## Why is relativity so hard to learn?[1]

Discussions on the philosophical foundations, assumptions, and implications of science, including the natural sciences.

### Re: Why is relativity so hard to learn?[1]

Hi All,

Jorrie wrote:PS: Dave_O, thanks for you patience, but the floor is now yours... ;)

I got lost when you rotated the Epstein Graph. I thought it made sense when the X-axis was depicted as Velocity being 0.6 speed of light and the Y-axis was depicted as proper time (Clock Dilation) or 0.8 Time which translates as: "60% Speed of Light = 80% Clock Rate".

When you rotated the Graph, it seemed to imply that one could exchange velocity through Space with velocity through Time. Or in other words, both X and Y axis represented velocity. This is what I wanted clarification about.

Now I've heard many Relativists say virtually this exact same thing but never understood it. Specifically.. how one could have variable Velocity through Time.

It is reasonable to suggest that given a race between two vehicles that started at the same point, that if one has a higher velocity, then there would exist a growing spatial separation between them. If both hold their respective rates then they can never meet again until one speeds up.. or the other slows down. Something has to change for them to meet again at the same place in Space and Time somewhere ahead.

But the same should apply if one accepts velocity through Time. That if one has a higher velocity through Time, that a temporal separation should emerge. That this separation must continue to exist until something changes or one speeds up through Time or the other slows down through Time, in order for them to meet again at the same place in Space and Time somewhere ahead.

So.. if it was true that velocity was exchangeable between Space and Time, then I would expect that the Alice and Bob, when they reconnect after Alice's trip, would be equally caught up with each other on both Place and Time. That the rules for Distance should also apply to the rules of Time.

Thus, one would find this exchangeable velocity concept acceptable if Alice's clock matched Bob's clock when they rejoined each other after her trip. But this appears not to be the case in reality.

The only logical conclusion is that Alice's clock wasn't really measuring Real coordinate Time. That her clock was measuring something other than Velocity through Coordinate Time.

I've heard a few times that some have hypothesized that Time is a form of Entropy. Perhaps velocity has physically changed the Matter-Energy composition of Alice and reduced her Energy Functions. Thus clocks run slower for Alice and she ages less that Bob, due to a real physical change in her physical entropy because of her higher velocity.

If this is the case, then clocks measure Entropy and not Time. That Alice and Bob both always maintained the exact same Velocity through Time (Speed of Light).. but she was operating at a lower energy level while her velocity through space was greater than Bob's.

So it's not so much about the Math of Relativity as much as the interpretation of what is Physically happening. If Relativists were to swap terminology from "Proper Time" to "Proper Entropy" (or some such equivalence) then the true concept of "Time" may be much more obvious. Simultaneity is easy to understand given the Finite Speed of Light.

I predict that within the next decade or two, that Engineers and Physicists will create a device called an Ansible (in current science fiction literature). A device that exploits Entanglement for instantaneous two-way communication over any distance.

If we could employ such a device with our Alice and Bob scenario, we would discover that Alice and Bob can communicate instantly throughout her Journey. But.. she would perceive Bob is talking at a higher pitch and more words per minute than usual (like a sped up recorder), while Bob would perceive just the opposite and hear Alice like a slowed down recorder.. all the while holding a real time conversation.

This is in direct violation of the Premise that BOTH would perceive the Other as being slower in communication rates than themselves. I find this current Premise logically annoying because it doesn't add up.

Anyway, I wasn't going to comment again on this thread as the Goal was to teach Relativity in a manner easy enough for the common Layman to understand (I thought). I didn't want to confuse this endeavor with my personal observations. On the other hand, I'm not sure that the average reader received much enlightenment from this thread as is (I may be wrong).

In simple terms one could have just said: "Alice took off at really high speed and Bob was stationary. When Alice returned back to Bob.. she had aged less than Bob during her trip".

All the Graphs and Charts (and English) never clearly explained.. WHY.

Does raw speed actually slow down "Time".. or just simply stretch-reduce energy consumption over distance? Do Clocks measure Time or Energy?

