Events, Intervals and Speed

[BurtJordaan]

Bangstrom, I think you are still thinking about the wrong paper. Here is a lengthy quote with my emphasis. I have also attached the full arXiv.pdf for convenience, should you want to look at the paper as a whole, including their references.

3 Conclusion

It is shown herein that emission and absorption processes are quantitatively well-defined
in the transactional (direct-action) picture, and are essentially the same as in the standard
theory of quantum electrodynamics, except for the replacement of the quantized field by
the response of charged currents jj to an emitting current ji. Such emissions and responses
cannot be predicted–they are inherently indeterministic. But the physical circumstances of
their occurrence can be defined and quantified by identifying the coupling constant between
interacting fields (e in the case of the electromagnetic interaction) as the amplitude for
generation of an OW (Fock state |ki) or CW (dual Fock state hk| ), both being required
for the existence of a ‘real photon,’ which in the direct-action picture is described by a
Fock state projection operator |kihk|.
Virtual photons are identified as the basic timesymmetric connections or propagators between currents, which do not prompt responses, do not precipitate the non-unitary transition, and thus remain an aspect of unitary (forcebased) interactions only.

Thus, virtual photons (time-symmetric propagator) convey force
only, while real photons (projection operators, quanta of a real-valued field) convey real
10energy and break linearity. The latter is just an expression of what Einstein noted long
ago: real electromagnetic energy (the actualized photon |kihk| ) is emitted and absorbed
as a particle (projection operator with definite spatial momentum ~k) [16]. It has been
shown herein that the product of the amplitudes of emission and absorption constitute
the squaring process for obtaining the probability of either radiative process considered
separately, thus demonstrating that the Born Rule arises naturally in the direct-action
theory of fields, in which both processes must always occur together (i.e., there is never
emission without absorption, and vice versa).

Finally, any quantized field theory can be re-expressed as a direct action theory, as
shown by Narlikar [17]. Therefore, any field for which the basic Davies model holds is a
component of the transactional model, and transfers of real quanta of those fields can be understood as the result of actualized transactions. (However, there is an asymmetry between
gauge boson fields and their fermionic sources, and in general such sources participate in
transactions indirectly, by way of boson confirmations [18]). While the direct-action theory
has historically been regarded with distrust, it is perfectly self-consistent; and it should also
be noted here that as recently as 2003, Wheeler himself was advocating reconsideration of
the direct-action picture [19].

The transfer of a quantum of energy (Cramer unfortunately calls it a photon) is instant and complete with the collapse of the superposition state. The interaction is nonlocal and simultaneous at both ends with no need for a physical object, as either a particle or a wave, to pass through space transporting energy from one electron to the other.

I'm aware of your personal theory about this aspect, but as I said to Faradave above, you should shift over to Personal Theory for discussions of that.

Again, TI is not about "collapse of the superposition state", it is about the real transmission and absorption of e.m. energy by means of photon exchange between non-entangled atoms. Just like your WiFi signal comes to your device.

BTW, Cramer still seems quite happy with the terminology 'photon' here...

[bangstrom]

Bangstrom, I think you are still thinking about the wrong paper. Here is a lengthy quote with my emphasis. I have also attached the full arXiv.pdf for convenience, should you want to look at the paper as a whole, including their references.

3 Conclusion

It is shown herein that emission and absorption processes are quantitatively well-defined
in the transactional (direct-action) picture, and are essentially the same as in the standard
theory of quantum electrodynamics, except for the replacement of the quantized field by
the response of charged currents jj to an emitting current ji. .

The essential difference between Faradave’s and my "personal" theories is that they are consistent with Cramer’s TIQM and your personal interpretation is not.

For instance, can you explain the meaning of jj and ji in the first sentence that you underlined or show where the theory mentions anything about a photon traveling through space at speed c.
The energy exchange ends and becomes evident to observers with the loss of superposition and there is no more to it. I don’t agree with your understanding of virtual and real photons but that is a minor issue.

[BurtJordaan]

For instance, can you explain the meaning of jj and ji in the first sentence that you underlined or show where the theory mentions anything about a photon traveling through space at speed c.

The currents j_j and j_i are defined on pages 4and 5, eq's. 5. to 8.

We can now make use of standard results from quantum electrodynamics (QED) regarding ‘emission’ and ‘absorption’ processes; all we need to do is to recall that any occurrence
of the field Aµ(x) represents the combined effect at x of all currents j_j. This includes
the Coulomb field (zeroth component, A0), which is not quantized in the Davies theory,
but we are interested in radiative phenomena (emission and absorption), corresponding to
quanta of the field. For the latter to occur, we require a response to a current j_i from at
least one other current j_j such that cancellation/reinforcement of the appropriate fields is
achieved, thus creating a ‘free field’ corresponding to a photon Fock state |k_i (it is actually a projection operator as shown below). Without the appropriately phased absorber
response, we have only non-quantized virtual photons, represented by the time-symmetric
propagator (first term on the right hand side of (4)), as opposed to Fock states (second
term on the right hands side of (4)). A useful way to conceptualize this distinction is that
‘virtual photons are force carriers, but only real photons are energy carriers.’

