## Events, Intervals and Speed

Discussions on classical and modern physics, quantum mechanics, particle physics, thermodynamics, general and special relativity, etc.

### Re: No Two Ways About It

Jorrie wrote:The spacetime interval seemingly does not exist in the Rovelli model, where it is just our perception to assist us in calculations.
I'm not convinced people perceive intervals consciously. Certainly space-time intervals are embedded in today's physics. My curved-space radial-time model preserves and illuminates such intervals with Euclidean interval-time coordinates. This model simply rearranges the space-like interval formula to get rid of the nagging minus sign. Otherwise space, time and interval are well preserved with no distortion and no added dimensions (e.g. hyperspace) to add complexity.

Jorrie wrote:So things like the hyper-radius and Hubble radius can go both ways and are not entropy related.
Clever but even more complex in that unidirectional time is not explicit in the model. We don’t experience 2-way hyperspace in any testable way that I'm aware of.

Faradave wrote: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.

Jorrie wrote:This is not unique to your model. All space-propertime representations sport that.
Nonsense! Other models postulate limit c. My model uniquely explains it (simply & geometrically). Huge, advantage! Other models don’t show how light can get to the future (of the cosmos) and yet not age. My tangent interval path does. Your welcome.

"Why is the speed of light the same in all reference frames? I don’t know the answer to that question, and I don’t even know how to approach it. … The constancy [invariance] of the speed of light is unexplained." - Styer p.21

Jorrie wrote: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.
If that's the world you want to live in, fine. Not only does it "complicate calculations horribly" but one has to labor to create a model where light has a different speed on the return trip. What are we to do with one-way relations like c = λf? I prefer the simplest model possible, which is what Phyxed endeavors to offer.

If you stop neglecting the invariant zero-interval path of light, there are physically no two ways about it. There is no path either way (direction yes, path length no). Embrace null vectors.

Jorrie wrote:there is no reason to think that early particles aged slower than late particles, whatever that may mean.
What it means is given by the half life of a radioactive sample of particles (or even a single muon). Drop the sample straight into a black hole. As it approaches the event horizon the half life increases without bound. Its aging (or “clock”) has slowed while the cosmos keeps getting older (bigger). This would be true for thermal clocks as well. The sample approaches absolute zero toward the event horizon, where even quarks in the nuclei must slow down.

When the mass-energy of the cosmos was much higher (as uniformly as you like and similar to a quark star if not a black hole) the clocks of those particles were running slower than the clock of the cosmos (its unidirectional radius). That gives you a physical readout as a function (i.e. scale factor) of the radius.

Jorrie wrote: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.

"…in every gravitational field, a clock will go…according to the position…" Einstein p.81

I'm suggesting the size (age) of the cosmos ignores this. The future (of the cosmos) is invariant. Aging (of cosmic contents) is relative.

Jorrie wrote: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
All light is received from the past, no matter who or where the observer is.

Jorrie wrote: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.
The observer down there sees the cosmos expanding much faster, he might even call it "rapid inflation".

Jorrie wrote: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.
This compares clocks in the cosmos to each other rather than to the size of the cosmos at large (i.e. the cosmic clock).

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### Re: Re:

BurtJordaan » October 28th, 2020, 9:14 am wrote:
bangstrom » 28 Oct 2020, 07:16 wrote: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.

If the universe is expanding while remaining the same in mass, then the gravitational density of the universe in the distant past must have been greater than it is at present. It must have been considerably greater for hydrogen to fuse to helium and the lighter elements.

I know the definition is debatable but I consider any massive body having a gravitational density so great that its escape velocity is greater than c qualifies as a black hole. As is often said, ‘Not even light can escape.’
This implies that any closed universe is essentially a black hole. This means our universe must have been, and possibly still is, a black hole. We could be a black hole inside an even larger universe.

Distances are shorter and time passes slower in a dense gravitational field so the observations of being in an expanding universe are equivalent to emergence from a gravitational well.

I also second what Faradave had to say in the previous post.
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### Re: No Two Ways About It

Faradave » 28 Oct 2020, 21:51 wrote:
Jorrie wrote:The spacetime interval seemingly does not exist in the Rovelli model, where it is just our perception to assist us in calculations.
I'm not convinced people perceive intervals consciously. Certainly space-time intervals are embedded in today's physics.

That's Rovelli's idea, not his model. It operates at the quantum-gravity level, where time does not exist - perhaps...