Ok, bedtime for me.. back later.

Best Regards,
Dave :^)

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### Re: Time to consider aging.

Clocks measure time experienced (i.e. aging) on the way to the future. That's why biological, mechanical and atomic clocks work equally well.

Velocity changes the orientation (i.e. angle) of a particle's worldline with respect to proper time, thus its aging component with respect to an observer's rest frame.

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### Re: Why is relativity so hard to learn?[1]

Not bad. If time is slowed in a Black Hole, does that mean it has a lower velocity through Time than myself? And if so, why doesn't it disappear into my past? It would seem that a Black Hole and myself share the same Velocity forward in Time to co-exist simultaneously.

Again.. my issue is relating a slowed clock with a Temporal Velocity.

Best wishes,
Dave :^)

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### Re: Why is relativity so hard to learn?[1]

Hi Dave, glad to have you back, because you represent a class of amateur relativist that will make a good "case study" of where and why we relativists fail in our efforts to make proper relativity understandable.

Dave_Oblad » 11 May 2017, 14:42 wrote:When you rotated the Graph, it seemed to imply that one could exchange velocity through Space with velocity through Time. Or in other words, both X and Y axis represented velocity. This is what I wanted clarification about.

Now I've heard many Relativists say virtually this exact same thing but never understood it. Specifically.. how one could have variable Velocity through Time.

The first point that I want to make is that "velocity through time" is an oxymoron - it simply does not make any sense. In simple terms, velocity is a spatial displacement, divided by the observed time that this displacement took. It goes (almost) without saying that both measurements must be made in the same reference frame.

When space and time are combined into spacetime, as relativity requires, it starts to make some sense to talk about velocity through spacetime. If we express a spacetime displacement as a distance (which we can do by multiplying an observed time interval by the universal constant 'c'), then we can obviously take a spacetime displacement and divide it by the time that it took to achieve that displacement. But we have just done away with time! So where do we now get it from?

The obvious answer is that we haven't done away with time - we still had to take the time interval as recorded by some or other clock and multiplied that time by 'c'. In relativity, the question is always, which clock? A reasonable answer is that it should be a clock that has done that spacetime displacement, physically. After all, such a clock would be present at the start and the end of that spacetime displacement. For that clock the two events happen at the same place, but not at the same time (obviously). Their separation in time is called the invariant spacetime interval and it is the closest thing that we have to 'absolute time'.

But Dave, I know that this standard relativistic argument is nor satisfactory for you. You desperately want there to be an absolute frame of reference where you can say: "this clock is moving relative to that 'absolute frame' and hence it does not measure an absolute time - somewhere there must be a clock (or set of clocks) that is/are stationary in this absolute frame and must record the absolute time.

Luckily, there is no such clocks and no such frame. If there was, we would have been in trouble - like that we would not have been able to calculate/predict what we are observing in the dynamic world around us. We can discuss the reasons why we would be in trouble later, but please first try to understand exactly what I have said before that - and feel free to ask about it.

The whole Epstein diagram and my space-propertime diagrams are based on the relativistic premises that I stated. The same old premises, just (maybe) stated somewhat differently. The relative orientation of the Blue and Red axes, having the same lengths, is an application of the stated premises.

But please, get rid of the notion that time has a velocity!

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### Re: Why is relativity so hard to learn?[1]

Dave_Oblad » 11 May 2017, 19:48 wrote:Again.. my issue is relating a slowed clock with a Temporal Velocity.

Sorry for chirping in Dave, but please also get rid of the notion of a "slowed clock", at least in the SR environment. One should also get rid of that idea in GR, but it is not so easy to say why... ;)

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### Re: Back to the Future (displacement).

Dave_Oblad » May 11th, 2017, 1:48 pm wrote:If time is slowed in a Black Hole, does that mean it has a lower velocity through Time than myself? And if so, why doesn't it disappear into my past?

I don't want to distract too much from Jorrie's project. But to my point, gravitational time dilation would mean that objects in that field age more slowly. That's quite distinct from future displacement (i.e. going to the future*). The black hole doesn't disappear as an object (though it certainly does visually) because its worldline is future directed (as with all objects in the Standard Model).

