Proper (and coordinate) times re the Twin paradox

[tophatphysicist]

"I once had a conversation" is not a valid reference. And your post neglects the entire issue.

Are there any physical objects which are 2D?

Rather than use an invalid reference, I'll just make it my own comment: We live in a world of 3-D objects.

I don't recall 2-D phenomena being referred to as objects in any of my physics courses.

 

[jbriggs444]

Rather than use an invalid reference, I'll just make it my own comment: We live in a world of 3-D objects.

The point that I see @Dale driving at is that we think of our world as a world of 3-D objects in the Newtonian picture. The objects have length, width and height. We think of their extent in time as something else -- something irrelevant to their dimensionality. Dropping down to 2-D makes it more clear that dropping a dimension out of an objects's extent makes the object un-physical.

If you consider a 2-D object you are forced to admit that it is ephemeral. Less than a single atom thick. A shadow of a wisp of a paper-thin dividing plane. A thing with zero mass, completely invisible. A thing which we would be utterly unable to detect.

Similarly, a 3-D "object" would exist for an instant only^(*). Less than a blink of an eye. A shadow of a wisp of a paper-thin hyper-plane. A thing which is still invisible (the probability of it interacting with even a single photon is zero) and a thing which, for any continuous interaction, can deliver zero impulse. Like the 2-D case, we would also be unable to detect a 3-D "object".

(*) Taking the easy case of a 3-D slice of a 4-D object taken through a hyper-plane of simultaneity in our chosen reference frame.

 

[Dale]

I don't recall 2-D phenomena being referred to as objects in any of my physics courses.

If you believe that you are justified in discarding one dimension then you should also be able to discard two with the same justification. There is no physical 2D object, and there is no physical 3D object for the same reason. Physical objects are 4D

 

[tophatphysicist]

Similarly, a 3-D "object" would exist for an instant only.

I see what you are driving at, jbriggs444. I'm just thinking that there is a world of difference (literally) between a 3-D object and a 2-D surface. Now, your comment about existing for an instant only could be considered from a little different point of view. If the 4-D object "exists", then all of the 3-D volumes that make it up must exist along with the 4-D object. I don't think it's a good idea for me to try to get into the meaning of existence here. But, the fleetingness has more to do with the motion of consciousness along an observer's world line. Hermann Weyl (great mathematician and physicist, close friend of Einstein's) described the observer "crawling" along his world line. Some would say the observer moves along his world line at the speed of light.

 

[tophatphysicist]

If you believe that you are justified in discarding one dimension then you should also be able to discard two with the same justification. There is no physical 2D object, and there is no physical 3D object for the same reason. Physical objects are 4D

Why?

I am certainly agreeing with you in recognizing objects are 4-dimensional. The 3-D world we live in with 3-D objects are parts of the 4-D structure. We observers just don't observe the 4-D world that we are a part of. But, we do observe a 3-D world with 3-D objects.

 

[jbriggs444]

IIf the 4-D object "exists", then all of the 3-D volumes that make it up must exist along with the 4-D object. I don't think it's a good idea for me to try to get into the meaning of existence here.

Rather than get into discussions about existence and consciousness (thank you for refraining from doing so), we can stay grounded in the world of science. If you can measure it, it is physical. No experiment can detect the presence or absence of a single 2-D plane from a 3-D cube. No experiment can detect the presence or absence of a 3-D instant from a 4-D world-tube.

Our usual models use a continuum approximation so that we assume that every 3-D slice of a 4-D object is real. But that's just the model talking. It does not follow from any experimental result.

 

[Dale]

But, we do observe a 3-D world with 3-D objects.

No, we don't. All of the objects we observe have some nonzero extension in the 4th dimension.

