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So the point particle that is "you" is moving along a path which is dictated by the curvature of space-time, which in turn, is a result of the Stress-energy tensor, which is a sort of measure of energy and momentum change and density in space-time. The entity experiencing time is just arbitrary, and you refer to it as a 'test particle'. You can make the test particle a collection of test particles if you want, and call it "i". Also you need to choose your type of spacetime too. You haven't made it clear, Minkowski spacetime is flat in special relativity, whereas you could be referring to the Riemannian manifold of space time in general relativity.

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When you say the point particle, that is me, is moving what do you mean? Does it not in the model exist at all the times along the path, so that it never leaves one coordinate of spacetime to arrive at another, but instead exists all along the curve? Though you show the "hypersurface of the present" in your diagram, I am not sure in the standard spacetime model how the "present" is distinguished from other times. Perhaps you could explain? I thought different observers could argue about what "present" of mine was simultaneous to theirs and all be correct in the standard interpretation. I am not clear of the difference between Minkowski spacetime or the Riemannian manifold of spacetime, so feel free to choose either when answering, but if it is just a gravity issue, then perhaps choose Minkowski to keep it simpler, unless you feel that the complication is relevant.

So the point particle that is "you" is moving along a path which is dictated by the curvature of space-time, which in turn, is a result of the Stress-energy tensor, which is a sort of measure of energy and momentum change and density in space-time. The entity experiencing time is just arbitrary, and you refer to it as a 'test particle'. You can make the test particle a collection of test particles if you want, and call it "i". Also you need to choose your type of spacetime too. You haven't made it clear, Minkowski spacetime is flat in special relativity, whereas you could be referring to the Riemannian manifold of space time in general relativity.

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Nugatory

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The curve is just a trace of the path the particle (or you) are following through spacetime.Does it not in the model exist at all the times along the path, so that it never leaves one coordinate of spacetime to arrive at another, but instead exists all along the curve?

When I'm walking across the ground I leave footprints. We can join them together to define a curved path across along the ground, but that doesn't mean that I exist at all points on that path or that I haven't moved along that path. I always exist at one point, the one at the end of that curved path, and every step that I take extends the tip by one step. Your path (properly called a "worldline") through spacetime works the same way - you exist at the tip of the path, and it moves forward by one second every second.

You are right. Different observers moving at different speeds will have different hypersurfaces of simultaneity. Thus, the spacetime diagram doesn't distinguish "present" from other times. Instead, it distinguishes three types of events:Though you show the "hypersurface of the present" in your diagram, I am not sure in the standard spacetime model how the "present" is distinguished from other times. Perhaps you could explain? I thought different observers could argue about what "present" of mine was simultaneous to theirs and all be correct in the standard interpretation.

1) Those in the future light cone. All observers agree that these happened after the event at the apex of the light cone.

2) Those in the past light cone. All observers agree that these happened before the event at the apex of the light cone.

3) Those outside of both light cones. This is the only region that can contain any observer's hypersurface of simultaneity, and different observers moving at different speeds will draw different hypersurfaces of simultaneity through this region.

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Dale

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Usually, if we have a worldline, ##a##, then there exists an affine parameter, ##\tau## called the proper time which represents the time experienced by ##a##. Then, ##a(\tau)## picks out an event along that worldline, and the past light cone defines their "experience".

The "now" that is represented by simultaneity is not something that is experienced. It is calculated after the fact. What is experienced is in the past light cone, everything beyond that is prediction and conjecture.

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But the experienced reality is that the present is distinguishable from other times. I experience the present as being the point I am currently at in my journey through time. Like with a journey across sand, there could be footsteps/memories of where I once was, but there will only be one point, so to speak, where I am. The spacetime model however seems to have me existing as a continuum across the spacetime coordinates, and as you mention, it doesn't reflect the reality of there being anything travelling through time experiencing the present, as it doesn't distinguish a present, nor does it allow for there to be a correct answer as to what you are experiencing while I am experiencing what I am experiencing, for any given moment of my experience, the model suggests that it is correct to suggest that you were experiencing multiple things (as different observers would be equally correct with their different suggestions of what you were experiencing).You are right. Different observers moving at different speeds will have different hypersurfaces of simultaneity. Thus, the spacetime diagram doesn't distinguish "present" from other times. Instead, it distinguishes three types of events:

1) Those in the future light cone. All observers agree that these happened after the event at the apex of the light cone.

