Time Dilation. The faster you travel the longer I have to wait for you to return?

ghwellsjr

Yes, that's because in Special Relativity, a given scenario is presented in the context of just one IRF, or if it isn't, calculations are made to eventually get it into a single IRF. Otherwise, it will be ambiguous and impossible to analyze.
I start with the IRF presented by the OP and make a graph corresponding to that IRF. Now in that graph, I calculate the spacing of the dots for each observer, including the stationary one, using the time dilation equation (not the Lorentz Transform). So for each observer/clock, I use the speed assigned by the OP to calculate gamma and gamma times speed. Then I space the dots along the time axis according to gamma and space the dots along the distance axis according to gamma times speed. The Lorentz Transformation is not used to create the data for the original scenario in its IRF, only the Time Dilation factor (gamma) and the speed are used.

You should not think of the blue vertical line with the blue dots as being associated with the time coordinate of the IRF anymore than for the other observer/clock. In another scenario, an OP might not have any observer/clock at rest in the IRF and so there would be no vertical line with dots in the defining IRF.
As K^2 pointed out, there is only one set of coordinates, clearly labeled and marked and providing grid lines so that the coordinates of any event can be easily determined. What you are calling coordinate time axes are not axes at all, they simply show how the Proper Time of each observer/clock advances as a function of the clearly labeled coordinate time

I could have numbered the dots to make it easier to see what time is on each clock but that would have been more work for me so I leave it up to the viewer to count the dots if they care what the Proper Time is at any point in the diagram.

The whole purpose of this exercise is to show that Time Dilation is the ratio of accumulated Coordinate Time to accumulated Proper Time and that it changes with each IRF but still everything comes out the same for anything that the observers/clocks can see, observe and measure.

Since you want to talk only in terms of coordinate time, what is your definition of Time Dilation?
If you want to see how the speed of light remains c with respect to the IRF even after you transform to a different IRF, I will show you a bunch of graphs illustrating this. Keep in mind once I set up the original scenario, I merely put in a speed parameter to get each of these different graphs. It is the super simple Lorentz Transformation calculation done on all the points (events) of the original graph that creates each new graph. (I do have to do a little more work to limit the scope of each graph to the significant area.) Since I can only upload three graphs in each post, I will continue this in a second post.

First. a repeat of the original scenario with a flash of light sent out by both observers each month according to their own clocks. The thicker yellow lines are sent out by the blue observer and the thinner black lines are sent out by the black observer.



You can note that during the first part of the scenario, each observer sees the other ones clock advancing by the same amount. For example, after 19 months for each observer, they are seeing the other observer at 11 months.

Similarly, during the last part of the scenario, each observer sees the other ones clock advancing by the same (but different than before) amount. For example, between blue's Proper Time going from 41 to 48 months which is 7 months, he sees 12 new flashes coming from the black observer and for the black observer between the coordinates of about 38 and 46, his clock advances by 7 months and he sees 12 new flashes coming from the blue observer.

Now for the next two graphs transformed at 0.5c and -0.5c:





If you care to count out how each observer sees the other ones time progressing just like I described earlier, you can count out the dots to see that it doesn't make any difference what IRF we use, the same information is present in all of them.

Continued on next post...

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ghwellsjr

Now I want to show three more IRF's. The first two are at a transformed speed where the speed of the two observers is identical for the first part of the trip (0.268) and for the last part of the trip (-0.268).



Note that since the speeds of the two observers are the same in these two IRF's for a part of the trip, their Time Dilations are also the same. Can you see that?



Now for one more IRF at an arbitrary random transformed speed of (0.35c) just to show that it doesn't have to be associated with anything in particular that is happening in the scenario and yet all the same information is present.



Each observer still sees everything identically to what they see in any other IRF. All measurements are identical. All observations are identical. But the Time Dilations are all different but still follow the same definition of being the ratio of accumulated Coordinate Time to accumulated Proper Time.
I appreciate your congenial attitude but you should understand that I'm not trying to minimize the information--it's already minimized. There is no more information from which to minimize.