 

[tophatphysicist]

Actually, I could understand if you wish to make a point out of we, as observers, when observing an object, probably are observing the result of a brain/consciousness process that presents an image of an object that includes 4 dimensions. This is in the sense that the image has probably been averaged over something like 0.3 seconds (depending on your response time). So, in reality you consider in what sense you are experiencing the mental display of a 4-D object. Consider how far the observer moves along his world line in 0.3 sec (quite a distance along the brain 4-D fiber bundle).

 

[jbriggs444]

I really think that we should leave consciousness out of this. As scientists, we can measure with instruments that are not limited by 0.3 second cognition times.

Scientific instruments are still limited. For instance, if you open the shutter on a camera for an exposure of 0 seconds, you will not succeed in exposing your film.

 

[Dale]

@tophatphysicist
I am not talking about consciousness.

I am also not talking about "reality" or any other philosophical concept. I am talking exclusively about "physical" meaning "experimentally measurable". There has never been any experimental detection of a 3D object, so they are not physical for the same reason that 2D objects are not physical.

Any further posts mentioning consciousness will be deleted. It is not a relevant topic for this thread.

 

[Dale]

I am certainly agreeing with you in recognizing objects are 4-dimensional

So if you feel that a 3D slice is physical then why is it not physical to take a 2D slice?

 

[Ebeb]

@tophatphysicist
Any further posts mentioning consciousness will be deleted. It is not a relevant topic for this thread.

I would regret that, because I find Tophat's note on consciousness very interesting, for the simple reason that Tophat probably -unintentionally?- solved the issue I had in this thread! His latest posts all of a sudden make me realize why "3D object" indeed doesn't make sense. Because a 2D section through a rock is NOT the same as a slice (being 3D) of the 3D rock, hence a 3D section through 4D spacetime is not the same as a slice (being 4D) out of/part of full 4D object. I thought the difference is rather nitpicking, but I bet this is why we didn't understand each other, isn't it, Dale? We probably do have the same special relativity analysis in mind, but because of this 3D section not being same as 'slice', we couldn't get agreement. I think I now also understand all the other posts :-) Let's see...

If you think about it, our perception delivered by the brain after receiving
information from the optical nerves is an averaged out "image", average over
somewhere around the last 300,000 miles or so of travel along the 4th dimension
(if you set a mode of consciousness watching the continuous sequence of 3-D
cross-sections of the neuron 4-fibre bundle as it advances along the observer
world line at the speed of light -- and assuming some conscious response time).
One way of interpreting that might be to say that consciousness observes a running
average of 4-D sections (3-D cross-sections extending 300,000 miles along the
4th dimension). In a sense you might say that we are actually observing 4-D objects.

Actually, I could understand if you wish to make a point out of we, as observers, when observing an object, probably are observing the result of a brain/consciousness process that presents an image of an object that includes 4 dimensions. This is in the sense that the image has probably been averaged over something like 0.3 seconds (depending on your response time). So, in reality you consider in what sense you are experiencing the mental display of a 4-D object. Consider how far the observer moves along his world line in 0.3 sec (quite a distance along the brain 4-D fiber bundle).

Very good posts, Tophat. Your comment about the 0.3 timelapse made me think, and forces me to jump in again. Actually, such a timelapse includes 4D extention. But your "averaged out image", is a 3D object without time "thickness" making it a non issue, because that 3D construct is only a mental thing of your brain, not an object out there to be/being observed. I now have to admit that when I compared a 2D section through a 3D rock with a "2D" slice of bread still being an object, I was -unintentionaly- cheating, because the slice of bread necessarily does have a small part of (extention into) the 3rd dimension. Hence the section though the rock I had in mind also needed a 'thickness' to be able to consider it the set of 3D rock atoms 'along' that section.
This indeed means that in special relativity a 3D object of simultaeous events doesn't make sense, because an object 'needs' a 4D extention. And this also makes a 3D world a non issue, because a 3D world is only an illusion (your "averaged out image") produced by your mind. The 3D world you and I had in mind does contain a slight 4D extention, making it a 4D object. From now on I should use "4D slice of simultaneous events" instead of "3D section of simultaneous events". Doesn't it make sense?

