# Shape of Spacetime: Exploring Relativity & Simultaneity

• B
• NoahsArk
Just like a map that doesn't show all of the streets and neighborhoods is still useful for navigation, a model that doesn't include all of the details is still useful for understanding a phenomenon.f

#### NoahsArk

Gold Member
It's been a couple of years since I've posted here, and am trying to get back into learning SR. I wanted to start with a general question: You often hear the phrase "we are moving through time". I've also seen space-time described many times as like a block. Another way I've seen it described is like a group of photographs of each moment stacked on top of one another. A speaker on a NOVA program said "it's like seeing the whole movie at once. Firstly, is it true that space-time is a block where all moments exist at once? Also, based on what I remember, relativity of simultaneity determines which part of the block we are in and in what order the "photographs" are stacked up for us. Is this correct? Regarding the phrase we are moving through space-time, are we really moving through it? Or, is time moving? I think we all feel subjectively that it is time that is moving. For example, when we are sitting still, we don't feel like we are moving through anything. Rather we feel all the clocks around us moving.

is it true that space-time is a block where all moments exist at once?

This is a common viewpoint, but it's really a question of philosophy or metaphysics, not physics. There is no way to test it by experiment.

relativity of simultaneity determines which part of the block we are in and in what order the "photographs" are stacked up for us

Not really. It determines the "angle" at which the photographs (the 3-d "slices" out of the 4-d block) are "cut".

Regarding the phrase we are moving through space-time, are we really moving through it? Or, is time moving?

Again, this is not testable by experiment, so it's not really a question of physics.

I think we all feel subjectively that it is time that is moving

Whether or not this is true (I'm not sure it is), subjective feelings are not, in themselves, evidence for one viewpoint vs. another being "really" true.

pinball1970
This is a common viewpoint, but it's really a question of philosophy or metaphysics, not physics. There is no way to test it by experiment.

Does it at least make sense to describe it that way to be able to better visualize it- just like we can describe phenomenon with a line on an X-Y graph?

Firstly, is it true that space-time is a block where all moments exist at once?

When scientists work on problems, they often set up a model where the position of objects is tracked in both space and time. One of the key features of this model is that once you place objects in your model, then their position in spacetime is determined for the entirety of the past and the future. Or would be if we could place every object in existence into our model and perform the infinite number of calculations to find their positions in the past and future. So if we take our model and try to say that it accurately represents reality, then every point in space and time is tracked by the model. You could say that 'all moments exist at once', but that's prone to cause misunderstandings, as this thread demonstrates. They exist simultaneously as quantities in our model, but that's it. Anything beyond this is mostly philosophy.

Another way I've seen it described is like a group of photographs of each moment stacked on top of one another.

If you take the previous model and look at small time-steps, then you get 'slices' of spacetime. There's no physical significance to this. The pattern of holes in a block of swiss cheese are unchanged regardless of whether or not you cut it up into many slices.

Also, based on what I remember, relativity of simultaneity determines which part of the block we are in and in what order the "photographs" are stacked up for us.

If I understand things correctly, if you and I had two identical blocks of cheese, I might choose to make nice, even slices in mine, whereas you might choose to make your slices by cutting at an angle. Thus each of our slices would be different, but the pattern of holes in the block remains unchanged.

Regarding the phrase we are moving through space-time, are we really moving through it? Or, is time moving? I think we all feel subjectively that it is time that is moving. For example, when we are sitting still, we don't feel like we are moving through anything. Rather we feel all the clocks around us moving.

Yes, we are moving through it in the sense that in our model of spacetime our time variable continues to change.

Does it at least make sense to describe it that way to be able to better visualize it

As an aid to visualization, sure, you can think about it this way. It's a model, and models can be very helpful in making good predictions and understanding the implications of a theory. You just have to be careful not to start making claims about "how things really are" based on a model. One version of the saying goes like this: "All models are wrong but some are useful".

Grinkle
Does it at least make sense to describe it that way to be able to better visualize it- just like we can describe phenomenon with a line on an X-Y graph?

We see line-shaped clouds or contrails produced by jet plane engines. Somewhat like contrails everything in spacetime is expressed as a line, not a point. Things survive in chronological changes and form individual lines in spacetime. They are called world lines. The points in spacetime represent not THINGS but EVENTS in definite places and definite times.