Faradave » 28 Oct 2020, 21:51 wrote:
Jorrie wrote:So things like the hyper-radius and Hubble radius can go both ways and are not entropy related.
Clever but even more complex in that unidirectional time is not explicit in the model. We don’t experience 2-way hyperspace in any testable way that I'm aware of.

Unidirectional time is explicit, but not unidirectional hyper-radius. Einstein's original model could contract or expand. Models like de-Sitter's has contracted before our T0 and then expand - physically simple and feasible.

Faradave wrote: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.

Jorrie wrote:This is not unique to your model. All space-propertime representations sport that.

Nonsense! Other models postulate limit c. My model uniquely explains it (simply & geometrically). Huge, advantage! Other models don’t show how light can get to the future (of the cosmos) and yet not age. My tangent interval path does. Your welcome.

I disagree with you claims. The constancy of the speed of light in an inertial frame was explained by Maxwell's equations and later utilized by Einstein to formulate it more generally as the equivalence of all inertial frames.

Talking about "nonsense" - your radial time model is exactly that! You cannot combine the hyper-radial dimension with propertime - they need to be orthogonal to each other. Then all the physic works as expected, the natural speed-limit is "explained" graphically and that is not your invention. It exists from the 1960s. As I have said before, all space-propertime depictions "explains" it graphically.

As I have also wrote before, the one-way speed of light is conventional, a function of the choice of coordinate system. It is only the two-speed of light's isotropy that's mysterious.

Enough said...
Last edited by BurtJordaan on October 29th, 2020, 3:11 am, edited 1 time in total.

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### Re: On a Tangent

Jorrie wrote:The constancy of the speed of light in an inertial frame was explained by Maxwell's equations and later utilized by Einstein to formulate it more generally as the equivalence of all inertial frames.
Brilliant achievements, I admit. However, as I noted (and everyone knows) Einstein took limit c as a postulate thus, not an explanation.

Maxwell, what a mathematician! But his derivation of limit c relies on measured values for the electric (ε0) and magnetic (μ0) constants. Though this provides great insight into the nature of light as an electromagnetic phenomenon, it is no more "explanatory" of c as a limit than if he simply measured light directly.

I will credit Maxwell with two other accomplishments.
1. Maxwell's c works as a one-way or two-way limit (ε0 & μ0 are agnostic of path).
2. Maxwell unwittingly gave us the propagation speed of gravity disturbances (and all massless interaction) as well! Of course, my geometric explanation provides such a unified limit c.

Jorrie wrote:the natural speed-limit is "explained" graphically and that is not your invention. It exists from the 1960s.
Recall that Epstein admitted his model can’t handle individual light quanta, using the term “myth”. You acknowledged that it "excludes photons (null or light-like intervals) and all space-like intervals." My model makes no such exclusion. Curved-space, radial-time is distinct from Epstein diagrams (his space isn't even curved) though I admire his advance toward Euclidean simplicity. He was intuiting in the right direction.

Jorrie wrote:You cannot combine the hyper-radial dimension with propertime - they need to be orthogonal to each other.
Clearly your diagram and my curved-space, radial-time are different. My intervals occur in tangent 3-planes at every curved spatial location. Both interval and space are normal (orthogonal) to radial time at any (every) tangent point.

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### Re: On a Tangent

Faradave » 29 Oct 2020, 19:13 wrote:
Jorrie wrote:You cannot combine the hyper-radial dimension with propertime - they need to be orthogonal to each other.
Clearly your diagram and my curved-space, radial-time are different. My intervals occur in tangent 3-planes at every curved spatial location. Both interval and space are normal (orthogonal) to radial time at any (every) tangent point

Despite previously banning your model from the mainstream physics side, I have looked at it again. I still want to see how you show radial expansion and cosmic time as separate dimensions, because they are not 1:1 related
Faradave » 24 May 2020, 20:34 wrote:

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).

My feeling is that instead of 3 spatial, 1 hyper-spatial and 1 time dimensions (5 total, of which we usually suppress 2 spatial, leaving us with 3 in depicting cosmological models), you will need a 6th dimension (or more) to accommodate your "interval plane", whatever that may mean. To mix it up with one of the space dimensions does not cut muster.

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### Re: Just four, no more.

Jorrie wrote:I still want to see how you show radial expansion and cosmic time as separate dimensions, because they are not 1:1 related.
With curved-space, radial-time (diagram above), the radius is the invariant proper time of the cosmos and, in principle, any isolated objects which happen to share that isotropic rest frame. However, objects (such as clocks) at translational rest with the cosmos still age slower than the cosmos if subject to gravity (as everything is, to some extent). Thus, the size of the cosmos (i.e. its radius) will not have a linear relation to aging by any other clock. There will, of necessity, be a scale function.