All you are doing is heaping the same information presented in different ways onto the same graph and thinking that it is more information and then you think that I'm trying to minimize the information when I don't do that.

I could, if I really wanted to, develop a computer program that would allow me to transform a scenario into another IRF but instead of presenting the coordinates in a normal square pattern (like on graph paper), I could distort the axes so that the physical locations of the events would remain in the same physical places as in the original scenario and then overlay the two plots so that you don't see the events move to new locations but instead see the axes with their labels and grid lines in different locations. That's all that is done in a conventional Minkowski diagram except that usually the grid lines are eliminated forcing the viewer to mentally establish their locations. I just don't see any advantage in doing that.

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bobc2

Semifaded, by now you understand that it does not work that way. I will try to summarize for you the points of view that have been expressed.

First, since there is some interest in presenting the information in the most efficient manner, avoiding additional or redundant information, I'll just provide sketches of the three inertial frames that indicate how much clock time (proper time) is accumulated for each frame associated with the twin paradox scenario. Note that for the frame which represents the travelling twin's return trip, I have started his proper time reading at 21 months, since that is what that twin's clock was reading on arrival at the turning point. ghwellsjr wisely idealized the scenario to allow an instant turn-around. Thus, there is no lost turn-around time for the traveling twin's clock, and his clock time at the final meeting of the twins is read directly on the time scale of the chart. You can then compare that time to the clock time of the final meeting event shown on the stay-at-home's clock. Please credit ghwellsjr for the basic graphic, which I have simply copied from his screens and photo shopped a little.



Beyond that, ghwellsjr has taken this same approach with the addition of more information, particularly with his initial sketch charting the spacing of the proper times for each frame describing the scenario. As he has pointed out, you can compare directly on the stay-at-home frame the time increments between the three frames (illustrating the time dilation concept). This is a particularly good choice for those who like to avoid any inference about Minkowski's 4-dimensional space-time, which may not have been a motive of ghwellsjr's since I think he was trying to boil the presentation down to the simplest principles.

My embellishments to ghwellsjr's graphical presentation (see post #65) was intended to carry the picture into the context of the Minkowski 4-dimensional space-time picture. Of course you will decide if it is of any interest to you. You may have picked up on something of a controversial aspect on the special relativity topic.

There are those who feel that the 4-dimensional geometric interpretation of Minkowski should not be taken literally, because there may be other different interpretations of time dilation and length contraction besides Minkowski's (Lorentz Ether Theory--LET--is the most popular contender). Many physicists feel that special relativity theory does not select any particular one of these interpretations--so it is best to not slant presentations of special relativity (particularly on a forum that tries to avoid speculative ideas, i.e., just stick to fundmental observations and do not make more of these than are directly inferred). It is felt that discussion of these alternative interpretations of relativity should be reserved for the philosophy forum. Many of those who reject the physical reality interpretation of the 4-dimensional spac-time still embrace it as a valuable mathematical representation of special relatity that does not infer a physical reality.

Vandam and I may be the only members of the forum here who feel that the Minkowski geometric picture of special relativity directly refers to a 4-dimensional external physical reality (many refer to this as the "block universe").

However, we are not the only ones in the larger community of physicists who feel that the Minkowski 4-dimensional space-time picture should be understood as physical reality. Paul Davies, in his book "About Time" claims that most physicists hold this view, but I've never seen anything like a poll of physicists to back up his statement. Certainly there are many very prominent physicists who hold this view.

So, given these differing views it is not surprizing that you will find some tension among the posts on this forum. When it gets to the point of circular comments and personalizing the discussions, or too philosophical, the forum arbitrator will step in.

DaleSpam

No, there are many other block-universe sympathizers on the forums, including myself.