However, objects observed falling toward a black hole's event horizon will be found to age in every respect more slowly, even as they continue to appear in the same future as the distant observer. At the event horizon, all aging ceases and so no further signals will be forthcoming. All the information content of the falling system is however, thought to persist there, indefinitely into the future.

*"Future" should be defined as any occurrence of the universe older than it is now (by the best acknowledged cosmological measures). This, as opposed to "age" or more specifically "elapsed proper time", which is a quantity of recognizably periodic changes, such as the frequency of an atomic process (e.g. decay of a quantity of radioactive isotope) or anything configurable as a "clock".

Dave_O wrote:It would seem that a Black Hole and myself share the same Velocity forward in Time to co-exist simultaneously.

Yes. That's future displacement! By contrast, I would translate your "velocity through time" as "relative aging", which compares the aging of two observables.

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### Re: Why is relativity so hard to learn?[1]

Hi All,

I've been searching this site for hours and could find no statement by Jorrie that was meant to mean that our Velocity through Time is anything other than the Speed of Light. It's not variable.

It was Don Lincoln that repeatedly said that there is only one velocity through Space-Time and that is the Speed of Light. That Speed through Space-Time is a composite Velocity of both Time and Space. That an increase in Velocity through Space is a decrease in Velocity through Time.

For example:
Don Lincoln wrote:the upshot is that you can show that all objects move through spacetime at a single speed, which is c. Thus an object travelling through space at the speed of light has no residual motion through time. And an object that is stationary in space is moving through time at c.

http://www.sciencechatforum.com/viewtopic.php?f=2&t=23451&start=60#p316587

I thought Jorrie had said the same thing somewhere, but I can't find such and thus Jorrie and I agree that the Velocity through Time is a constant for all parties, regardless of their respective Velocities through Space.

Thus, such a stance comes at a price: That Clocks don't really measure Real True Time.

This came up several years ago and I posted a graph like the one below:

Time and Space, Alice vs Bob

Per the Graph above, we see at the bottom that Alice and Bob are co-located in Space-Time, neither have any Velocity through Space, both share the same Velocity from Past to Future, call this the Speed of Light through the Vertical Temporal Axis. Both have synced their Clocks. Then Alice takes off through Space at the bottom Blue line and returns back stationary with Bob at the upper Blue Line. They notice that Alice's Clock has fallen behind Bob's Clock. But their Velocity through Real Time from Past to Future was always identical.

Thus, how can we defend the Idea that Alice's (or any) Clock actually measures Real Time? True, we build them to show a correlation with Time, but all Clocks are subject to alteration by Velocity through Space.

Why? Perhaps Atomic Frequencies drop due to Spatial Velocity (stretched over distance) or Atomic Energy levels are reduced due to Speed. Granted, there is a direct correlation between Aging and Clocks and the travelers perception of Time Passing is consistent with their Clocks.

But there exists only One Real Time that marches forward at a Constant Rate (Speed of Light) for everything, regardless of what their Clocks are doing.

This caused some confusion on my part earlier with the Rotation of an Epstein Diagram. That rotation seemed to imply that we could swap our Velocity through Space with our Velocity through Time. That kinda messed with my head when I believed Jorrie was firm that we only have one Velocity through Time.

Anyway, I'm just bothered by the act of mixing True Time with what Clocks measure, even when it looks like Clocks measure Time.

Why this distinction between True Time and what Clocks measure? Because that would define Space-Time as just 4D Space.

I expect that this distinction between Real Time and Clock Time is covered by the term "Proper Time" for Clock Time in Relativity.

As long as we accept that the Arrow of Time is a Constant Velocity though Real Time.. then it's Time that I shut up now.. lol.

Jorrie wrote:please also get rid of the notion of a "slowed clock", at least in the SR environment.

Sorry Jorrie, but that feels too much like denying the obvious. If Alice's Clock fell behind Bob's Clock during this test, then her clock had to be running slower than Bob's.