I won't get into the details of whether the 3-D cross-sections make up a continuum
or whether they are discrete, perhaps with Planck time sequences. But, we already
know that the optical nerves/brain system has a relatively enormously long time
constant.

For what it's worth. Your final comment in post #190 is more important for the discussion than it seems. Because if the spacetime continuum is discrete, one would be able to talk of a 3D section being a 3D object, with no 'time-lapse'/time extention?

One last thought. Just to make sure what we have in mind when considering an event. Consider a car hitting a tree. We can give the event coordinates to locate it relative to ref frames, but what about dimensions of the event itself? Because, if there is no time extention part of the event itself, wouldn't this mean that there cannot be an event, nor car, nor tree? Because when comparing with the rock: we can locate an atom inside the rock by labeling it with coordinates, but the rock atom itself is a 3D object. Wouldn't that make an event a 4D 'object'? I has to be because that's how a collection of simultaneous events is a 4D (not 3D) slice/part out of the full 4D... If we use a ref frame to locate an event, the event (absolute building block of absolute 4D spacetime) itself must have dimensions, otherwise there is nothing to be measured... (cfr atom in the rock slice: if a rock molecule has no dimensions, there is no molecue, hence there is nothing to be labeled with coordinates...).

@Dale, and @Jbriggs, ... is this getting closer to what you were trying to get across?

 

[tophatphysicist]

Very interesting comments, Ebeb. I will be contemplating this while sitting in the church pew this morning. I think we both have more regard for Dale's and Peter's points than it might seem.

 

[jbriggs444]

@Ebeb, that was a long post. I will try to keep this response brief.

It seems that we have reached agreement about the distinction between a thin section of an object (e.g. a slice of bread) and an infinitesimal dividing plane through an object (e.g. the place where we intend to cut the bread).

Just to make sure what we have in mind when considering an event. Consider a car hitting a tree. We can give the event coordinates to locate it relative to ref frames, but what about dimensions of the event itself? Because, if there is no time extention part of the event itself, wouldn't this mean that there cannot be an event, nor car, nor tree? Because when comparing with the rock: we can locate an atom inside the rock by labeling it with coordinates, but the rock atom itself is a 3D object. Wouldn't that make an event a 4D 'object'? I has to be because that's how a collection of simultaneous events is a 4D (not 3D) slice/part out of the full 4D... If we use a ref frame to locate an event, the event (absolute building block of absolute 4D spacetime) itself must have dimensions, otherwise there is nothing to be measured... (cfr atom in the rock slice: if a rock molecule has no dimensions, there is no molecue, hence there is nothing to be labeled with coordinates...).

Physically, a car hitting a tree is a process with four-dimensional extent. It extends right, left, up, down, forward into the tree and back into the car. It does not just crumple a point on the bumper. It crumples a three dimensional region. It does not just crush the bark on the tree at one point. It makes a three dimensional scar. It does not occur at an instant. It takes place over a [short] time interval.

For most purposes, we do not care about the complete details of the collision. For purposes of our models, it is enough that we know the mass, momentum and energy of the car and of the tree. For the police report, we only need to know that it occurred on Fourth and Elm at 2:00 pm. [we assume that it took place at ground level]. The "event" associated with the collision is the exact four dimensional location which is only approximately where and when the diffuse process took place. The process is physical. The "event" is a labelled feature in our model.

But I agree that one could reasonably say that a collision "event" is physically a four-dimensional process.

 

[tophatphysicist]

So if you feel that a 3D slice is physical then why is it not physical to take a 2D slice?

I can handle a 3-D object, inspect it, move it around in my 3-D world. I can carve out a 3-D chunk of an object and put it on the table to inspect it. I cannot carve out a 2-D section. I cannot make an object out of it. The 3-D object has volume -- the 2-D cross-section has no volume to form an object.