As for the 2nd part of you question, they mention real photons repeatedly. "Traveling through space at speed c" is what real photons do - no scientist expects to have to define a photon or what 'energy carriers' mean.

The energy exchange ends and becomes evident to observers with the loss of superposition and there is no more to it.

If there is any loss of superposition, it is during the handshake actions with advanced and retarded waves, without any energy transfer. Then follows the normal transfer of energy through real photons. Not my interpretation: this is contemporary science - what you say is not, unless I have missed your point completely.

[TheVat]

Just curious... how would lightsails work if photons aren't really particles or particle-like in their propagation? I am not arguing any position, not being up on this subject, but wonder how that would work.

[BurtJordaan]

Just curious... how would lightsails work if photons aren't really particles or particle-like in their propagation?

Particle-wave duality and the momentum of radiation make it physically irrelevant which one of the two we use for the calculation of the pressure on solar sails. However, experiments like two-slit light interference indicate that light travel as waves and is detected as particles. It is simpler to explain solar sail pressure when considering light as photons, but it does not really matter.

[bangstrom]

The currents j_j and j_i are defined on pages 4and 5, eq's. 5. to 8.

The values of the currents jj and ji are used but not defined in the article or you would know what they are. The currents only work if the electrons are in immediate contact or acting nonlocally over distance. This is why a photon carrying energy from one electron to the other is not necessary.

As for the 2nd part of you question, they mention real photons repeatedly. "Traveling through space at speed c" is what real photons do - no scientist expects to have to define a photon or what 'energy carriers' mean.

In Cramer’s theory, a “photon” is a single quantum of energy and not something that travels through space as in the classical photon theory. This is why it is unfortunate that Cramer calls it a “photon” because that leads to so much confusion.

[bangstrom]

Just curious... how would lightsails work if photons aren't really particles or particle-like in their propagation? I am not arguing any position, not being up on this subject, but wonder how that would work.

Light sails would work in space but just barely. There is a tiny amount of recoil when an electron loses or gains energy. It was once thought that light sails should work like the vanes in a Crooks radiometer but a radiometer is driven by thermal transpiration which is a stronger effect working against the direction of light pressure. Thermal transpiration requires the presence of air molecules.

A radiometer will rotate like a solar sail in a near-perfect vacuum if the vanes can overcome the resistance but the rotation is in reverse of the normal direction.

[Faradave]

I am talking about real 4-spacetime. It is flat and undistorted if we are taking SR spacetime…

As regards Special Relativity, That's not what Rindler says:
"Such maps necessarily distort metric relations and one has to compensate for this distortion." p.90

That's not what Feynman says:
"Although the geometry of space-time is not Euclidean in the ordinary sense, there is a geometry which is very similar, but peculiar in certain respects [refers to minus sign]." p.97

That's not what Wikipedia says:
"A very important pseudo-Euclidean space is Minkowski space, which is the mathematical setting in which Albert Einstein's theory of special relativity is formulated."

Why do you bring maps into it?

Because your diagram needs the asymptotes (a.k.a. "light cones") to exhibit zero magnitude.

Treating the earth as a sphere, every surface location is a pole in relation to its associated diameter. There can be a Mercator projection for every longitudinal direction from each pole. All those maps show the pole as projected contact (with infinite coordinate designations), which are a single actual point. As on a globe, our spacetime model needs a c-dependent pole available at every event.

Physics uses models. To model zero interval separation realistically, I offer a curved-space, radial-time model. A temporal 4-field radiates unidirectionally (outward only) from the singularity of the Big Bang. In the rest frame of the cosmos (isotropic background radiation), an enclosing 3-surface is curved-space (a simultaneity) at any particular age of the cosmos.

Importantly, for every location on any spatial 3-sphere, there exists a tangent interval 3-plane. That event is thus, identified by zero interval separation in every XYZ direction (corresponding to those of space) at that cosmic age. A future (expanded) 3-sphere offers a corresponding event differing only by ∆t. As the cosmos ages, spatial arcs tend to local flatness and the relation between ∆t, space (say ∆x), and interval (∆d) get closer and closer to a recognized equation for spatial intervals: ∆x² = ∆d² + ∆t². After 13.8 billion years, I think that makes a respectable model.

A radial temporal 4-field emanating from the Big Bang is enclosed by 3-sphere (space now) and at a later (∆t) cosmic age (future space). For any 4D event (e.g. pink dot now), there can be modeled a tangent interval 3-plane (shown as a disk).