Ok, I think I get the gist of what you are trying to teach: Alice's clock didn't slow down, but her trip took her through a different (shorter) path through Time. I'll have to consider this concept and see if I can find any obvious flaws that jump out at me (assuming I interpreted you correctly).

Meanwhile..

Would this be a good time to solidify what a "Frame" actually is and how it works?

Regards,
Dave :^)

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### Re: Back to the Future II

Don's comment, while popular among physicists, lacked qualification. That's why Jorrie immediately attempted to provide some.

To say that an object moving at speed c has "no residual motion through time" clearly contradicts the fact that all light travels to the future! Thus, we see images of the way things were. So, what Don meant was that objects moving at speed c are fully "time dilated", which is a confusing way of saying they don't age. But by conservation of mass-energy, everything still moves to the future (allowing for changes in form).

Note that objects falling into a black hole's event horizon, age more slowly until they stop aging on the horizon. That coincides with their reaching speed limit c!

Why is Relativity so hard to learn? A big part of the problem is ambiguity of terms such as "time", which in this case, is resolved by making the distinction between "future displacement" and "aging".

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### Re: Why is relativity so hard to learn?[1]

I think the word "aging" triggers faulty intuitions about what is happening. Better to say that the observer sees that the separation between events increases when observing another frame that is moving at high relativistic velocity or is near a BH event horizon. No one, within the spacetime structure of their own frame, is aging more slowly. You will still be emitting a little groan when you are 80 and getting out of a chair.

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### Re: Entering Old Age

BiV wrote:I think the word "aging" triggers faulty intuitions about what is happening. ... No one, within the spacetime structure of their own frame, is aging more slowly.

Agreed. That's why "aging" is given more specifically as "elapsed proper time".

Inasmuch as I define "Future" as "any occurrence of the universe older than it is now", I refer to the total elapsed time of the rest frame of the cosmic background radiation. While that "cosmic frame" is also relative*, it has the convenience of being universally accessible (at least by calculation) and no observer who comes to rest with the cosmic frame will have an older age (more accumulated elapsed time) than it has. That is: Nothing in the universe is older than the universe.

*observers in motion relative to the cosmic frame will see it aging slower than they are. However, the acceleration required to enter the cosmic frame will always cause the observer to see the cosmic frame advance in age more than enough to compensate (thus surpassing the observer's aging).

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### Re: Why is relativity so hard to learn?[1]

I think that's confusing for some readers. They would expect any significant speed WRT to the CMB to blueshift the CMB (i.e. the news your eye is getting from the quark-gluon plasma in the very early universe, as it enters the Epoch of Recombination and hydrogen starts to form) and thus indicate less separation between events (EMF wave peaks) and therefore a faster "aging" universe. I think there's a problem (for my sense of things anyway) with giving photons the "cosmic frame," a frame which for them yields a universe that is instantaneous and has zero separations. I guess my bias is that only matter gets to have its own frame, because only matter can observe anything else and do so within a genuine spacetime structure. "Energy," as found in the CMB, is really just a tale of two events: emission, and absorption. (or maybe that's just one event, heh heh...nudge nudge....) Can I hang a frame on that? I know I'm missing something, because the rest of your post seems valid.

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### Re: Back to the Future II

Faradave » 12 May 2017, 16:40 wrote:To say that an object moving at speed c has "no residual motion through time" clearly contradicts the fact that all light travels to the future! Thus, we see images of the way things were. So, what Don meant was that objects moving at speed c are fully "time dilated", which is a confusing way of saying they don't age.

Hmm... FD, while this has the right 'ring' to it, it can be relatively confusing as stated. Even if you take photons as "objects", they only 'move at c' and 'into the future' relative to reference frames. Light itself has no 'future into which it can move' and has no 'age' or a concept of traveling through space, even in principle.

I would rather qualify it as "there is an event (1), when a photon is emitted and another event (2), when that photon is absorbed. In all inertial frames, event (2) happens after event (1) and in that sense photons 'move into the future' of all inertial frames. It is probably the same thing as what you said, but perhaps less susceptible to misinterpretation.