I actually accept the concept of the 4-D object as described by Dale and Peter, but hopefully we will not stumble into a discussion of how a 3-D observer can cause an object to move around when the object is actually 4-dimensional and already exists as a fixed 4-D object with no possibility of the observer altering the 4-D object along its future world line. I don't think this forum is a suitable place for that kind of discussion.

 

[Dale]

I bet this is why we didn't understand each other, isn't it, Dale?

That sounds likely to me also. Or at least a big part of it. The other part is just the math vs physical bit.

Consider a car hitting a tree. We can give the event coordinates to locate it relative to ref frames, but what about dimensions of the event itself? Because, if there is no time extention part of the event itself, wouldn't this mean that there cannot be an event, nor car, nor tree?

So mathematically an event is 0 dimensional. Just a point at an instant. Nothing physical meets that criteria, but we can use the math as a simplification when the actual 4D interaction is very small compared to our scale of interest.

 

[Dale]

I can handle a 3-D object, inspect it, move it around in my 3-D world

No, you can't. A 3D object would disappear before you could touch it, see it, or move it.

I can carve out a 3-D chunk of an object and put it on the table to inspect it.

I would be very impressed if you could instantaneously carve anything, instantaneously move it to a table, or instantaneously inspect anything. To do all three before a 3D object disappears is beyond belief.

I cannot carve out a 2-D section. I cannot make an object out of it.

This is true, but you are just fooling yourself that you can do it with the 3D object.

 

[PeterDonis]

I can handle a 3-D object, inspect it, move it around in my 3-D world.

No, you can't. You are limited to moving slower than light, so any influence you exert on an object will not be on any 3-D spacelike section of that object. It will start at one point of the object and propagate through it slower than light. So you can only act on a 4-D section of the object, not a 3-D section.

 

[tophatphysicist]

Good interesting comments, Dale and Peter. This will be nice to sleep on.

 

[Ebeb]

That sounds likely to me also. Or at least a big part of it. The other part is just the math vs physical bit.
So mathematically an event is 0 dimensional. Just a point at an instant. Nothing physical meets that criteria, but we can use the math as a simplification when the actual 4D interaction is very small compared to our scale of interest.

I can live with that.

@Ebeb, that was a long post.

I know, I thought it was necessay to make it that long ;)

I will try to keep this response brief.

It seems that we have reached agreement about the distinction between a thin section of an object (e.g. a slice of bread) and an infinitesimal dividing plane through an object (e.g. the place where we intend to cut the bread).

Yes. But the disagreement being between 'section' and 'slice', I would prefer saying 'slice' of 4D object. The 'dividing plane' being the 'section'...

Physically, a car hitting a tree is a process with four-dimensional extent. It extends right, left, up, down, forward into the tree and back into the car. It does not just crumple a point on the bumper. It crumples a three dimensional region. It does not just crush the bark on the tree at one point. It makes a three dimensional scar. It does not occur at an instant. It takes place over a [short] time interval.

For most purposes, we do not care about the complete details of the collision. For purposes of our models, it is enough that we know the mass, momentum and energy of the car and of the tree. For the police report, we only need to know that it occurred on Fourth and Elm at 2:00 pm. [we assume that it took place at ground level]. The "event" associated with the collision is the exact four dimensional location which is only approximately where and when the diffuse process took place. The process is physical. The "event" is a labelled feature in our model.

But I agree that one could reasonably say that a collision "event" is physically a four-dimensional process.

I agree. Let me dig a littgle further. In the car/tree collision we can talk of a 'process' over time, but let's say the car explodes during the collision, and left the tree black instead of green. If I consider a tree event after the collision, i.e. an event black tree, is not a process over time... but again, we can consider it a 4D slice of tree, because we agreed a 3D tree cannot exist without a time extention. This makes the 4D slice of 4D object/world a "physically real" object, but when we consider events having 0 dimension, the collection of events cannot be a "physically real" object.
I would agree that a section/plane deals with 'event' points of 0 dimension, but that section/plane deals with a "physically real 4D slice of the 4D object/world.
(Another metaphor: if I draw a section though a building, the coordinates/dimensions I indicate are sort of part of the section itself, but they deal with physically real walls and floors along that 'section plane'...)