With increasing relative speed the cosmos shortens in the direction of motion (x). At speed c, when ∆t = ∆x, there is zero interval separation from the emission event. Persistent tangency of the interval 3-plane (including zero intervals), despite varied relative motion, exhibits its invariance (including c).

[This is the] (physics) section. …start a thread under Personal Theories

I've worn out yet another welcome {…sigh}. Enjoy your thread. Back to the lab for me. (I've still got that flying car to finish. After three small fires, I needed the break. – Thanks!)

[BurtJordaan]

The values of the currents jj and ji are used but not defined in the article or you would know what they are. The currents only work if the electrons are in immediate contact or acting nonlocally over distance. This is why a photon carrying energy from one electron to the other is not necessary.

I thought currents j_j and j_i were adequately defined if one reads the two pages and inspects the equations (or better, read the whole paper and references therein). If still not clear, the currents are simply the RF current (j_i) of the accelerated (charged or excited) electrons in the emitter (sending a virtual offer wave backwards in time) and the RF current (j_j) of all the responding electrons (virtual confirmation waves) of potential absorbers.

This is the handshake process, which happens a-temporally and non-locally, with offer and conformation waves and hence comprises no energy transfer - they call it direct action through virtual photons. Its only purpose is to sort out which absorber will get the real photons (energy transfer) later. This in a nutshell, is what Kastner and Cramer (2018) wrote - I hope you don't deny that Cramer was party to the paper...

It seems to me that you are sticking to an old TIQM paper of Cramer, which was updated a few times in response to valid critique. Their latest interpretation is called RTI for relativistic TI. This science is evolving rapidly a.t.m.

[BurtJordaan]

It looks like Faradave is leaving for his flying car, but for other readers that might be interested in the science behind the controversy, the following.

I am talking about real 4-spacetime. It is flat and undistorted if we are taking SR spacetime…, [but it can be curved in GR]

As regards Special Relativity, That's not what Rindler says: ....

I completed the quote with the [] brackets to show its context. I was not referring to mappings. Minkowki spacetime is flat for all inertial observers in a non-accelerating, non-gravitational field scenario. This means spacetime paths (geodesics) for all inertial objects (and for light) are gun-barrel straight.

Physics uses models. To model zero interval separation realistically, I offer a curved-space, radial-time model. A temporal 4-field radiates unidirectionally (outward only) from the singularity of the Big Bang. In the rest frame of the cosmos (isotropic background radiation), an enclosing 3-surface is curved-space (a simultaneity) at any particular age of the cosmos.

I have commented on the problems of this model many times before. It does not yield a realistic cosmological model. It can only work for an expansion factor rate (da/dt) that is constant, which is not what we observe.

I think this thread has run its course, so I am not going to post here again, but others are welcome to continue.

Ps: Faradave, success with you 'flying car'. If it was not tongue in the cheek, I would love to hear about it in the engineering sub-forum...

[TheVat]

Just curious... how would lightsails work if photons aren't really particles or particle-like in their propagation?

Particle-wave duality and the momentum of radiation make it physically irrelevant which one of the two we use for the calculation of the pressure on solar sails. However, experiments like two-slit light interference indicate that light travel as waves and is detected as particles. It is simpler to explain solar sail pressure when considering light as photons, but it does not really matter.

Thanks, I was wondering if the transfer of momentum, or "push" effect, was easy to misconstrue in a classical image and I guess it is. I have had to shed old notions of momentum when dealing with massless "particles. "

[bangstrom]

I will also need a few days to rewire my cyclotron for ftl signaling.

I thought currents j_j and j_i were adequately defined if one reads the two pages and inspects the equations (or better, read the whole paper and references therein). If still not clear, the currents are simply the RF current (j_i) of the accelerated (charged or excited) electrons in the emitter (sending a virtual offer wave backwards in time) and the RF current (j_j) of all the responding electrons (virtual confirmation waves) of potential absorbers.

That is basically right except the energy transfer, as it appears to observers who see a spacetime interval between signal and sink, is not limited to radio frequencies. Specifically, the calculations refer to the rotation of a magnet and its ability to induce a current in a conductor. The current jj is generated by the first pass of a magnetic pole and the second current ji is generated by the passing the opposite pole.

With light energy, the electrons at signal and receiver function as rotating magnets so the same calculations apply. The first current is generated in the first quadrant of the electron’s polar rotation and the second is generated by the other pole in the third quadrant when the current vectors lie on the same 180 degree plane. The calculations are derived from complex numbers in Euler’s Formula for a circular rotation.

The energy transfer takes place when current vectors are in opposite directions where one vector acts as a push and the other is a pull. The magnetic field of the participating electrons is extremely short. That is why the exchange must take place over distance when both electrons are in superposition.

The transfer of energy only takes place when the vectors are precisely in phase such that one electron can emit a quantum of energy and the other can simultaneously receive the same quantity of energy. Both electrons are equal participants in the exchange unlike in classical theory.