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### Re: Entering Old Age

Faradave » 12 May 2017, 18:27 wrote:Inasmuch as I define "Future" as "any occurrence of the universe older than it is now", I refer to the total elapsed time of the rest frame of the cosmic background radiation.

Again, I think you should specify this better in order to avoid confusion. I think I (and some others) may read this (correctly?) as meaning: the total elapsed time 'recorded' since the CMB emission event, by a massive particle that has always seen the CMB radiation as isotropic, until "now", whatever 'now' may mean in this context.

I think that by going down this line of discussion, we may make SR even harder to understand. I prefer to just stick to inertial observers moving and accelerating relative one another at this stage. Even that seems to be hard enough to explain, never mind to understand.

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### Re: Why is relativity so hard to learn?[1]

Dave_Oblad » 12 May 2017, 14:23 wrote:Ok, I think I get the gist of what you are trying to teach: Alice's clock didn't slow down, but her trip took her through a different (shorter) path through Time. I'll have to consider this concept and see if I can find any obvious flaws that jump out at me (assuming I interpreted you correctly).

Now this is a sensible line of thought Dave! Just take into account that it is only true because Alice is the one who has changed spacetime structure, i.e. has accelerated somewhere during the process under consideration. There are a few other caveats as well, but this is the essence of my preaching. ;)

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### Re: Back to the Future II

Faradave » May 12th, 2017, 9:40 am wrote:
To say that an object moving at speed c has "no residual motion through time" clearly contradicts the fact that all light travels to the future! Thus, we see images of the way things were. So, what Don meant was that objects moving at speed c are fully "time dilated", which is a confusing way of saying they don't age. But by conservation of mass-energy, everything still moves to the future (allowing for changes in form).

I agree that, "All light travels to the future." Or, you could say all light we can see is coming from our past. From the perspective of light, emission and absorption are simultaneous events so light "travels" only in the present. Any object remote from our position in space is in our past so we can only send light signals to the past but, looking at it from the receiving end, the light we see is coming from our future.

I find that this point of view simplifies SR enormously even though it requires a definitely non-Newtonian understanding of time..
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### Re: Why is relativity so hard to learn?[1]

BurtJordaan » May 11th, 2017, 2:34 pm wrote:
The obvious answer is that we haven't done away with time - we still had to take the time interval as recorded by some or other clock and multiplied that time by 'c'. In relativity, the question is always, which clock? A reasonable answer is that it should be a clock that has done that spacetime displacement, physically. After all, such a clock would be present at the start and the end of that spacetime displacement. For that clock the two events happen at the same place, but not at the same time (obviously). Their separation in time is called the invariant spacetime interval and it is the closest thing that we have to 'absolute time'.

" We still had to take the time interval as recorded by some or other clock and multiplied that time by 'c'."

That doesn’t look right. A time interval multiplied by ‘c’ (300,000 km/ sec) would give you a distance.
How about taking the time interval measured by the “away” clock plus the distance as measured by the stationary observer times 1/c? That should give you the arrival time as observed by the stationary observer.
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### Re: Why is relativity so hard to learn?[1]

bangstrom » 13 May 2017, 12:10 wrote:
BurtJordaan » May 11th, 2017, 2:34 pm wrote:We still had to take the time interval as recorded by some or other clock and multiplied that time by 'c'.

That doesn’t look right. A time interval multiplied by ‘c’ (300,000 km/ sec) would give you a distance.

That's what a spacetime diagram is: distance plotted against cT, which is also distance, just rotated by 90 degrees.

How about taking the time interval measured by the “away” clock plus the distance as measured by the stationary observer times 1/c? That should give you the arrival time as observed by the stationary observer.

Nope, won't work in relativistic spacetime. Normally, you would need the Lorentz transformation, but I haven't mentioned it in this thread, because you can just look at a space-propertime diagram and read the time off directly. This is also what Epstein diagrams illustrate - it visualizes the process of the Lorentz transformation.

My method is just an extension of the Epstein diagram.