Gravity was most intense with the huge mass-energy density of the early cosmos. This is when "rapid inflation", the greatest discrepancy between the rate cosmic size increase and clock rates, would have occurred.

Jorrie wrote:[Regarding my curve-space, radial-time diagram]My feeling is that instead of 3 spatial, 1 hyper-spatial and 1 time dimensions (5 total, of which we usually suppress 2 spatial, leaving us with 3 in depicting cosmological models), you will need a 6th dimension (or more) to accommodate your "interval plane", whatever that may mean. To mix it up with one of the space dimensions does not cut muster.
The only "mixing" of interval and space, is at common tangent points. The model employs only 4D, all of which are entailed by the unidirectional radial 4-field emanating outward from a central big bang (BB) event. The cosmos at any given size, is the spatial 3-sphere enclosing the BB at that radius (e.g. dashed circle "space now" as 2D cross-section).

Unidirectional fields are the norm in nature as evidenced by Gaussian gravity and electric fields. My temporal field is one dimension up at 4D, while Gaussian fields are 3D.

Any event (e.g. pink dot) has a spatial location in the cosmos at that cosmic age (radius). Without adding any new dimensions there exists a 3-plane (shown maroon) tangent to that event. This is no less feasible than realizing a flat cardboard can be tangent to a basketball without adding any new dimensions.

That tangent plane corresponds to spacetime intervals. This is evident from the space-like interval expression given as a Pythagorean relation: ∆x² = ∆d² + ∆t², where ∆d occurs on a maroon arrow in the tangent interval plane and ∆t falls on a radial element of the temporal field. ∆x is a spatial arc, so locally flat that it is indistinguishable from its chord, forming the hypotenuse.

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### Re: Just four, no more.

Faradave » 02 Nov 2020, 18:06 wrote:Gravity was most intense with the huge mass-energy density of the early cosmos. This is when "rapid inflation", the greatest discrepancy between the rate cosmic size increase and clock rates, would have occurred.

But where, I ask for the n'th time, is that cosmic size in your depiction of the cosmic model?

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### Re: Making a Mad Dash

BurtJordaan wrote:But where, I ask for the n'th time, is that cosmic size in your depiction of the cosmic model?
To be safe, I've read your question n times. It seems straight forward. Perhaps I'm still missing something. Maybe TheVat can explain it to me.

The cosmos, at any given time, is a spatial 3-sphere, enclosing the central big bang event (yellow-red burst). Specifically, the cosmos right now is represented by the dark grey dashed circle labeled "space now". Its size is naturally a function of the temporal radius (i.e. its invariant cosmic age). Here,now (requiring 4 coordinates) is shown as a pink dot. The future cosmos is expanded to a greater size, indicated by the light grey dashed circle. This is simply an adaptation of the balloon analogy.

Of course, the diagram shows the cosmic 3-sphere in cross section, with its current curvature enormously exaggerated. The cosmos is understood to contain particles including clocks, all of which run slow compared to the age of the cosmos because of gravitational influence. That influence varies with average mass-energy density of the cosmos.

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### Re: c the video

Below is a recent, entertaining and educational clip (20 min.) conveying Jorrie's position about measuring 1-way vs. 2-way speed of light.

In terms of directly measuring speed c, I agree with these arguments. However, we're not limited to measuring c directly. The comment I posted on YouTube appears below:

Don't forget, Einstein based special relativity upon a postulate of invariant speed limit c. He was inspired by the fact the Maxwell’s brilliant derivation of c is independent of inertial frame, which means it is also independent of direction. So, limit c is the same in all directions (including each leg of a 2-way trip).

Another way of realizing this is to consider light, not in terms of conventional speed (∆x/∆t, which is merely relative) but in terms of its interval speed (∆d/∆t), which is invariant. Einstein considered invariant values more "real" than relative values because observers in all inertial frames agree on invariant values. The magnitude of a lightlike interval (∆d) is zero! Therefor, light's invariant interval speed is also zero, which is the same to all observers and in all directions. c is an absolute speed limit because nothing is slower than absolute rest!

Note also that c=λf, where λ is wavelength and f is frequency. If the frequency of sent and reflected light are the same, it follows that c is the same in both directions.

For a simple and brief geometric explanation (that physics does not provide) of why speed limit c exists, check out 'c' for Yourself.