The implication is that the electrons can only exchange a quantum of energy as a single quantum jump during that tiny window of time when they are precisely in phase. This view is not consistent with a later exchange of energy as in classical photon theory.

This is the handshake process, which happens a-temporally and non-locally, with offer and conformation waves and hence comprises no energy transfer - they call it direct action through virtual photons. Its only purpose is to sort out which absorber will get the real photons (energy transfer) later. This in a nutshell, is what Kastner and Cramer (2018) wrote - I hope you don't deny that Cramer was party to the paper...

I am sure they never wrote about a later transfer of energy. That would be redundant to the theory. More importantly, a later transfer of energy through space at speed is not consistent with recent quantum experiments involving Wheeler’s delayed choice or the quantum eraser experiments.

It seems to me that you are sticking to an old TIQM paper of Cramer, which was updated a few times in response to valid critique. Their latest interpretation is called RTI for relativistic TI. This science is evolving rapidly a.t.m.

Kastner’s change was to take Cramer’s transactional process from a spacetime background to Hilbert space and it includes Heisenberg’s concept of “potentiae” that exist alongside actual reality in space and time. She did mot change the instant action of the theory. There is no change in the timing between the old and new theories.

[BurtJordaan]

For the benefit of readers who might have been left confused by all the different individual interpretations above, here are the diagrams and annotations by John Cramer himself, in 2009, https://www.researchgate.net/publication/226312851_Transactional_Interpretation_of_Quantum_Mechanics

But first a short quote from his later paper The Quantum Handshake Explored, 2017.

The Transactional Interpretation of quantum mechanics, inspired by the structure of the quantum wave mechanics formalism itself, views each quantum event as a Wheeler-Feynman “handshake” or “transaction” process extending across spacetime that involves the exchange of advanced and retarded quantum wave functions to enforce the conservation of certain quantities (energy, momentum, angular momentum, etc.). It asserts that each quantum transition forms in four stages: (1) emission, (2) response, (3) stochastic choice, and (4) repetition to completion.

Stage 1:

An emiter produces a retarded wave (solid) toward an absorber and an advanced wave (dashed) in the other time direction.

Stage 2 & 3:

An absorber responds with an advance wave (dashed) back to the emmitter and a retarded wave (solid).

Stage 3 & 4: (some overlapping)

Schematic of the completed transaction. Extra waves cancel, leaving an advanced-retarded “handshake” that transfers energy h ω and momentum hk from emitter to absorber.

The straight dotted line is part of the lightcone of a Minkowski diagram. The handshakes occur atemporarily in the "quantum world", while the energy transfer occurs temporally in the "real world".

If in doubt about this statement, also look at this image from the same document:

Space-time schematic of a nonlocal “V” transaction for visualizing the polarization-entangled Freedman-Clauser EPR experiment. Offer waves ψ_L and ψ_R (blue/solid)

[BadgerJelly]

Some points surrounding the issue of time for physicists and our subjective appreciation of time:

https://www.youtube.com/watch?v=-6rWqJhDv7M

If anyone has anything to build on from this relevant to the topic of the OP I’d be willing to dip my foot in a little.

[bangstrom]

I think the issues of the nature of time and entanglement can best be understood by examining how the quantum eraser experiments work. The experiments themselves are enormously complicated but they are a collection of simple optical experiments that have been known and understood for more than a century so it isn't that complicated. Unfortunately, the interpretations of what is taking place get lost in the metaphysical weeds which distracts from the most important part of the laser experiments and that is the nature of the BBO crystal.

The BBO crystal is an ordinary non-linear polarizing crystal like calcite except that it is more heat resistant and the results of the eraser experimenters are what happens when oppositely polarized beams of light interfere constructively and destructively. The only observation that challenges the classical notion of light is that the results are best explained if the emission and absorption of light are simultaneous events. There are other explanations involving photons going back in time to erase the past or consciousness affecting the results or multiverses but I think these are a bit over the line.

Some experiments that shed light on the results of the quantum eraser experiments are experiments involving birefringent crystals and Dirac's three polarizer experiment. It is also helpful to know the basics of Thomas Young's double-slit experiment and what spontaneous parametric down-conversion SPDC is.

The quantum eraser probably should be a topic of its own.

[bangstrom]

For the benefit of readers who might have been left confused by all the different individual interpretations above, here are the diagrams and annotations by John Cramer himself, in 2009, https://www.researchgate.net/publication/226312851_Transactional_Interpretation_of_Quantum_Mechanics

But first a short quote from his later paper The Quantum Handshake Explored, 2017.

The Transactional Interpretation of quantum mechanics, inspired by the structure of the quantum wave mechanics formalism itself, views each quantum event as a Wheeler-Feynman “handshake” or “transaction” process extending across spacetime that involves the exchange of advanced and retarded quantum wave functions to enforce the conservation of certain quantities (energy, momentum, angular momentum, etc.). It asserts that each quantum transition forms in four stages: (1) emission, (2) response, (3) stochastic choice, and (4) repetition to completion.