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### Re: Why is relativity so hard to learn?[1]

BurtJordaan » May 13th, 2017, 9:10 am wrote:
That's what a spacetime diagram is: distance plotted against cT, which is also distance, just rotated by 90 degrees.

Yes, cT is a distance value but, if you are looking for Alice's arrival time at most distant point from the perspective of the stationary observer, Bob. You are looking for a time value. Bob's "non-rotated" distance is known from the start.
BurtJordaan » May 13th, 2017, 9:10 am wrote:
How about taking the time interval measured by the “away” clock plus the distance as measured by the stationary observer times 1/c? That should give you the arrival time as observed by the stationary observer.

Nope, won't work in relativistic spacetime. Normally, you would need the Lorentz transformation, but I haven't mentioned it in this thread, because you can just look at a space-propertime diagram and read the time off directly. This is also what Epstein diagrams illustrate - it visualizes the process of the Lorentz transformation.

My method is just an extension of the Epstein diagram.

Yes again, Alice's clock time is Lorentz shortened as one can calculate. Or, as the diagram illustrates, but Bob sees Alice reach the turnaround point at Alice's time plus the time interval of Bob's distance times 1/c.
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### Re: Lighting the Way

Jorrie, your restatements of my comments above seem correct. If they are more understandable to others, great!

Braininvat wrote:They would expect any significant speed WRT to the CMB to blueshift the CMB

Yes. There would be Doppler blue shift in the direction of motion and Doppler red shift in the opposite direction (i.e. in the rear view mirror). In the rest frame of the CMB, an observer would find isotropic red shift attributable to cosmic expansion. I consider that to be the rest frame of the universe.

I agree that photons have no inertial frame in that the proper time and forward spatial coordinate become indistinguishable (i.e. they collapse together in that velocity "rotation"). And you recall that I interpret photons differently because of that. I'm not intending to steer this thread in that direction. Interpreting light however, remains one of the reasons relativity is so hard to learn. Epstein was utterly flummoxed by it.

bangstrom wrote:I agree that, "All light travels to the future." Or, you could say all light we can see is coming from our past. From the perspective of light, emission and absorption are simultaneous events so light "travels" only in the present. Any object remote from our position in space is in our past so we can only send light signals to the past but, looking at it from the receiving end, the light we see is coming from our future.

I agree with the first part. Absorption events always occur in an older universe (i.e. in the future) than emission events. That's true regardless of how a light quantum may interpret its own trajectory.

Any real observer who leaves the rest frame of the CMB will, upon returning to it, find that the CMB has aged more than the observer. That's just restating the twin paradox. To my mind, that means the observer bypassed some of the time experienced by the CMB (i.e. the universe). At speed limit c, light will have bypassed all of it. But the light quantum still ends up displaced into the future, just as it is displaced spatially. The ratio of those displacements defines c.

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### Re: Lighting the Way

Faradave » 13 May 2017, 20:47 wrote:In the rest frame of the CMB, an observer would find isotropic red shift attributable to cosmic expansion. I consider that to be the rest frame of the universe.

Careful with the wording - neither the universe, nor the CMB can have an inertial rest frame, in the sense that we are talking about here. The best we can do is to say that an inertial observer, so positioned that the average temperature of the CMB is the same in all directions (isotropic), can set up an inertial frame in the immediate vicinity. The problem is that for every new location, it requires a different inertial frame, and these frames are all moving relative to each other. Even in a spatially flat, but expanding universe, there is no universal inertial reference frame.

FD wrote:Any real observer who leaves the rest frame of the CMB will, upon returning to it, find that the CMB has aged more than the observer. That's just restating the twin paradox. To my mind, that means the observer bypassed some of the time experienced by the CMB (i.e. the universe).

In the light of my first remark, this does not make much sense. To me it also looks too much like sneaking in an absolute time (or at least may be interpreted by beginners as such). The whole picture does not fit the SR/GR concept of 'only local inertial frames are possible'. Rather keep it simple - GR and cosmology should not concern the beginner until SR is mastered.