 

[Mister T]

One last thought. Just to make sure what we have in mind when considering an event. Consider a car hitting a tree. We can give the event coordinates to locate it relative to ref frames, but what about dimensions of the event itself? Because, if there is no time extention part of the event itself, wouldn't this mean that there cannot be an event, nor car, nor tree?

This is an idea that goes back quite a way. Zeno's paradox about the moving arrow. The riddle was solved when calculus was invented. Thus it's a central feature also of Newtonian physics. Events have no duration in time. A moving object has a specific location, but spends no time there. It's called the particle model because the object also has zero extent in space. It's a model, a fiction.

The same idea applies to an imaginary slice through a rock. It has zero thickness.

 

[Ebeb]

This is an idea that goes back quite a way. Zeno's paradox about the moving arrow. The riddle was solved when calculus was invented. Thus it's a central feature also of Newtonian physics. Events have no duration in time. A moving object has a specific location, but spends no time there. It's called the particle model because the object also has zero extent in space. It's a model, a fiction.

The same idea applies to an imaginary slice through a rock. It has zero thickness.

Correct, the dividing plane has zero tickness. But we can take a slice with slight non-zero thickness. That difference is the issue discussed.
I agree the car actually does not move at that split second in time, but we stil deal with a car. Would you say a car object is a fiction? That's not what I read in this thread.

 

[tophatphysicist]

Having accepted the physical 4-D universe, I can't help but ask the following questions. Do we then give up the notion of cause and effect? Do we abandon the idea of forces causing acceleration of masses as a true physical process (as opposed to merely a mathematical tool)? Should we account for the illusion of things moving in our perceived world as simply the movement of our consciousness along our neuron bundle world line? Otherwise, how does our perception of the world happen? If the universe did not initiate with the Big Bang and then evolve from that point in time, does physics have any explanation for the presence of the 4-D universe, "all there at once?" Are the configurations of 4-D world lines organized in such a manner as to be consistent with the laws of classical physics in the aggregate in the large scales, but possessing random structure on the Planck scale (while surprisingly conforming to random collections that include phase)? Does that mean that we no longer have a need to find a more fundamental basis for Quantum Mechanics, nor worry about merging Q.M. with General Relativity?

Are these questions outside of the realm of physics? Or at least out of bounds for the Physics Forums? If so, I withdraw them.

 

[Dale]

Do we then give up the notion of cause and effect?

Most definitely not! The universe does not seem to care about simultaneity, but it does seem to care about causality. Causes always come before effects. There is a lot of physical evidence for that.

 

[Mister T]

Correct, the dividing plane has zero tickness. But we can take a slice with slight non-zero thickness. That difference is the issue discussed.

How slight?

I agree the car actually does not move at that split second in time,

The car is moving.

 

[tophatphysicist]

Most definitely not! The universe does not seem to care about simultaneity, but it does seem to care about causality. Causes always come before effects. There is a lot of physical evidence for that

You seem to be using the idea of causality in a different way, perhaps as a description of the related geometric patterns of bundles of 4-D fibers along the 4th dimension. You have already indicated that the universe is a 4-D object with everything already there. So, if the "future" part of the 4-D structure is already there, how do you now cause it?

 

[Ebeb]

Most definitely not! The universe does not seem to care about simultaneity, but it does seem to care about causality. Causes always come before effects. There is a lot of physical evidence for that.

Let me ventilate my thoughts on this...
If A/ an hollywood actor throws a stone towards a window, and B/ the stone hits the window, then B follows A. Of course.
If I watch a pre-digital movie roll of that happening, frame B follows frame A, but all the frames are already there on the film roll. The fact that they are fixed and allways been (and always wil be) on the filmroll doesn't mean that there is no cause and effect between the frames.