Stage 1:

An emiter produces a retarded wave (solid) toward an absorber and an advanced wave (dashed) in the other time direction.

Stage 2 & 3:

An absorber responds with an advance wave (dashed) back to the emmitter and a retarded wave (solid).

Stage 3 & 4: (some overlapping)

Schematic of the completed transaction. Extra waves cancel, leaving an advanced-retarded “handshake” that transfers energy h ω and momentum hk from emitter to absorber.

As a much-belated response to Burt Jordan’s post from last May, I have never found any suggestion in John Cramer’s theory that all four stages mentioned above are not essentially simultaneous events including step (4) repetition to completion. This makes me skeptical of Burt’s statement below.

The straight dotted line is part of the lightcone of a Minkowski diagram. The handshakes occur atemporarily in the "quantum world", while the energy transfer occurs temporally in the "real world".

If in doubt about this statement, also look at this image from the same document:

Space-time schematic of a nonlocal “V” transaction for visualizing the polarization-entangled Freedman-Clauser EPR experiment. Offer waves ψ_L and ψ_R (blue/solid)

Where is the support for “this statement” that the energy transfer is temporal?

The quantum eraser experiments test the timing of the events by extending the distance of one of the two branches so that “in theory” the light should reach one of the detectors before the other creating temporal before and after arrival times for the light energy. The results of the experiments fail to detect any time difference between the predicted before and after suggesting that the energy transfer is simultaneous with emission and not temporal.

Our “real world” observation of the events is consistent with Minkowski’s diagrams where time and space are inseparable so that every 300,000 km of distance comes with an observed one second time delay. This makes c a dimensional constant unrelated to the speed of the energy transfer (speed of light) which is instant.

[BurtJordaan]

Where is the support for “this statement” that the energy transfer is temporal?

In the stage 3/4 schematic and text copied from Cramer himself.



The red retarded wave transfers energy and momentum temporally, but only when an advanced wave (coming from the future) has been detected by the emitter. The dotted line is a normal Minkowski lightcone, giving the elapsed time between emission and absorption.

Figure 5 is about polarization detection, not energy transfer. Maybe it is not an illuminating figure to offer in the energy transfer debate.

Anyway, if you can proof atemporal energy transfer, you better start by rewriting all relevant physics, so that you can base your proof on the "new physics".

[bangstrom]

In the stage 3/4 schematic and text copied from Cramer himself.



The red retarded wave transfers energy and momentum temporally, but only when an advanced wave (coming from the future) has been detected by the emitter. The dotted line is a normal Minkowski lightcone, giving the elapsed time between emission and absorption.

The red line is the present line for the emitter and the blue line is the present line for the receiver but the blue line exists in the future of the emitter and the red line exists in the past of the receiver. As you said, the advanced wave is coming from the future on its way to the emitter. Together, both the red line and blue lines exist simultaneously on the Minkowski light cone.

In your view, what is the elapsed time for the advanced and retarded waves to travel the required distance between the two?

If I recall correctly, you said the red line is the path energy takes in a temporal fashion as it follows the blue line back to the absorber. This makes sense if the two are in intimate proximity but what if they are light hours apart or years apart? How does the blue path leave a trail to follow and how does the energy locate the emitter if it has moved on from its original location?

Your interpretation is not consistent with Cramer’s model where all the events from emission to absorption are essentially simultaneous.

Anyway, if you can proof atemporal energy transfer, you better start by rewriting all relevant physics, so that you can base your proof on the "new physics".

There is ample evidence that the transfer of EM energy is atemporal and I have posted a number of references in the past to support that view. There are several theories explaining the atemporal nature of light dating from a century ago to the present.

Did you watch the video Badger Jelly posted? Take note of what Carlo Rovelli says starting from the 39 minute point. https://www.youtube.com/watch?v=-6rWqJhDv7M
The “granularity” of time is Minkowski’s spacetime. Light is at infinite speed and the light cone is a bubble of one single time where all things are simultaneous.

Hermann Bondi taught in his relativity classes that c should not be thought of as a speed. Thinking of c as a speed leads leads to confusion and paradoxes when trying to understand relativity. The pole and barn paradox for example. Instead, Bondi taught that c was simply a conversion factor for converting between units of time and distance.

The charts of Minkowski and Epstein work because they combine space and time as a constant ratio for all types movement through space. Light can travel instantly from one point to another on the chart without adding any “in-flight” time of its own to the spacetime distance between the two points.

The atemporal nature of light has long been recognized but the “folklore” (A. F. Kracklauer’s word) that light has a speed persists.