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### Re: Location & Locomotion

BurtJordaan wrote:neither the universe, nor the CMB can have an inertial rest frame, ... The best we can do is to say that an inertial observer, so positioned that the average temperature of the CMB is the same in all directions (isotropic), can set up an inertial frame in the immediate vicinity. The problem is that for every new location, it requires a different inertial frame, and these frames are all moving relative to each other. Even in a spatially flat, but expanding universe, there is no universal inertial reference frame.

That's an interesting concern, as it forces us to address coordinate choices. Let's consider an expanding earth as a mapped* version of the balloon analogy for the expanding universe.

If you are located at 0° (prime meridian) on the equator and the earth increases volume by 25% did you move? Your coordinates are the same (but they may have gained measurable precision). Granted you are now more separate from other mapped locations (from say 10° on the equator) than you were before. If we define motion as changing location over time, you aren't moving as the surface expands. If we define motion as changing separation over time, you are. Motion is of course, still relative but in this case, relative to the map.

In view of the fact that universal speed limit c does not apply to the rate of recession (due to cosmic expansion), it would seem that relativity adopts the 1st definition of motion as changing location over time (strictly, "locomotion").

*in this case, by conventional latitude and longitude. I'm not sure how the cosmos is mapped, but I'm of the impression that a similar means (spherical coordinates) is used.

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### Re: Location & Locomotion

Faradave » 14 May 2017, 17:33 wrote:*in this case, by conventional latitude and longitude. I'm not sure how the cosmos is mapped, but I'm of the impression that a similar means (spherical coordinates) is used.

However we decide to 'map' it does not change the physics, but for convenience, we use comoving coordinates, which may resemble spherical coordinates, but they are actually quite different. Out best information today is that the universe is spatially flat, but spacetime is curved - as evidenced by the galaxy recession rates that we observe.

Curved spacetime in flat space can be loosely imagined (in 2-D) as a straight spatial axis, but the worldlines are not straight - they are either converging or diverging relative each other. Our universe is of the latter type and we can have both your "changing location [spatial coordinate] over time" and "changing separation over time" present. The prior is limited to 'c' and the latter is unlimited, because it is not 'movement through space', but rather just a "stretch" of the spatial coordinates. In the light of this, you should reconsider your point.

To go into this fully is far too advanced for this thread, so I suggest you ask a question about it in Astro/Cosmo.

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### Re: Lighting the Way

Faradave » May 13th, 2017, 1:47 pm wrote:
Any real observer who leaves the rest frame of the CMB will, upon returning to it, find that the CMB has aged more than the observer. That's just restating the twin paradox. To my mind, that means the observer bypassed some of the time experienced by the CMB (i.e. the universe). At speed limit c, light will have bypassed all of it. But the light quantum still ends up displaced into the future, just as it is displaced spatially. The ratio of those displacements defines c.

Defining c as a ratio of displacements impresses me as a far better understanding of c than defining c as a speed of any kind.
bangstrom
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### Re: Lighting the Way

BurtJordaan » May 14th, 2017, 1:03 am wrote:
In the light of my first remark, this does not make much sense. To me it also looks too much like sneaking in an absolute time (or at least may be interpreted by beginners as such). The whole picture does not fit the SR/GR concept of 'only local inertial frames are possible'. Rather keep it simple - GR and cosmology should not concern the beginner until SR is mastered.

The CMB is an absolute of time and it is successfully used as such in cosmology where the error bars are in billions of years. The total mass and distribution of the stars was Ernst Mach’s universal inertial frame and it remains the inertial frame in which all local inertial frames are embedded. An isotropic universe requires a global inertial frame of space and time.

The concept of 'only local inertial frames are possible’ assumes the caveat ‘whenever accuracy is required.’
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### Re: Lighting the Way

bangstrom » 15 May 2017, 00:16 wrote:The CMB is an absolute of time and it is successfully used as such in cosmology where the error bars are in billions of years. The total mass and distribution of the stars was Ernst Mach’s universal inertial frame and it remains the inertial frame in which all local inertial frames are embedded. An isotropic universe requires a global inertial frame of space and time.