Thank you for the responses.

This question may be because I don't have a solid enough understanding of SR, but can't we actually deduce that space time is a block? I was thinking yesterday about this example: if I am staionary between two points A and B whose clocks are synchronized in my frame of reference, as soon as I start excellerating towards B, B's clocks will have elapsed more tome then A's. All I need to do is choose how fast I want to go and I can reach any future time at B. For this to be possible, doesn't it have to be the case that all future times for B already exist?

No. It's far and away the easiest interpretation of relativity but it is not the only one. Lorentz Ether Theory is another - essentially it's SR with the added assumption that one frame is actually real, and all others are in some sense not real. The chosen frame is not detectable, so this largely fell by the wayside in favour of the 4d block universe interpretation. But neither interpretation is wrong or right - they're just a visualisation you choose to put on top of the maths. Most people seem to think the block universe is the easier interpretation once they've been introduced, to the point that it's usually treated as The Truth. But you can use whichever one works for you.

if I am staionary between two points A and B whose clocks are synchronized in my frame of reference, as soon as I start excellerating towards B, B's clocks will have elapsed more tome then A's.

No, both clocks will appear to tick at the same rate for you (after accounting for the fact that you're moving towards B but away from A).

All I need to do is choose how fast I want to go and I can reach any future time at B. For this to be possible, doesn't it have to be the case that all future times for B already exist?

Why would that be necessary?

if I am staionary between two points A and B whose clocks are synchronized in my frame of reference, as soon as I start excellerating towards B, B's clocks will have elapsed more tome then A's.
No, both clocks will appear to tick at the same rate for you (after accounting for the fact that you're moving towards B but away from A).
Worth noting that the clocks do tick at the same rate, but are offset from each other in a frame where they are moving. In fact clock B is behind clock A. It's also worth noting that if you accelerate you are in a non-inertial frame, and you need to define quite carefully what you mean by "as soon as I start". There isn't a naive answer.

Drakkith
Lorentz Ether Theory is another - essentially it's SR with the added assumption that one frame is actually real, and all others are in some sense not real.

Interesting. What does it mean that in some sense they aren't real?

I did not mean that when I start moving to point B, that B's clock begins ticking at a different rate. I only meant that if, when I was stationary between the two points, both A's and B's clocks showed the same time, then once I start moving their clocks will have different times. I am assuming that I was stationary, and then began moving at a constant speed (the acceleration was just the part when I went from being at rest to moving).

Also, if I start moving towards B, then it will mean that both A and B are moving past me where A's clocks are leading. Doesn't that mean that A's clocks will be lagging behind B's?

I just read the article "The Block Universe". Although I can't say I understood all of it, it was interesting. I did not know that the shape/nature of space-time is something being actively discussed in the science world, or that there were alternate theories to the block universe one. Peter, what does the second premise (that you said is not necessarily true), that "all observers’ 3D worlds are real at every event", mean? Just for the purpose of understanding the argument, does it mean that even if, at a given time, a certain event hasn't occurred in my frame of reference, but it has occurred in another frame of reference, it is still real in my frame?

Is it possible that we will one day have definite answers about this? Is it a matter of having more observations/ more accurate tools in order to know?

Why would that be necessary?

It's hard to say. If you can get to a point in space, then it means that point already existed. Similarly, it seems if you can get to a point in time, then it already existed. In physical space, the faster you travel, then the faster you can get to another point. If I am understanding it correctly, because of relativity of simultaneity, you can also reach other points in time, and the faster you go, the more distant future points you can reach. If B's clocks to me read 12am on September 19, 2018 when I am stationary with respect to the clocks, won't they read some future time to me the instant I start moving?

It's hard to say. If you can get to a point in space, then it means that point already existed. Similarly, it seems if you can get to a point in time, then it already existed.

But why would this need to be true? We already know time is 'special' in certain ways. And our usual definition of 'existence' already excludes things that occupy future points in time, but not current points. Why would we need to change our definition? But I guess this is why it's an interpretation of a model and nothing more. It doesn't have an effect on our calculations or how we use the model, so I choose to ignore it.

