. At any point on any thread you can cut the amber perpendicularly to the thread. Not all threads will be perpendicular to that cut, and there is nothing special about that cut other than the fact that it was perpendicular to one thread at that one point. That cut will intersect different threads at different lengths. The fact that different threads have different lengths marked at that cut is a bit of trivia that poses no existential conundrum for the threads nor for the amber.

There is no amber, but there are threads.

 

[Grasshopper]

Not exactly. The clock we see will be the clock from the past (its hands indicate this) and since we are in the same gravitational field strength, we should not be able to see this "past" clock anymore (like we could at the top of the building), but we do. We are not seeing the clock in the same time slice as we are currently in otherwise we would see its hands match those on our wrist watch as it would be in our present.

I would say, if you’re going to interpret looking at the clock as looking at the past, that the CLOCK is not in the past, but rather the EVENT of the clock ticking at a particular tick-mark as in the past. When you move to that clock, you are not seeing that EVENT because that event is in the past.