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### Re: Making a Mad Dash

Yea, I hope Vat would explain to you where your argument goes wrong.
I give up on that...

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### Re: That's about the size of it.

BurtJordaan wrote: I ask for the n'th time, is that cosmic size in your depiction of the cosmic model?
BurtJordaan wrote:I give up on that...
Fair enough. But my model remains consistent with accepted interval geometry, while avoiding the distortion of spacetime coordinates.

Euclidean interval-time coordinates are available at every event (e.g. here,now = pink dot) in a curved-space, radial-time model of the universe. Local flatness make a spatial arc indistinguishable from its chord (Δx). Interval = Δd. Future displacement = Δt.

In case by "cosmic size" you meant its volume, that's the surface of a an enclosing 3-sphere. The formula for this is given below dimension n = 4 in the Wikipedia diagram below as 2pi2R3 where R is the radius. In my model, R = cosmic age x speed limit c in appropriate units.

The radius of an n-ball yields its interior "volume" and surface "area" by the formulas corresponding to the n-th dimension.

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### Re: That's about the size of it.

Faradave » November 8th, 2020, 9:11 pm wrote:
BurtJordaan wrote: I ask for the n'th time, is that cosmic size in your depiction of the cosmic model?
BurtJordaan wrote:I give up on that...
Fair enough. But my model remains consistent with accepted interval geometry, while avoiding the distortion of spacetime coordinates.

tangent interval plane eq..png

In case by "cosmic size" you meant its volume, that's the surface of a an enclosing 3-sphere. The formula for this is given below dimension n = 4 in the Wikipedia diagram below as 2pi2R3 where R is the radius. In my model, R = cosmic age x speed limit c in appropriate units.

n-ball size.png

http://www.sciencechatforum.com/viewtopic.php?f=39&t=35937

viewtopic.php?f=39&t=35937

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### Re: Agonize or Antagonize?

Yes, I remember being impressed by your finding and had jotted a few notes in the way of a reply. But then I recalled a few hints that you don't like seeing my posts. Possibly miss-interpreted, but I hesitated and set the notes aside. If I find them (or remember what I was thinking) I'll post a reply there. Interesting.

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### Re: No Two Ways About It

Faradave » October 28th, 2020, 7:51 pm wrote:Other models postulate limit c. My model uniquely explains it (simply & geometrically). Huge, advantage! Other models don’t show how light can get to the future (of the cosmos) and yet not age. My tangent interval path does. Your welcome.

"Why is the speed of light the same in all reference frames? I don’t know the answer to that question, and I don’t even know how to approach it. … The constancy [invariance] of the speed of light is unexplained." - Styer p.21

Why should a zero spacetime interval give an observed speed limit of c, rather than some other finite value? Is this just a brute fact about our particular universe?

Mathematically, how can the manipulation of zero (zero spacetime distance = contact) and infinity (infinite speed = instant transfer = non-aging) produce a specific finite number?
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### Re: E-asy Access

Positor wrote:Why should a zero spacetime interval give an observed speed limit of c, rather than some other finite value? Is this just a brute fact about our particular universe?
Fair question. The only thing that matters is that there is a finite speed limit. All the consequences of relativity follow from that. Specific units are of no real consequence. Aliens will give the limit a different value than we do.

However, c represents a real ratio of space to time, such that the two are equal in span, no matter what units they're measured in. The conversion factor between them will be what any observer (alien or otherwise) arrives at as the value for "c".

Ultimately, like all fundamental constants of the universe (e.g. pi, e, the fine structure constant α), c is dimensionless. That is, considering space and time each as separators of events (in 4D), we have c as a ratio of separation/separation. Since those separations must be equal to result in the zero interval associated with light (and any other massless energy transfer), the ratio is ultimately, simply and conveniently 1!

"The true constants have to be pure numbers, not quantities that have dimensions," - Barrow p.36 (Truthfully, Barrow never got around to acknowledging c as one of these. - pity
He did come close on p.19 "...the speed of light c. Again, this quantity transcends human standards. It has fundamental significance.")

Regardless of units, as spatial and temporal separations become equal, the interval separating emitter and absorber vanishes - establishing interval contact.

Remember that c is a ratio, which is a slope (or direction) of a lightlike worldline in (4D) spacetime. That is quite different than the magnitude of lightlike separation, which is zero. Thus, light quanta have trajectories described by null vectors with direction 1 and magnitude 0. So the "interval contact", I refer to is speed dependent (specifically c-dependent). These pinholes (particle-interaction wormholes) are accessible only to energy (E).