If I am understanding it correctly, because of relativity of simultaneity, you can also reach other points in time, and the faster you go, the more distant future points you can reach. If B's clocks to me read 12am on September 19, 2018 when I am stationary with respect to the clocks, won't they read some future time to me the instant I start moving?

No, the instant you start moving the clock will still read 12 am. Or you could say that it reads an infinitesimally small amount past 12 am. Either way the result is the same. If you are moving, then the rate at which time passes for B will be slower for you than if you are stationary with respect to B. But there are no sudden jumps as you move around. Everything is a continual process, just with different rates depending on your relative motion.

if I am staionary between two points A and B whose clocks are synchronized in my frame of reference, as soon as I start excellerating towards B, B's clocks will have elapsed more tome then A's.

This doesn't sound right to me. I don't see how your motion relative to those clocks can have any effect on the readings on those clocks. Clocks keep proper time, and proper time is a relativistic invariant.

All I need to do is choose how fast I want to go and I can reach any future time at B.

You can't go faster than ##c## so there are a bunch of events happening at B that you can't possibly be present for. Also, claiming those events are in B's future is peculiar because for some observers your launch is an event that occurs after those events at B. Your launch is an event that has a spacelike separation from some events that occur at B.

what does the second premise (that you said is not necessarily true), that "all observers’ 3D worlds are real at every event", mean?

This is explained in the article. Is there a particular part of the explanation that you have questions about?

does it mean that even if, at a given time, a certain event hasn't occurred in my frame of reference, but it has occurred in another frame of reference, it is still real in my frame?

Events occur in all frames of reference. The only difference is what coordinates get assigned to them.

I would like to add something to the discussion if i may.

Firstly, is it true that space-time is a block where all moments exist at once?

Its very strange sentence. It suggests to me, that there is some time outside of time so that you can say all time happened in single moment of some another time.

Does it at least make sense to describe it that way to be able to better visualize it- just like we can describe phenomenon with a line on an X-Y graph?

I would just say spacetime is some kind of block that puts time and space together into single entity. I don't see how saying that this single entity exists "at once" helps for visualization. Its like saying all sides of square exists at once. Well, its true if you draw it on the paper, but square as such doesn't care about any time. Its timeless mathematical entity.

Edit: to make my analogy with square clearer: When you say someone what is square, you say "its geometrical object with right angles and with all sides the same". You don't add "at once". You can do it, but why would you?

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This thread provides me a good oppourtunity to learn about "block universe". Are quantum mechanical views, e.g. instead of worldline a group of probability amplitude or something like probability clouds for observers in such and such IFRs, observations that cause collapses of wavefunction do or do not take place in sucha and such spacetime points, incorporated in the theory?

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Are quantum mechanical views, e.g. instead of worldline a group of probability amplitude or something like probability clouds for observers in such and such IFRs, observations that cause collapses of wavefunction do or do not take place in sucha and such spacetime points, incorporated in the theory?

The "block universe" is not a theory. It's an interpretation of special relativity. Since SR is a classical theory, it does not include any quantum phenomena.

Quantum field theory is formulated on a fixed background spacetime which is usually the flat Minkowski spacetime of SR; however, I don't know if any serious work has been done on a "block universe" type of interpretation of QFT.

sweet springs
As others have mentioned, a block universe is a philosophical ontology; it is not physics. It therefore should not be discussed in a physics forum unless there can be presented some evidence for it. I would be interested if someone can point me to such evidence.

Thank you again for all the helpful responses.

This doesn't sound right to me. I don't see how your motion relative to those clocks can have any effect on the readings on those clocks. Clocks keep proper time, and proper time is a relativistic invariant.

What I meant to say was that when I am in between points A and B, and I am stationary with respect to A and B, then I am in their same frame of reference. But, once I start moving relative to A and B, then events which were once simultaneous in that frame now become not simultaneous in my new frame. So, if two flashes occurred (one at A and one at B) simultaneously in the A-B frame, then, to me who is moving towards B, the flash which occurred at B would have occurred earlier than the one at A. Is this true so far? If that's true, then I think it is also true that if both clocks in the A-B frame struck 12am on a certain date simultaneously in the A-B frame, then to me the clock at B would've struck that time earlier, and, therefore, the clock at B should be reading a later time then the clock at A. The more I increase my speed, the more B's clocks will be ahead of A's. Please let me know if I'm wrong on this.