The distinction that you and Vandam have is that you are the only members that don't seem to realize that it is just an untestable philosophical interpretation of SR and not an unavoidable scientific deduction. In your fervor to promote a philosophical viewpoint you step way beyond what is scientifically justifiable. Most of the opposition you face is opposition to you and Vandam's overreaching assertion of an untestable philosophy, rather than opposition to the block universe concept itself.

bobc2

ghwellsjr, I was immersed in preparing my last post for Semifaded and by the time I got it posted I had to bail out here for an appointment. I'm anxious to get back to it. At a glance it looks like you have done a very nice job of presenting the kinds of details that further enhance the time dilation picture for the twin paradox scenario. I'm sure Semifaded will gain more insight from it. Thanks.

Vandam

As far as I can remember -at least a general impression I got- you have problems with block universe because you refuse accepting there are events out there, ready to be observed. For you, only your own now event is 'real'. Period. No wonder any discussion about the meaning of a mathematical number becomes problematic and can be considered philosophy...
If you think there are no pace-like events out there, ready to be observed (Ghwellsjr also literally said he is not interesed in the origin of observations), then not only Block Universe, but also Special Realtivity has to move to philosophy! The whole lot. And we then have to discuss what you mean by 'observers' and 'observing'. And we will definitely have to look what space and time cooridinates stand for. Even throw in some semantics.
You probably are too much influenced by QM. Do you believe the moon is out there if you do not look at it? Be carefull not to slide into solipsism. Solipsism is methaphysics, not physics. This is a physics forum. Einstein believed in an observer independent world, so it's fair the work in that context.
I think it might me necessary to go through a discussion of relativity of simultaneity again. I will show you that if you believe in an observer independent world, SR automatically leads to block universe. I might start a new thread on that (but not before next year..).

In the sketches below I show two time coordinate charts of two relative moving space travelers. Lorentz Tranformations, gamma, etc will give you the numbers. But physics is more than mathematics. More than just charts with coordinates. I show you where the observations making up the charts come from: 3D world sections through 4D block spacetime.

DaleSpam

You recall incorrectly. I have no problems with the block universe interpretation. I only have problems with your presentations of it.

Here is a good example. I have never posted anything remotely in support of solipsim, nor has anyone else that I noticed. I don't understand your weird penchant for labeling anyone who disagrees with you as a "solipsist".

And this is simply false. LET is an alternative interpretation of SR with an observer independent world that is not the block universe.

They are both interpretations of SR meaning that they lead to the same experimental predictions in all cases and therefore cannot be distinguished experimentally.

bobc2

Good point, DaleSpam. In my comments I should have made a distinction between those who are favorable to the block universe concept based on philosophical considerations vs. those who feel that block universe is directly implied as a requirement of special relativity. You are probably correct in recognizing Vandam and I as the only forum members who feel that block universe is a requirement of special relativity.

I understand the distinction you are recognizing. And certainly with a theory like special relativity there is potential for some to interpret special relativity under the influence of his philosophical bias rather than basing the interpretation on measured data.

But, I want to emphasize that Vandam and I feel this model is based correctly on physical measurements and theoretical predictions. I presented the theoretical motivation in my original post in this thread. No one has responded with a counter argument that would logically refute the logic I presented. Vandam and I have both presented examples of measurements that would validate the theory. We contend that is physics, not philosophy. However, some have drawn on their philosophical bias to refute the block universe.

I'm not suggesting you have based your analysis on philosophical bias, because you have pointed to LET as a theory that predicts the same outcome as Einstein's special relativity. Thus, one could not single out block universe as unique.

Nevertherless, here are a couple of points that influence me:

1) LET is a largely discarded (or at least, ignored) theory. Virtually all physicists doing work in relativity (especially the general case) do it in the context of a 4-dimensional geometry. Einstein acknowledged that without Minkowski's 4-dimensional concept he would have gotten nowhere with general relativity.

2) The Einstein-Minkowski picture of special relativity is foundational, whereas LET is ad hoc.