2) Those in the past light cone. All observers agree that these happened before the event at the apex of the light cone.

3) Those outside of both light cones. This is the only region that can contain any observer's hypersurface of simultaneity, and different observers moving at different speeds will draw different hypersurfaces of simultaneity through this region.

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One thing worth pointing out that a lot of the ideas discussed thus far

can be seen in the ordinary position-vs-time graph of PHY 101 (a Galilean spacetime diagram).

When distinguishes the spacetime diagram of special-relativity from Galilean-relativity is the

geometric notion of**perpendicularity** (orthogonality) as defined by the metric...

(which can be described as tangent to the unit-"circle").

Given a worldline and an event on that worldline ["NOW, on that observer's worldline"],

the hyperplane that is "perpendicular [in that geometry]" to the tangent-vector is used to define "simultaneity according to that observer".

In the PHY-101 diagram, it turns out that, for a given event "NOW", the planes of simultaneity are co-planar (independent of the worldline through that NOW event)... hence "absolute simultaneity".

In Special relativity, these corresponding planes are not co-planar... hence, no absolute simultaneity.

(For an inertial observer in special-relativity, these planes correspond with hyperplanes from radar measurements.)

The Euclidean analogue of this diagram already shows this non-coplanarity.

can be seen in the ordinary position-vs-time graph of PHY 101 (a Galilean spacetime diagram).

When distinguishes the spacetime diagram of special-relativity from Galilean-relativity is the

geometric notion of

(which can be described as tangent to the unit-"circle").

Given a worldline and an event on that worldline ["NOW, on that observer's worldline"],

the hyperplane that is "perpendicular [in that geometry]" to the tangent-vector is used to define "simultaneity according to that observer".

In the PHY-101 diagram, it turns out that, for a given event "NOW", the planes of simultaneity are co-planar (independent of the worldline through that NOW event)... hence "absolute simultaneity".

In Special relativity, these corresponding planes are not co-planar... hence, no absolute simultaneity.

(For an inertial observer in special-relativity, these planes correspond with hyperplanes from radar measurements.)

The Euclidean analogue of this diagram already shows this non-coplanarity.

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The experienced reality is I am travelling through time in a certain direction, and where I am on that journey I can refer to as the present. It is that only one point would ever be the present, and that point is changing as the I that experiences it travels through time. With the standard spacetime model though it seems like a static geometry. I exist just as much in my past as I do in the present, it is just that I am spread across the coordinates. There is doesn't seem to be anything moving through time. The I that does isn't represented in it.Usually, if we have a worldline, ##a##, then there exists an affine parameter, ##\tau## called the proper time which represents the time experienced by ##a##. Then, ##a(\tau)## picks out an event along that worldline, and the past light cone defines their "experience".

The "now" that is represented by simultaneity is not something that is experienced. It is calculated after the fact. What is experienced is in the past light cone, everything beyond that is prediction and conjecture.

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Dale

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Yes. That is ##a(\tau)## as I described above.It is that only one point would ever be the present, and that point is changing as the I that experiences it travels through time.

That is just a philosophical interpretation. It doesn't matter mathematically or physically if you consider proper time as a parameter along a 1D path in a 4D spacetime or a parameter that selects a 0D point in a parameterized family of 3D spaces.With the standard spacetime model though it seems like a static geometry. I exist just as much in my past as I do in the present, it is just that I am spread across the coordinates. There is doesn't seem to be anything moving through time. The I that does isn't represented in it.

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Ibix

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Pick the interpretation that makes most sense to you. It doesn't make any difference to the physics.

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Nugatory

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The experienced reality is that the presentBut the experienced reality is that the present is distinguishable from other times.

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Proper time is a real number. The real numbers form a complete totally ordered field. The math doesn't define a t which "moves" forward similar to footsteps walking along a path. This apparent movement is a result of the second law of thermodynamics. You need to provide a mathematical description of this movement. You need to provide math which shows 6:00 doesn't exist at 6:01. You have only made vague claims that they are mathematically equivalent.Yes. That is ##a(\tau)## as I described above.

That is just a philosophical interpretation. It doesn't matter mathematically or physically if you consider proper time as a parameter along a 1D path in a 4D spacetime or a parameter that selects a 0D point in a parameterized family of 3D spaces.

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But the issue is how the model relates to reality.Yes. That is ##a(\tau)## as I described above.