Events occur in all frames of reference. The only difference is what coordinates get assigned to them.

That's one of the things for me about SR that has been difficult to grasp, and it makes the definition of words like when and now start to blur. If for example I am traveling with respect to someone on Earth with a gamma factor of 2, and when I left Earth the clocks on Earth and my ship were set at 0, then it means after one year of my traveling, I'll measure half a year passing on earth. For the person on earth, they will say that when a half year has passed for them, only a quarter of a year has passed for me. So, if in my reference frame a flash occurred on my ship on the one year mark of my journey, then for the person on Earth the flash won't have even occurred yet, and won't occur for anyone on Earth until 2 years go by on their clocks. So is it possible that something which happened in one frame hasn't happened yet in another? Also, if when a year has gone by for me, people on Earth only measure a quarter of a year going by, then it means that at the same moment my clocks will read both one year, and also a quarter of a year (if we are taking into account both reference frames). Typically the word moment or now refers to everything going on in the world in a particular frame of reference. Can we speak of a moment or of a now with respect to two or more frames of reference?

Its very strange sentence. It suggests to me, that there is some time outside of time so that you can say all time happened in single moment of some another time.

This relates, I think, to the paragraph above.

if when a year has gone by for me, people on Earth only measure a quarter of a year going by, then it means that at the same moment my clocks will read both one year, and also a quarter of a year (if we are taking into account both reference frames).
“at the same moment” automatically implies reference to one single inertial frame, it cannot refer to two distinct ones.

PeroK
I think it is also true that if both clocks in the A-B frame struck 12am on a certain date simultaneously in the A-B frame, then to me the clock at B would've struck that time earlier, and, therefore, the clock at B should be reading a later time then the clock at A.

If they chime at noon, then all observers will agree that the clocks read noon when the chimes were sounded.

then for the person on Earth the flash won't have even occurred yet, and won't occur for anyone on Earth until 2 years go by on their clocks. So is it possible that something which happened in one frame hasn't happened yet in another?
IFR, Inertial Frame of Reference, has infinite volume in spacetime. IFR of the Earth is not limited around the Earth but extends beyond solar system, our galaxy, to infinity. There is no bound in time also from infinite past and infinite future. There lies a dense network of clocks and measures in the infinite volume. The traveler who is far from Earth are surrounded by clocks which are still in Earth IFR. These clocks record time of the flash in that moment.

What I meant to say was that when I am in between points A and B, and I am stationary with respect to A and B, then I am in their same frame of reference. But, once I start moving relative to A and B, then events which were once simultaneous in that frame now become not simultaneous in my new frame. So, if two flashes occurred (one at A and one at B) simultaneously in the A-B frame, then, to me who is moving towards B, the flash which occurred at B would have occurred earlier than the one at A. Is this true so far? If that's true, then I think it is also true that if both clocks in the A-B frame struck 12am on a certain date simultaneously in the A-B frame, then to me the clock at B would've struck that time earlier, and, therefore, the clock at B should be reading a later time then the clock at A. The more I increase my speed, the more B's clocks will be ahead of A's. Please let me know if I'm wrong on this.

Yes, but they would tick at the same rate. All you would see is that the clocks (and all events too) at different places become shifted relative to each other, but they would still show the same rate of time. Also, you would still see that when clocks A sounds noon it is the middle of the day, when clocks B sounds noon it is also in the middle of its day. Physically meaningfull are only time differences not some absolute value of time and all the clocks at rest in that frame would agree on those.

So is it possible that something which happened in one frame hasn't happened yet in another?
How would you tell? Is there some time that is "above" reference frames to be able to compare them in absolute way as you are trying? The novelty of STR is that there is no absolute time, all time is relative in the sense that you must say who is measuring it. There is no way to make sense of what you said.

When two different observers measure time passed between two events, their measurements would be different. You can calculate how much, but you must admit they are measuring different things. That can be nicely seen from minkowsky diagram. The events and their sepparation in 4D spacetime is invariant. When you measure time passed, you are measuring projection of this space-time separation onto time axis. But different observers have different time axes and therefore they measure different projections. They all measure something else!