We agreed only 4D objects exist, and our brain considers a 4D slice out of that 4D object, Such a slice contains f.ex. The physical proper time display on the clock, at some distance from us. Another observer considers a different slice out of the 4D object, f.ex a slice where the clock displays another time. That's relativity of simultaneity. 4D universe means past, present and future is out there, but the observer considers a 4D slice being his present 'now'.

I agree 4D universe 'doesn't care' about simultaneity. But we, observers do care, because our mind considers successive time events, successive 'nows' and successive layers of 4D slices - what in everyday's common language would be called 3D world as it is 'now'.
Strictly speaking it is not necessay to even imagine a 4D slice out of the 4D object, but if we don't do it, then we can as well forget about dealing with special relativity's relativity of simultaneity. What would simultaneity mean if it doesn't refer to a 4D slice? If simultaneity doesn't refer to A 4D slice, then we cannot consider the display on the clock at some distance from me being a physical real clock display. What would be left then to deal with? That's why I asked in my post #186 << Maybe you consider ONLY your present own event as something physical, but not all the other events happening around you? Would that be logical?Is that what you have in mind? Let's hope not.>>

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

I read it twice, but I find it too heavy to digest. I'll get back to this when I did.

 

[jbriggs444]

I agree 4D universe 'doesn't care' about simultaneity. But we, observers do care, because our mind considers successive time events, successive 'nows' and successive layers of 4D slices

The universe does not care about simultaneity. But it does care about light cones.

You may think that you care about simultaneity and layers. But what you really need to care about is light cones. Light is fast enough that the difference is often negligible.

 

[tophatphysicist]

The universe does not care about simultaneity.

I'm not so sure about that. I have a hunch that the universe cares about those special sets of coordinates for which the special geometric features are always consistent with the laws of physics. There are special symmetries associated with those special coordinates, which includes special 3-D spaces related to particular world lines. Not every arbitrary set of coordinates satisfies this special relationship.

 

[jbriggs444]

I'm not so sure about that.

Your suspicions notwithstanding, why should the universe care whether I do my calculations in my instantaneous rest frame or yours?

 

[tophatphysicist]

Your suspicions notwithstanding, why should the universe care whether I do my calculations in my instantaneous rest frame or yours?

Nature wouldn't care about that, because our spaces are both special. I'm just saying that nature has selected out special frames for which the laws of physics work in a natural and special way. The laws of physics work in spaces like the ones below. Notice I'm talking about the spaces for which the photon four-fiber bisects the world line of an observer and his 3-D space.

 

[jbriggs444]

Nature wouldn't care about that

Right. Nature does not care about simultaneity. Simultaneity is a human invention.

 

[Dale]

You seem to be using the idea of causality in a different way, perhaps as a description of the related geometric patterns of bundles of 4-D fibers along the 4th dimension. You have already indicated that the universe is a 4-D object with everything already there. So, if the "future" part of the 4-D structure is already there, how do you now cause it?

Umm, I am using causality in the usual manner. I don't know why you think the dimensionality of the universe is relevant to causality.

My favorite example of causality in physics is Jefimenko's equations.

I'm not so sure about that. I have a hunch that the universe cares about those special sets of coordinates ...

Can you provide any evidence that the universe cares about any set of coordinates? I mean, something more peer-reviewed than your hunch.

From what I can tell nature doesn't care about any coordinates, inertial or not. Only we do.

 

[Dale]

I agree 4D universe 'doesn't care' about simultaneity. But we, observers do care

Yes, I agree.

 

[Mister T]

Correct, the dividing plane has zero tickness. But we can take a slice with slight non-zero thickness. That difference is the issue discussed.

Sorry, but I just don't see where the issue I'm thinking of was discussed.

If the slice has zero thickness it's two-dimensional. It it has some nonzero thickness, however slight, it's three-dimensional. I know a lot of things were said about 3D, and how it compares to 2D, but I don't recall seeing this discussed.