[BurtJordaan]

Some points surrounding the issue of time for physicists and our subjective appreciation of time:

https://www.youtube.com/watch?v=-6rWqJhDv7M

If anyone has anything to build on from this relevant to the topic of the OP I’d be willing to dip my foot in a little.

A little philosophical, but I think the connection to the OP is in this snippet from the OP:

It is important to emphasize that although the coordinates for an event are different in different inertial frames, it is static in spacetime for all inertial frames. It has happened, has been recorded in arbitrary many inertial frames and that's that.

Rivollli points out that time is essential something our brains need in order to learn from the past and predict the future. Effectively he says time is a personal (coordinate dependent) phenomena that does not exist in the fundamentals of science. There are many things that we use as clocks, but that is only our perceptions and the universe don't care. Deeper down, there is no time, says Rivolli.

If we listen to Roger Penrose, the natural state of the universe is one with maximal entropy (with no time, even at the macro level), and our low entropy epoch is just a transient between two maximal entropy states. The way Penrose restarts sequential eons, through conformal re-scaling, to get to a new low entropy state, is still controversial.

My philosophy, in order to keep my sanity between these and other scientific issues, was always to see timekeeping as a useful human invention, defined so that it is as simple as possible ('but not simpler'). Einstein did that for the general case and I love the utility of it. He may have hoped that his definition would hold for the macro and the micro scales. Today we know that it probable does not hold near the Planck scale, but so what?

We have our recipes that work near the Planck scale. Together with Einstein's work, we can explain (say) 99.9999% of all observations. How much are we prepared to spend to add another 9 to the end of that? And where do we stop?

[Faradave]

[Optional aside]

Mass is considered invariant because by convention it refers to the rest frame of a particle (the one in which mass-energy is minimal). Similarly, the maximal rate aging of the cosmos is in the rest frame of the cosmos. That frame is also identified by the related measures of cosmic size, cosmic entropy, cosmic temperature and isotropic background radiation. Thus, future displacement, defined as an increase in cosmic age is also invariant (agreed by all observers).

In the twin paradox, for example, both twins rejoin at the same future-displaced event, even though the round-trip twin aged more slowly. Future displacement is invariant despite the traveling twin's accelerations and velocities, so this definition fits SR & GR.

Future displacement is therefor the best choice for the temporal axis of invariant interval-time coordinates.

[BurtJordaan]

Mass is considered invariant because by convention it refers to the rest frame of a particle (the one in which mass-energy is minimal). Similarly, the maximal rate aging of the cosmos is in the rest frame of the cosmos.

Firstly, the rest frame of the cosmos is an impossible concept in practice, simply because the gravitational potential varies from point to point due to local energy density. Yes one can use the average potential, but then the "oldest part of the universe" will be somewhere near the center of the biggest void.

Secondly, velocity observed as an anisotropy of the CMB radiation (i.e. peculiar velocity) does not guarantee a lesser elapsed proper time being recorded between two events. Consider this thought experiment. Two clocks A and B float inertially in close proximity to each other, near the center of a large void. Let them have some peculiar velocity V. Now B is boosted until it's detectors observe an isotropic CMB (i.e. zero peculiar velocity), but still located near the center of the void. Leave B there for a long time and then boost it back to A again. Which clock will show the least elapsed time between the two events, i.e. B departing and B arriving?

The clock that has been boosted (B) will show the least elapsed time, just like in the well known "twins paradox". This is despite the fact been that B sat "motionless" relative to the "rest frame of the cosmos" for a long time. It hence did not achieve "maximal rate aging".

It boils down to Rivolli's point: time for the cosmos does not exist. It only exists for the two clocks and for us who observe/contemplate the times recorded by them. And that must be relevant to events common to both clocks.

BTW, I think I know where your thinking got skewed: by your private theory of "radial cosmic time". I have "been there, done it" as well. ;-)

[bangstrom]

Secondly, velocity observed as an anisotropy of the CMB radiation (i.e. peculiar velocity) does not guarantee a lesser elapsed proper time being recorded between two events.

Is it possible to observe velocity as an anisotrophy to the CMB?

The outer boundary of the CMB is the point where the most distant radiation is redshifted to invisibility. Movement towards one side of the CMB should blueshift invisible radiation from the CMB into the visible range while radiation from the CMB to the rear is redshifted to invisibility so any point, moving or not, should appear to be at the isotropic center of the CMB. This is like moving through a fog where you always appear to be at the center of a clear spot in the fog.

I think Ernst Mach was right with his view that the closest thing we have to an absolute frame of any kind must involve the total mass of the universe itself

[Faradave]

…the gravitational potential varies from point to point due to local energy density

Good point! And one that helps make mine: nothing in the cosmos ages faster than the cosmos. I agree, anything with mass-energy ages slower because of its own gravity.
Inasmuch as there can be an estimated age of the cosmos (which is presumably increasing), one can argue future displacement is invariant by that measure (from its maximal perspective).