Also, if when a year has gone by for me, people on Earth only measure a quarter of a year going by, then it means that at the same moment my clocks will read both one year, and also a quarter of a year (if we are taking into account both reference frames).
You clocks measure one year. When you look at the clocks you are seeing one year passed, you don't see two values. Just like when you look at your clocks right now you see 7:38 at the morning, you don't see many different values. When you look on earth, you will see they were not able to do much work, they are slowed down, but your clocks measure one year no matter how slow everything is on earth. The reading of two values is you mental doing, it is not what your clocks show..

All you would see is that the clocks at different places become shifted relative to each other,
Just to be clear, you don't see this. You change your definition of how to correct for the lightspeed delay, so you calculate that the clocks are out of sync. What you actually see is that the clock in front of you blue shifts and starts racing while the clock behind redshifts and starts lagging. But you ascribe the difference in rates to the changing distances.

Umaxo
The reading of two values is you mental doing, it is not what your clocks show..

P.S. what helped me personally with understanding of STR is to get rid of trying this mental gymnastics to come up with some absolute world-view using frame-dependent language. There is geometrical language in which you don't use frames and you have certain absolute world-view, but you must invent new language for that. You invent concepts like minkowski spacetime, spacetime interval etc. All those words have no reference to particular reference frame. But what you are trying to do is to use words that have meaning only in respect to some reference frame (like "time", "now" etc.) to come up with reference-frame-free view. That is nonsense and therefore you have feeling you don't understand STR. And it is (perhaps) only because you are trying to do something that cannot be done.

Just think about words you are using. What is their meaning? Do i need certain reference frame to give the word meaning or not? If so, i can use the word only once i have chocen reference frame. And i cannot mix different reference frames, because the meaning of the word would change. And anytime i use different reference frames i must be aware both words have different meaning and i need to convert (by LT) the meaning to the one i need.

Ibix
Yes, but they would tick at the same rate. All you would see is that the clocks (and all events too) at different places become shifted relative to each other, but they would still show the same rate of time. Also, you would still see that when clocks A sounds noon it is the middle of the day, when clocks B sounds noon it is also in the middle of its day. Physically meaningfull are only time differences not some absolute value of time and all the clocks at rest in that frame would agree on those.
All this talk about clocks makes me want to re-post these videos. Clocks are in abundance, there is also aberration (accurate) and doppler/beaming effects (qualitative). Bored of looking at clocks yet? ;)

I'll leave it there for now as this is B-level, but there is some explanatory text on the page.

This is an interesting topic ... when you work in Sentient Artificial Intelligence the time of events becomes extremely important especially in the modelling of the future and the modelling of the past ... and yes, unfortunately the past is also not known ! These models taken together with their controls are in effect sentience. The probability of these events having been as "allegedly observed" becomes important.

These matters were first deeply understood and expressed by Kalman c. 1960 and in subsequent "models of reality" thereafter.

This uncertainty happens on all scales (picoseconds, seconds, decades, etc) and so it seems clear that in a Heisenberg sense that nothing is certain and there is just a blur at the join of past time and future time. We can always peer deeper and deeper into that "blur" during observation but we can never find "the present" and that join of past and future can never become a nice crisp line. It seems it's always a blur on any scale even at Cern (judging by the literature). As time progresses further away from an event the likelihood of any part of the universe being able to recall any past universe state diminishes and is lost to increasing entropy in the universe (our arrow of time). In the end the universe always forgets it's past states.

I think that Physicists and Mathematicians and Logic Experts should get together to sort out exactly what they think they are doing and this site would be a good place to do that however some of the moderators do tend to stick to book thinking and peer review rather than allow any free thought or new models.

I would agree with the previous comments and think that our time is just an illusion and that the above conclusion about there being another time in which the universe "just appeared" as the shape of our space time is correct and I think that might actually be testable. If for example we push the our universe to the limits of making it decide on something it has never had to decide on ever before. Say a new energy level of a state of photons or matter that has never existed in the universe before, or the isolation of a photon so far away from the rest of the universe that it "forgets it's rules" as passed to it by the rest of the universe (there is a similarity to Higgs thinking here). That could allow us to test if the universe "already just is" or "can be modified" especially if we do these experiments at positions in the universe that are far away from each other so that they cannot communicate with each other even at the speed of light. We might see conflicting results which would lead us to suspect that we can create new rules of the universe or we might see the same results which suggests that the universe "just is" and that there is another time in which it all "just appeared". i.e. The field we are testing here is the area of "where are the rules of the universe coming from" and I don't think that is metaphysics and is therefore non-testable and I do think it could be testable and is the job of our clever experimental and theoretical Physicists with the help of Mathematicians and Logic experts to sort out if that is a class of experiment that can be subjected to a test.