3) It has been pointed out (sorry I cannot give you a reference) that LET is manifestly incompatible with the experimental results of entanglement tests, whereas block universe can be analyzed as compatible with those results.

But, my main point here is that I maintain that the block universe is a concept which is an integral part of special relativity (not a separate theory), derived from the special theory of relativity and also supported by measurements. The philosophy of physics was a required course for our PhD curriculum. On the last day of the course our professor asserted that "...physics never has and never will contribute anything to the understanding of physical reality...." I've been leary of philosophers ever since.

So, you should not characterize my position as one based on philosophy.

I may be guilty of faulty logic in interpreting the theoretical and experimental results.

PeterDonis

Just to add some more thoughts to the discussion:

(1) If by "the block universe is integral to SR" you just mean "SR uses 4-dimensional spacetime to construct models", then of course nobody can dispute that. The disagreement, to the extent there is one, is about claims like "SR uses 4-D spacetime, so the block universe is what reality is really like".

(2) SR, as a physical theory, is wrong. It uses flat spacetime, but we know that spacetime is curved if there is any stress-energy present, and we know there is stress-energy present in the real universe. So we can't use SR, by itself, to justify claims about "what reality is really like".

(3) GR, as a physical theory, allows spacetime to be curved, and it also uses 4-D spacetime, so if we are going to argue that 4-D spacetime is "what reality is really like", we would do better to base such arguments on GR, not SR.

(4) However, there are formulations of GR, such as the ADM formalism, that view a 4-D spacetime model as a model of a 3-space "evolving in time". So the "block universe" is not the only possible interpretation of GR either.

(5) More importantly, though, GR, as a physical theory, is also wrong, because it doesn't include quantum mechanics. So we can't use GR, by itself, to justify claims about "what reality is really like" either.

(6) When we include quantum mechanics, we don't have a good theory (yet) that includes gravity. However, we do know one thing: quantum mechanics introduces an element of uncertainty that is not present in classical GR. And a key feature of GR (or SR) that is necessary to any argument that the block universe is "what reality is really like" is determinism. So when we include quantum mechanics, we can no longer argue that GR (or SR) leads us to the "block universe".

bobc2

Thanks for your very well reasoned response. I'll try to add in a couple of my points of view.

Then, in your mind what does the 4-dimensional space-time model represent?

We are interested first in understanding physical reality locally. Then, of course it must continue to be a part of the more general model.

Of course. It's just more logical to develop the local concepts of physics, then generalize them for the curved 4-dimensional universe.

On the contrary I feel that the ADM formulation with the foliations maintains a picture of a block universe. There may be complications, mathematically and conceptually, with regard to foliating in particular ways to accomodate certain different world line paths through the curved universe. I don't think it is necessary to get side tracked with special issues like black holes. We are just recognizing a simple fundamental concept for which we may not have all of the details worked out.

Block universe in the special or general form does not have to include the usual concept of causality as considered casually. Notice that with the block universe causality does not have the same physical meaning as it does in the time evolving 3-dimensional model. So, causality at the elementary particle level is not necessary for the physical description. This should be true with both block universe and QM. That's why the entanglement experimental results are consistent with the block universe model.

That is incorrect. That's one of the significant aspects of the block universe--it is not necessary to predict the future in every detail. And the future does not have to be determined in a way that includes both macro and micro properties of the universe. The universe is just all there--the arrangement of worldlines of particles did not depend on the evolving in time of the 3-dimensional worlds (various hyperplanes--or GR foliations) at the elementary particle level. However the block universe was created or put together (we avoid any discussion of that, avoiding obvious traps into philosophy and theology), the presense of forces and response to forces (causality) were built in as part of the design. It would not be necessary to enforce the macro patterns of worldlines all the way down to the elementary particle. But, the observation and operation of physical laws in the sense of an evolving 3-D world is an illusion. Although, a clever construction of the block universe could arrange the elementary particle worldlines so as to present an appearance of causality emerging from interactions at the micro level.