That is just a philosophical interpretation. It doesn't matter mathematically or physically if you consider proper time as a parameter along a 1D path in a 4D spacetime or a parameter that selects a 0D point in a parameterized family of 3D spaces.

The standard interpretation as I understand it, has it that it is true that during a period of time of you experiencing, that I was experiencing a particular point in time... in the sense that one observer could correctly (according to the standard interpretation) claim that at a beginning point of the period of time that you experienced journeying through, I was experiencing a certain point X, and all through your journey through that period of time, other observers could correctly claim that simultaneous to whatever you were experiencing I was experiencing that certain point X. But reality we experience suggests that we are journeying through time, and that the answer will not be that I was experiencing one particular point in time for the whole duration of the period being considered that you were experiencing.

I realise that with the standard interpretation other observers could also correctly claim that I was experiencing other points during your journey. I realise that it might be questioned what I mean by simultaneously, but I do not think I risk being mislead in thinking that, assuming we are both experiencing, that while you are experiencing something, I am experiencing something, and that I do not experience more than one point of time simultaneously.

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This idea was pushed to its limits in the books "The Serial Universe" (1934) and "An Experiment With Time" (1927) by J.W.Dunne. He showed that if you are moving through time, then you have a rate of moving, which required a secondary time dimension - so many seconds of time1 per second of time2. And this in turn led to an infinite regress, so that an infinity of time dimensions was required.

Another approach was that of Fred Hoyle in his novel "October The First Is Too Late". (1966) He likened the present moment to a light moving along a film strip, lighting up each frame in turn, and then suggested that it did not matter in which order the frames were lit up, the result would be the same, and that provided the background for his time travel story. But he did not go the next step and say that all the frames could be lit up at the same time (note J.W.Dunne's secondary time dimension creeping in!). And that is the situation we experience - each moment on your timeline is its own "Now" and nothing moves into the future.

Movement through time, and the experience of change and movement is all an illusion based on what we experience now and the memory of the immediate past. But it sure is a convincing illusion!

Mike

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PAllen

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and my friends have Hoyle to thank for all the cryptic comments I make every October 1 from reading his book at an impressionable age not long after it first came out.

This idea was pushed to its limits in the books "The Serial Universe" (1934) and "An Experiment With Time" (1927) by J.W.Dunne. He showed that if you are moving through time, then you have a rate of moving, which required a secondary time dimension - so many seconds of time1 per second of time2. And this in turn led to an infinite regress, so that an infinity of time dimensions was required.

Another approach was that of Fred Hoyle in his novel "October The First Is Too Late". (1966) He likened the present moment to a light moving along a film strip, lighting up each frame in turn, and then suggested that it did not matter in which order the frames were lit up, the result would be the same, and that provided the background for his time travel story. But he did not go the next step and say that all the frames could be lit up at the same time (note J.W.Dunne's secondary time dimension creeping in!). And that is the situation we experience - each moment on your timeline is its own "Now" and nothing moves into the future.

Movement through time, and the experience of change and movement is all an illusion based on what we experience now and the memory of the immediate past. But it sure is a convincing illusion!

Mike

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Dale

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I don't recognize any of this as being part of any standard interpretation.The standard interpretation as I understand it, has it that it is true that during a period of time of you experiencing, that I was experiencing a particular point in time... in the sense that one observer could correctly (according to the standard interpretation) claim that at a beginning point of the period of time that you experienced journeying through, I was experiencing a certain point X, and all through your journey through that period of time, other observers could correctly claim that simultaneous to whatever you were experiencing I was experiencing that certain point X. But reality we experience suggests that we are journeying through time, and that the answer will not be that I was experiencing one particular point in time for the whole duration of the period being considered that you were experiencing.

If by "reality" you mean "the outcome of experiments" then the model relates to reality with an excellent degree of precision. This is what I mean when I say "reality".But the issue is how the model relates to reality.

If by "reality" you mean "the philosophical discipline of ontology", then the model is compatible with multiple ontologies, none of which are considered of great importance scientifically.