However ... all of these disciplines depend on thoughts (models) in a human brain and although that's the only basis we have at present there are brains coming along soon that will far surpass human brains so setting these brains off in a direction to search for and identify paradoxes (what Physicists do) and solve these by creating new models (i.e. new maths and Physics and new Logic Systems) seems to be the most important thing that humans can do right now as DNA life leaves it's 4 billion years of dominance and passes that highest intelligence (lowest entropy) over to new AI-beings.

We can always peer deeper and deeper into that "blur" during observation but we can never find "the present" and that join of past and future can never become a nice crisp line.
In relativity, there is no blur. At any event, other events in its past light cone are unambiguously in the past; events in its future light cone are unambiguously in the future; events outside the light cone aren't necessarily either in the future or the past. Where you draw the line is a matter of convenience to you.
I think that Physicists and Mathematicians and Logic Experts should got together to sort out exactly what they think they are doing and this site would be a good place to do that however some of the moderators do tend to stick to book thinking and peer review rather than allow any free thought or new models.
I think we have a perfectly clear idea of what we're talking about. If you don't understand then here is an excellent place to learn. Note, however, that this site is not for development of new theories - it's for teaching existing mainstream science. You may wish to review the rules you agreed to when you signed up.
I would agree with the previous comments and think that our time is just an illusion
I think you have misunderstood the comments, then. Time is not an illusion. The odd thing about time in relativity is that there is no unique way to synchronise two clocks that are not co-located, which means that what "at the same time in a different place" can mean different things to different people.

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Pencilvester
I wonder what would lead you to believe that "Time is not an illusion" ... i.e. is that just an opinion based on a particular model ?

Is it possible that there might be another better model (where time is an illusion) that produces the same result for space-time purposes ?

Also, after your next reply I am not going to go on about it ... it was just an idea really ... i.e .to get a much cleverer human to consider as it sounds like fun !

I wonder what would lead you to believe that "Time is not an illusion" ... i.e. is that just an opinion based on a particular model ?
No opinion, and no model:
Clocks are in abundance, ...
We could start and talk about the meaning of reality, resp. illusion, in philosophy, which we do not allow for many good reasons, or accept that time is simply a coordinate in our world: a measurable distance.
Is it possible that there might be another better model (where time is an illusion) that produces the same result for space-time purposes ?
If it produces the same results, then it cannot be different. And illusion isn't physically definable. This term is plain nonsense in natural sciences, except perhaps for neurology.
Also, after your next reply I am not going to go on about it ... it was just an idea really ... i.e .to get a much cleverer human to consider as it sounds like fun !
Good, because neither philosophy, nor meta-physics, nor what your interpretation of the two is, nor your (wild and confused) personal speculations as in post #28 are suited (allowed) subjects for a discussion here.

Pencilvester and Ibix
Just to be clear, when I calculate that the clocks are out of sync, this happens immediately when I switch reference frames correct?

Just to be clear, when I calculate that the clocks are out of sync, this happens immediately when I switch reference frames correct?
If you do your calculations using one reference frame you will calculate that the clocks are synchronized.
If you do your calculations using another reference frame you will calculate that the clocks are not synchronized.
So yes, if you change which reference frame you use, the answers you get will change immediately. It has to: the choice of frame is one of the inputs into the calculation, and when you change the input of a calculation you expect the correct answer to change immediately.

Just to be clear, when I calculate that the clocks are out of sync, this happens immediately when I switch reference frames correct?
Changing reference frame is a choice, not anything physical. So it takes as long as it takes you to redo your calculations in the new frame.

You aren't obliged to change frame if you accelerate. Some direct observables (e.g. Doppler shift, sensation of weight) do change immediately, but how you interpret those observables as giving information about the wider universe is up to you.

Dale
You aren't obliged to change frame if you accelerate.
Well said.