PeterDonis

A model, which works fine as an approximation in lots of situations.

That's an assumption about what "physical reality" is like. What if the true "physical reality" is not local?

It depends on what you mean by "block universe". Once again, if all you mean by it is "we can use 4-D spacetime as a model", then of course the ADM formulation is consistent with that. But the ADM formulation does not claim that a 4-D spacetime that "exists all at once" is what reality "is really like".

Why not? Both models use the light cones to determine which events are causally connected and which are not. You're going to have to elaborate on what you think the "physical meaning" of causality is if you think it's something more than just the light cone structure.

Why not? I don't see this either.

Huh? That's the whole *point* of the "block universe" as a claim about "reality" as opposed to just a model. It claims that the entire 4-D spacetime "exists all at once". That means a single self-consistent solution to whatever physical laws determine the 4-D spacetime structure is what "exists". If that doesn't include every detail, then it isn't a well-defined 4-D spacetime structure.

The word "future" doesn't have a well-defined meaning here. You should just say that the entire 4-D spacetime exists, period. But that 4-D spacetime has to include all "macro and micro properties"; otherwise what are you saying "exists"?

But it does depend on whatever physical laws determine the 4-D solution. In SR, that 4-D solution is flat Minkowski spacetime, period. In GR, the 4-D solution is determined by the Einstein Field Equation plus boundary conditions. The 4-D solution is "just all there" in the "block universe" view, but that doesn't mean it isn't determined by laws. The laws don't "act in time", but they still act.

You're also ignoring physical laws. See above. Physical laws are not "traps into philosophy and theology". They're the only justification for adopting any kind of viewpoint like the "block universe" in the first place. SR and GR are physical laws.

Sure, they're part of the laws; in this case, the laws that determine the stress-energy tensor, including whatever additional field equations (such as Maxwell's Equations) are needed to fully specify the 4-D solution for the stress-energy tensor.

This makes no sense. If you don't do this, you don't have a 4-D solution, hence you don't have a "block universe". Particle worldlines are part of the solution.

On the "block universe" view, yes, you could say this; but it would be very misleading if it induced people to draw the additional conclusion that there are no physical laws operating at all. As I said above, that is not at all the case.

As I said above, the elementary particle worldlines *are* arranged; they are determined as part of the 4-D solution. You can't just arbitrarily specify them; they are determined by the physical laws.

Also, you're again misunderstanding what "causality" means. In the 4-D spacetime view, causality just means the 4-D spacetime, as a geometric object, has a light cone structure, which determines whether any given pair of events is causally connected or not. That's all part of the 4-D spacetime solution; if you don't have it, you don't have a "block universe".

bobc2

Sorry to not respond to you, PeterDonis. I just spent considerable time responding to each point in your last post. However, the PF program timed out, and when I responded to the request to log back in I was shut out and all of my text was lost. But, I think we have both expressed our points of view pretty well.

At the end of my post I suggested we terminate our comments relative to block universe. Once you start getting into some of the implications of block universe it can get quite controversal and eventually get way too far out into the weeds. I'm not sure if it is a good idea to try again to respond to your post. If Semifaded and others here wish to see my response, I would be glad to oblige. But, I suspect there would be relief to see an end to this discussion.

You have presented an excellent summary of the main objections to be brought up against the block model (as well as some of ghwellsjr and DaleSpam's inputs). I think it is O.K. for us to agree to disagree on this subject.

Now, I still need to go back and look at ghwellsjr's latest nice graphs.