Positor wrote:Mathematically, how can the manipulation of zero (zero spacetime distance = contact) and infinity (infinite speed = instant transfer = non-aging) produce a specific finite number?
I hope I answered this above. I never said c involved infinite transfer of energy, the finite ratio of space to time is 1, which is its apparent speed, translated into whatever units the observer happens to be using.

I sometimes refer to the solid-angular velocity of "chronaxial spin" as inherently infinite (i.e. instantaneous) but that would confuse the issue of this post.

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### Re: E-asy Access

Faradave » 17 Nov 2020, 19:40 wrote:
I sometimes refer to the solid-angular velocity of "chronaxial spin" as inherently infinite (i.e. instantaneous) but that would confuse the issue of this post.

I'll be following Twitter's example. "These claims are disputed by scientists"

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### Re: Events, Intervals and Speed

These claims may be disputed by a multitude of scientists but not all. Recent experiments involving tests of Wheeler’s Delayed Choice and the Quantum Eraser experiments suggest an instant, space-like transfer of light energy.

Those who dispute the possibility of an instant transfer of light dismiss the results as more quantum weirdness or they claim that light can reverse course and travel backward in time to erase a previous “incorrect” path and continue on to a detector with no loss in travel time.

Old paradigms die hard. One grave at a time.
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### Re: No Two Ways About It

Positor » November 17th, 2020, 11:09 am wrote:
Faradave » October 28th, 2020, 7:51 pm wrote:
"Why is the speed of light the same in all reference frames? I don’t know the answer to that question, and I don’t even know how to approach it. … The constancy [invariance] of the speed of light is unexplained." - Styer p.21

If the speed of light is properly identified as a velocity, it should, as with all velocities, obey the rule of the composition of velocities, according to which the velocity of an object has to be different relative to differently moving observers.
The speed of light fails this criterion by being invariant therefore, logically, it cannot be a velocity. The question is, Why do we call c a velocity when it appears to be something else?

Positor » November 17th, 2020, 11:09 am wrote:
Why should a zero spacetime interval give an observed speed limit of c, rather than some other finite value? Is this just a brute fact about our particular universe?Mathematically, how can the manipulation of zero spacetime distance = contact) and infinity (infinite speed = instant transfer = non-aging) produce a specific finite number?
The zero spacetime interval is the relativistic proper time for light. For light, emission and absorption are simultaneous events with a zero spacetime interval between them.

From our perspective as observers, we see a spacetime interval between the emission and absorption of a light signal which has the distance divided by time properties of a speed but it has the invariant “brute fact” of a spacetime dimensional constant. Logically, this makes c a dimensional constant rather than a speed.

The specific number for the non-speed “speed of light “ can be found in Maxwell’s equations where c=1/ √μϵ.

Here c is the observed distance to time ratio between the emission and absorption of energy in an electromagnetic signal. (the so-called speed of light).
(mu) μ is the dielectric permeability of the medium and (epsilon) ϵ is the magnetic permittivity of the medium. Our observation of c is medium dependent with our media usually being air and the vacuum of space.

QM does not require direct physical contact between particles for one particle to have a direct and instant effect on a distant, and possibly extremely distant, particle. This is contrary to photon theory where physical contact is essential. Therefore we have the invention of the photon.

An electromagnetic signal involves two or more remote particles momentarily sharing a common resonance despite their distance as if they were side-by-side. Energy can be shared among similar “entangled” particles and, if the loss of entanglement leaves a previously low energy particle with a higher energy level than before while a high energy particle has simultaneously lost an equal amount of energy, we see this as an exchange of light energy.

This is a direct and instant “space-like” exchange of energy with no need for the energy to pass through the spacetime between. That is how light can be instant because it is a direct exchange and not slowed by the presence of our spacetime environment. Light energy "wormholes" through spacetime.

Our observation of the same event is “time-like” and limited by the physical properties of our spacetime environment. The proper relativistic “speed of light” is instant, but the dielectric permittivity and magnetic permeability of our spacetime environment creates an observed time delay for the apparent c related departure and arrival time of the signal.

Here is N. “Viv” Pope's explanation for the “instant” nature of a light signal, “It means that in relativistic proper-time, the interacting atoms are in direct quantum contact, regardless of observational distance, that on the quantum-informational level there is no such thing as distance, a quantum being an irreducible amount of energy transacted in zero proper time. This means that at the quantum-informational level the transactions take place in terms of pure proper-time-instantaneous action-at-a-distance.”
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