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Mister T

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None of this seems standard to me. What you say confuses me. It's not clear that you are talking about spacetime, only time. And you seem to be mixing up clock-readings with time intervals. Clock-readings last for no duration of time. You are saying that something that's a clock-reading to one person is a time interval to another. That cannot happen. Different observers may disagree on the clock-reading ##t## of some event, they may disagree on the time interval ##\Delta t## between two events, but at least they can make comparisons. There is no way to compare a clock-reading ##t## to a time interval ##\Delta t## and say that what one person experiences as clock-reading another experiences as a time interval. It just doesn't make sense to do that.The standard interpretation as I understand it, has it that it is true that during a period of time of you experiencing, that I was experiencing a particular point in time... in the sense that one observer could correctly (according to the standard interpretation) claim that at a beginning point of the period of time that you experienced journeying through, I was experiencing a certain point X, and all through your journey through that period of time, other observers could correctly claim that simultaneous to whatever you were experiencing I was experiencing that certain point X. But reality we experience suggests that we are journeying through time, and that the answer will not be that I was experiencing one particular point in time for the whole duration of the period being considered that you were experiencing.

I realise that with the standard interpretation other observers could also correctly claim that I was experiencing other points during your journey. I realise that it might be questioned what I mean by simultaneously, but I do not think I risk being mislead in thinking that, assuming we are both experiencing, that while you are experiencing something, I am experiencing something, and that I do not experience more than one point of time simultaneously.

If two events occur at the same place and at the same time, they are simultaneous. That is something all observers will agree on. The issue of simultaneity for spatially separated events, now that's something different observers may disagree on.

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I do not see that there need be an infinite regress, only that it is silly to think you could describe the rate in seconds. If you played a video image at half speed, and only referenced the scenes in the slowed down video in order to describe the laws of physics that were being shown in it, they would be the same laws as if you were watching the video at normal speed. Things would be dropping at the same rate in terms of the physics. But there is the experienced sense in which things were dropping slower in the slowed down video than they were in the video at full speed.

This idea was pushed to its limits in the books "The Serial Universe" (1934) and "An Experiment With Time" (1927) by J.W.Dunne. He showed that if you are moving through time, then you have a rate of moving, which required a secondary time dimension - so many seconds of time1 per second of time2. And this in turn led to an infinite regress, so that an infinity of time dimensions was required.

Another approach was that of Fred Hoyle in his novel "October The First Is Too Late". (1966) He likened the present moment to a light moving along a film strip, lighting up each frame in turn, and then suggested that it did not matter in which order the frames were lit up, the result would be the same, and that provided the background for his time travel story. But he did not go the next step and say that all the frames could be lit up at the same time (note J.W.Dunne's secondary time dimension creeping in!). And that is the situation we experience - each moment on your timeline is its own "Now" and nothing moves into the future.

Movement through time, and the experience of change and movement is all an illusion based on what we experience now and the memory of the immediate past. But it sure is a convincing illusion!

Mike

As for the idea that it was an illusion that you were experiencing change, what were you thinking the reality was, that your experience was in fact static?

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Yes the experienced reality is that the present where I am is distinguishable from other times, and it is also that I am moving through time, or in other words I experience my experience changing. The issue I am getting at was that in the spacetime model the human I experience being does not move, it just exists along a path. Relating the change in experience to the clock times used in physics I do not experience being at one clock time point more than once on the journey. Yet as I have stated else where:The experienced reality is that the presentwhere you areis distinguishable from other times. I have no problem saying that 10:59 on my wristwatch came before 11:00, that at 10:59 the 11:00 tick hadn't happened yet, and that at 11:00 the 10:59 tick has already happened. But if If it's happening somewhere else right now, it's not part of my experienced reality until sometime later. For example, all sorts of interesting and exciting things may be happening on alpha centauri right now, but that's 4.3 light years away so it will be sometime in the spring of 2020 before I can know about them or be influenced them.... and then I'll subtract 4.3 years from the current date and conclude that these interesting and exciting things actually happened during a few days before Christmas 2015. That's a very different thing then experiencing these events as part of the present in December 2015.

The standard interpretation as I understand it, has it that it is true that during a period of time of you experiencing, that I was experiencing a particular point in time... in the sense that one observer could correctly (according to the standard interpretation) claim that at a beginning point of the period of time that you experienced journeying through, I was experiencing a certain point X, and all through your journey through that period of time, other observers could correctly claim that simultaneous to whatever you were experiencing I was experiencing that certain point X.

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For a concrete example, suppose you look at the Magellenic clouds, that are maybe 150-200 thousand light years away. Are you experiencing how they are "now", or how they used to be 150-200 thousand years ago?