Even someone traveling near lightspeed, who sees the cosmos contracted in the direction of motion, in principle, can use the other two spatial directions to obtain the corrected size (and background, etc.) of the cosmos as a cosmic clock reference.

The clock that has been boosted (B) will show the least elapsed time…despite [being] motionless…

Yes. But that invokes, forces for the boosts, which lock in lower aging. My explanation is that force is lightlike (having the same 4-direction as its purported "force carrier") and is thus non-aging (like light). So, application of a force to any object imparts a non-aging component to its timeline (its worldline as seen from the object’s rest frame). So, the timeline bends in a non-aging direction.
This is less obvious with a flat map. In a curved-space, radial-time model, force is non-aging because it is always tangent to curved space and perpendicular to radial time.

“Motionless” is of course, another way of saying constant velocity (non-accelerated, thus no force applied). Such slowed inertial aging is not "locked in" (invariant) because it can be transformed away by adopting the rest frame of the object in question.

Rivolli's point: time for the cosmos does not exist

I must yield to this philosophical point, as might be applied to an empty cosmos. No clocks, no aging, no contest.

[bangstrom]

…the gravitational potential varies from point to point due to local energy density

Good point! And one that helps make mine: nothing in the cosmos ages faster than the cosmos. I agree, anything with mass-energy ages slower because of its own gravity.

I agree that Jorie’s scenario where motion slows time supports- rather than detracts- from your observation that the cosmos ages and nothing ages faster than the cosmos. The total mass-density of the universe and its resultant gravity establishes the maximum rate at which the cosmos ages.

Even a clock at the center of a massive void would still be subject to the overwhelming and inescapable effect of the total mass of the universe itself. It might tick slightly faster than all other clocks but it would still tick no faster than the cosmic rate.

[BurtJordaan]

Is it possible to observe velocity as an anisotrophy to the CMB?

Yes, the spaceship in free space can calculate its peculiar velocity by detecting the anisotropy of the CMB. This then gives a velocity relative to the "rest frame of the cosmos".

The outer boundary of the CMB is the point where the most distant radiation is redshifted to invisibility. Movement towards one side of the CMB should blueshift invisible radiation from the CMB into the visible range while radiation from the CMB to the rear is redshifted to invisibility so any point, moving or not, should appear to be at the isotropic center of the CMB. This is like moving through a fog where you always appear to be at the center of a clear spot in the fog.

Yes, the CMB radiation comes from a spherical band presently about 46 billion light years around any random comoving point (i.e. following the "Hubble flow") we choose in the cosmos (somewhat like your fog example). But unlike the fog, we observe the CMB to be not isotropic in average temperature, because we have a peculiar velocity of some 600,000 km/s relative to the Hubble flow.

I think Ernst Mach was right with his view that the closest thing we have to an absolute frame of any kind must involve the total mass of the universe itself

Yes again. In general relativity we refer to it as the large scale gravitational field. The only problem is that it is quite warped in many places.

[BurtJordaan]

The clock that has been boosted (B) will show the least elapsed time…despite [being] motionless…

Yes. But that invokes, forces for the boosts, which lock in lower aging.

My objection to your radial time model is still what it always was: if you want to depict a spatially positively curved cosmos, the radial coordinate is a function of time, not actual cosmic time as in your radial time model. A better depiction is something like this "Rovelli-like' view:

Our perception of spatial expansion

where our perception of time 'flows' uniformly and perpendicular to the radial hyper-radius, in all possible directions tangent to the present sphere. So we cannot draw a line and say: "this is the direction of time".

In the Rovelli-view, there is no time, but only an increase in overall entropy, which is associated with the increase in the hyper-radius R - and hence with the distances that we observe on the large scale, but inside our observable portion...

[Faradave]

Re: Wait & c

I'm not familiar with the Rovelli model but I'm glad to see a recognizable spatial 3-sphere. Without time though, I can't be sure what he does with the concept of space-time interval.

The outward pointing arrows on hyperspace would suggest that if the radii of the 3-sphere are "spatial" they are unidirectional in that we only observe the Hubble sphere increase. If so, I would have to say that a one-way geometric separator is better characterized as time. By contrast, space provides the potential for geometric separation with two-way choices of direction for each spatial dimension. So, if hyperspace is one-way, his model is very similar to mine but introduces an unnecessary parameter.

Remember it's the unidirectionality of time in a curved-space, radial-time model which enforces a natural speed limit c (a ratio of space to time) which is finite, universal, constant, isotropic, and invariant. I don't think Rovelli's model offers a clue (as with all of conventional physics) as to why such a limit exists.

Late Addendum:

My objection to your radial time model is still what it always was: if you want to depict a spatially positively curved cosmos, the radial coordinate is a function of time, not actual cosmic time as in your radial time model.