The concept of 'only local inertial frames are possible’ assumes the caveat ‘whenever accuracy is required.’

The CMB frame is only a useful when we study the universe at large, where we average things out. There are actually parts of the universe (matter in large voids) that are older than the 13.8 Gyr of the average universe. To even view the CMB or the universe at large as useful inertial frame is a fallacy, because it stretches over significantly curved spacetime and will always be. Inertial frames need flat spacetime.

Also, think about the problems we would have had if the CMB-frame somehow defined an absolute space and time. Whenever we then wanted to calculate a local relativistic situation, we needed to know the speed of the specific point in question relative to the absolute frame at the moment of the test - "quelle horreur"!

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### Re: Why is relativity so hard to learn?[1]

The CMB is a reference frame but rarely a useful one which is why we don’t use it as a reference frame.
bangstrom
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### Re: Why is relativity so hard to learn?[1]

My I try to address what I believe is Dave's central concern (and misunderstanding) from a layman's point of view?

Dave likes the idea that there is some kind of "absolute clock". If you force him to consider things in relative terms, then he points out the (very reasonable) fact that if time contraction were to actually occur due to different velocities of two frame references, then this would be a symmetrical event: i.e. Alice "ages" more slowly in Bob's frame reference than he does, and vice versa.

So my suggestion is that Dave's agrees to simply pretend that Bob's clock measures the "absolute time".
Bob's frame actually has not suffered any acceleration and, as far as he is concerned, might well have been perfectly still all along.
And this would be true for anybody in his same reference frame, whether they have always remained there or they "have gone through a set of other reference frames".

The point is that, notwithstanding the symmetry (apart from the sign) in velocity differences, Alice starts by being in Bob's reference frame and she also ends in Bob's reference frame.
In this particular frame Alice (who was moving at high velocity with respect to this frame) has been "aging" more slowly, so that she finds herself much younger than Bob when she comes back.

It is important that the symmetry does not hold any more here: at difference with Bob, Alice cannot pretend her reference frame was still, because its velocity was changing in time (it "was moving with respect to itself", by moving through different inertial frame references).

In this perspective, whether there is an absolute space and/or time, and whether Bob's frame is moving at all, does not make any difference.

I apologize if this is trivial, inadequate or wrong.

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### Re: Why is relativity so hard to learn?[1]

Hi Neuro; what you have written is neither trivial, nor wrong. My only concern is the part: "she has been "aging" more slowly, so that she finds herself much younger than Bob when she comes back". This immediately invokes thoughts of "her clock is ticking slower" (than Bob's), which has no absolute truth to it.

I think Dave is presently busy processing the idea that maybe Alice has just covered less time, where time refers to "inertial time" (not absolute time), but at the same "clock rate" than Bob's. This is the central theme of this thread, using the Epstein space-propertime diagram as a crutch. I have brought in visible acceleration in order to (hopefully) make it more palatable.

I believe that the way in which physicists try to explain the effects to novices is doomed to fail, unless the novice is a student that simply has to learn it. Such students later begin to understand it and then the 'light goes on' (or not). How many novices can cope with "the relativity of simultaneity, time dilation, Lorentz contraction, etc.? I think those concepts are what make relativity so hard to learn.

I have tried to steer away from those and simply concentrated on the structure of spacetime and how it is changed by acceleration. The 'dreaded effects' that I have mentioned are still there, but IMO, they are secondary to inertial structure changes. And much more understandable once the central tenet is grasped.

I do not know if I will succeed in convincing the serious novice, but I think it is worth a try.

BurtJordaan
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### Re: Why is relativity so hard to learn?[1]

Let me try my question again? To paraphrase Michael Brooks: In "cold, hard science", when Alice gets back to Bob's frame of reference, how old is she really - in "hard science"? Whose clock are you using to say Alice's age when she is back with Bob?
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### Re: Why is relativity so hard to learn?[1]

I’ve meant to say that although I liked a post on the 3rd page of the thread that expressed regret, it was not because of the regret, I liked it because it mentioned other scales which I hope you might want to discuss more about at some stage.
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