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So imagine a 10 second period of your experience. I thought in the standard interpretation, an observer (moving at a certain velocity relative to us) could correctly claim that simultaneously to you experiencing the 1 second point, I was experiencing the 3 second point, and another observer (moving at a different certain velocity) could correctly claim that simultaneously to you experiencing the 5 second point I was experiencing the 3 second point, and that another observer (moving at a different certain velocity) could correctly claim that simultaneously to you experiencing the 9 second point I was experiencing the 3 second point. So that there could be a series of claims (by different observers) that amounted to a claim that simultaneously to you experiencing all of the points during that 10 second period it was true that I was experiencing the 3 second point.I don't recognize any of this as being part of any standard interpretation.The standard interpretation as I understand it, has it that it is true that during a period of time of you experiencing, that I was experiencing a particular point in time... in the sense that one observer could correctly (according to the standard interpretation) claim that at a beginning point of the period of time that you experienced journeying through, I was experiencing a certain point X, and all through your journey through that period of time, other observers could correctly claim that simultaneous to whatever you were experiencing I was experiencing that certain point X. But reality we experience suggests that we are journeying through time, and that the answer will not be that I was experiencing one particular point in time for the whole duration of the period being considered that you were experiencing.

Though just as a reminder I did also mention

Did I make claims incompatible with the standard interpretation?I realise that with the standard interpretation other observers could also correctly claim that I was experiencing other points during your journey. I realise that it might be questioned what I mean by simultaneously, but I do not think I risk being mislead in thinking that, assuming we are both experiencing, that while you are experiencing something, I am experiencing something, and that I do not experience more than one point of time simultaneously.

I mean by reality what I suspect has always been meant by reality. So that if God exists, then the reality is that God exists. If God does not exist then the reality is that God does not exist. If you were in some "matrix" type VR then reality is that you are in some "matrix" type VR. If you are not in some type of "matrix" type VR then reality is that you are not in some "matrix" type VR. If I am experiencing looking at a bunch of bananas as I type this then reality is that I am looking at a bunch of bananas as I type this, if I am not experiencing looking at a bunch of bananas as I type this then reality is that I am not looking at a bunch of bananas as I type this. And so on, I assume you get the idea. I do experience my experience changing, and so I experience what could be described as the passage of time, or me journeying through time. So I was asking how the standard spacetime model relates to my changing experience, because while the human that I experience being exists along a path, the I that has the changing experience does not seem to be represented because there is no "I" that is moving along the path, that was once at a point in the path but no longer is. I am not a single point on the path, nor all the points on the path.If by "reality" you mean "the outcome of experiments" then the model relates to reality with an excellent degree of precision. This is what I mean when I say "reality".

If by "reality" you mean "the philosophical discipline of ontology", then the model is compatible with multiple ontologies, none of which are considered of great importance scientifically.

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Dale

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What you describe is part of the math, not part of any interpretation.So imagine a 10 second period of your experience. I thought in the standard interpretation,...

There are two standard interpretations of the math. The block universe interpretation (BU) says that all of those statements are about drawing equally valid planes of simultaneity on the same 4D manifold. The Lorentz aether theory (LET) interpretation says that only one of those lines is right, but you cannot ever experimentally detect which one it is.

Well, a bit worse than that. Your claim is not even well defined. Your claim involved the word "simultaneously" repeatedly. Simultaneity is a frame-dependent concept, so whenever you use the term you must specify the reference frame.Did I make claims incompatible with the standard interpretation?

Your claim also repeatedly uses the word "experiencing" which is not well defined in the math. I gave what I thought was a reasonable mathematical representation of "experiencing" above. You didn't seem to like it but didn't offer any alternative.

That doesn't help much since different people have always meant different things by the word.I mean by reality what I suspect has always been meant by reality.

I told you what I mean fairly simply. You should do the same. But see next:

It sounds like our definitions are not too far off. You seem to believe that if bananas are really there then you could perform the experiment of looking, and if the data obtained by doing so is compatible with the hypothesis then you would accept that the bananas are really there.If I am experiencing looking at a bunch of bananas as I type this then reality is that I am looking at a bunch of bananas as I type this

At different points ##a(\tau)## along your worldline you have different past light cones. This accounts for your perception of changing experience.I was asking how the standard spacetime model relates to my changing experience,

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Ibix

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The first is the block universe, the second is Lorentz Ether.