From your recent post, it appears we agree that gravity causes clocks to run slow. So, in the early cosmos, when mass-energy density (thus, gravity) was much higher, clocks would be running much slower than now. Any such clock (even one at rest with the cosmos) would be displaced to a cosmic future, without having registered much elapsed much time. Such a clock would register a "function of cosmic time" rather than cosmic time (as given by the cosmic radius). The clock would see the cosmos as having been rapidly inflated relative to its own experience.

I'm suggesting that measures (clocks) such as temperature and entropy (possibly the frequency of red shifted light) read out functions of cosmic size that tell us a story of rapid inflation.

[BurtJordaan]

Re: Wait & c

I'm not familiar with the Rovelli model but I'm glad to see a recognizable spatial 3-sphere. Without time though, I can't be sure what he does with the concept of space-time interval.

Neither am I, and the depiction is my own "Rivolli-like", and it definitely has time. The spacetime interval seemingly does not exist in the Rivolli model, where it is just our perception to assist us in calculations.

The outward pointing arrows on hyperspace would suggest that if the radii of the 3-sphere are "spatial" they are unidirectional in that we only observe the Hubble sphere increase.

They are hyper-spatial and can in fact decrease as well, so they are not really entropy-equivalent. I think that I misstated that in context of Rivolli, probably because his ideas are foreign to me. For the most time, our universe is represented by de Sitter spacetime, which can expand or contract. So things like the hyper-radius and Hubble radius can go both ways and are not entropy related.

Remember it's the unidirectionality of time in a curved-space, radial-time model which enforces a natural speed limit c (a ratio of space to time) which is finite, universal, constant, isotropic, and invariant.

This is not unique to your model. All space-propertime representations sport that. Then there is a much more serious objection: the one-way speed of light is a chosen convention for convenience, not an absolute one. It is only the two-way average of the speed of light that is absolute. By simply choosing a different clock synchronization convention, that invariance fails. It is totally valid to choose another convention, but it is simply inconvenient, because it complicates calculations horribly.

My objection to your radial time model is still what it always was: if you want to depict a spatially positively curved cosmos, the radial coordinate is a function of time, not actual cosmic time as in your radial time model.

From your recent post, it appears we agree that gravity causes clocks to run slow. So, in the early cosmos, when mass-energy density (thus, gravity) was much higher, clocks would be running much slower than now.

No, gravity does not slow clocks down, it is gravitational potential differences that do, in the sense that a clock situated in lower gravitational potential region records less time than an identical clock sitting in a higher potential region. The "strength of gravity" is associated with the gradient of the potential energy. Now when the universe was very young its gravitational potential was smooth to 1 in 10⁵, so every particle 'aged' at the same rate.

On the very large scale, it is still roughly the same today, so there is no reason to think that early particles aged slower than late particles, whatever that may mean. On smaller scales the potential is more 'clumpy' and particles in some areas age slower than particles in other areas. That's about all that relativity/cosmology says about it. Applied correctly, I don't think the science supports your proposition and suggestion.

[bangstrom]

From your recent post, it appears we agree that gravity causes clocks to run slow. So, in the early cosmos, when mass-energy density (thus, gravity) was much higher, clocks would be running much slower than now.

No, gravity does not slow clocks down, it is gravitational potential differences that do, in the sense that a clock situated in lower gravitational potential region records less time than an identical clock sitting in a higher potential region. The "strength of gravity" is associated with the gradient of the potential energy. Now when the universe was very young its gravitational potential was smooth to 1 in 10⁵, so every particle 'aged' at the same rate.

On the very large scale, it is still roughly the same today, so there is no reason to think that early particles aged slower than late particles, whatever that may mean. On smaller scales the potential is more 'clumpy' and particles in some areas age slower than particles in other areas. That's about all that relativity/cosmology says about it. Applied correctly, I don't think the science supports your proposition and suggestion.

The gravitational potential in the very early universe may have been more uniform than at present so all particles aged at a similar rate but the gravitational density was far greater in the remote past with a smaller, denser universe so particles aged slower in the past than particles do now. I don’t see how less uniformity in the present negates the observation that "gravity slows clocks down."

Particles in the early universe were farther down in the gravitational well than we are at present so clocks ticked slower in the past.

[BurtJordaan]

Particles in the early universe were farther down in the gravitational well than we are at present so clocks ticked slower in the past.

This is only the case if we view the universe as starting as a black hole, which is not correct. Yes, we observe everything that has happened in the distant past as redshifted, but another hypothetical observer on a very distant galaxy observes us as redshifted to the same degree, due to the expansion of space. This not compatible with your statement above - neither theoretically nor observationally.

In the case of a black hole, things lower down its well looks redshifted to us, but we look blue-shifted to an observer around there.

So no, the early universe was not farther down a gravitational well - in fact due to the Milky way, Sun and Earth's gravity wells, everything at early times was in a lesser gravitational well than what we are today.