Vandam

(Sorry, I'm a bit late with this post.)
I think what Bob tries to convey is that Block Universe not only embraces deterministic but also indeterministic processes.
If all of a sudden a particle pops up 'out of nothing', the mathematics can only give us probabilities. But the particle popping out of nothing is already part of 4D spacetime. Causality is not necessarily a feature of Block universe. I guess you can have a block universe with ONLY indeterministic processes, but that would be really a weird one. Actually there might indeed be or a lot weird block universe bubbles out there, but in those Block universes 'life' as we now it might not work. That's probably why we are stuck in our Block universe.
In a fully deterministic Block universe 'causality is nothing more than the glue that holds the events together. Causality is not the 'cause' of events to happen. In block universe causality is only a result of first seeing A, and then B. (I think it was David Hume 250 years ago that brought that up). I do not know why our block universe is what it is so that we in the successioj of 3D cuts perceive causality and physical lanws. That discussion would indeed be a philosophical or theological issue... at this stage: maybe in a hundred years physics will have an explanation (hopefully thanks to Bob's and my, and many other's perseverance).
The interesting thing in physics is that our block universe apparently does not contain only fully deterministic relations (on a very small scale i.e). That's a great interesting discovery if it turns out to be correct... But it does't refute Block universe. On the contrary: Bob and I think QM proves that block universe is correct. But whether QM is compatible with Block universe or not is way off topic here (actually I am not that much involved in QM, I prefer to leave that topic to Bob). But SR's relativity of simultaneity = block universe. That's a good start.

PeterDonis

Which means that unless you *know* all the events at which particles "pop out of nothing", you don't have a well-defined 4D spacetime. From the 4D viewpoint, a particle "popping out of nothing" just means it has a worldline that doesn't extend all the way from minus infinity to plus infinity: instead it appears at some finite place. But in order to properly define a 4D spacetime, you have to define *all* the worldlines, including those that happen to start at a finite place (if there are any).

Sure it is; a worldline that happens to appear at a finite place still has to keep within the light cones along its entire length.

But first seeing A and then seeing B is still governed by laws. They may be probabilistic laws, but they're still laws. And the term "first" isn't really appropriate here, because the "block universe" viewpoint says that the entire 4D spacetime just exists, it doesn't evolve in time. So really "causality" in a block universe means that event A has a particular geometric relationship to event B. That's true: the 4D spacetime has a light cone structure even if some worldlines don't extend all the way from one boundary to the other. See above.

Nor does it *prove* it. Just following this statement you switch your ground, from this...

...to this...

QM being compatible with the block universe is very different from QM proving that the block universe is correct. I'll agree, for purposes of argument here, that QM can be made compatible with a "block universe" interpretation (though there are still lots of issues with doing that), but that does not show that QM *requires* a block universe interpretation. This is the same argument we've had about your claim that relativity of simultaneity requires a block universe; it doesn't. It's compatible with a block universe, but it doesn't require it.

Not if nobody except bobc2 agrees with it.

DaleSpam

I suspect that many of the mainstream physicists you refered to earlier may also fall into the same camp.

The problem is that those exact same measurements would also validate LET. They do not allow you to choose between the two on the basis of the proposed experiments. In fact, there is no possible experiment since both use the Lorentz transform for making all of their experimental predictions. Therefore the only possible criteria to choose one over the other is philosophical.

Agreed, but this is peer-pressure, not empirical evidence.

Agreed, but this is philosophy, not evidence.

This is false. Any result which would invalidate LET would also invalidate the block universe since both make all of the same predictions.

But your position is one based on philosophy, that is all that it possibly can be based on since it cannot be based on evidence.

If you prefer, you can say that it is based on aesthetics rather than philosophy. I am not sure there is any difference, but maybe "aesthetics" doesn't carry the negative connotation you have of "philosophy". I am certainly willing to use a different word if you feel that it would be less objectionable.

DaleSpam

Both of these are false. Both QM and the relativity of simultaneity are compatible with LET as well as the block universe.

Vandam

Please explain how relativity of simultaneity is compatible with LET.
That's a contradiction in terms.
Relativity of simultaneity is compatible with the Lorentz transformations. But not with LET. LET does not give a physical explanation of the LT (Lorentz admited this).
SR does. That's Einstein's contribution.
See also my post:
http://www.physicsforums.com/showpos...9&postcount=14