Photons: The Argument for their Existence?

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

Re: Staying in Touch

Postby Faradave on November 12th, 2019, 12:45 pm 

Positor wrote:I would be interested to know Faradave's view on this point.


Image

I stick with the conventional view & observations that spacelike trajectories are non-traversable. The may however serve as reference connections about which separate properties may be correlated.

Image
A tether is an example of a spacelike connection (here a tangible "entanglement") about which two umbilically attached astronauts my correlate their spins (total spin zero or total spin double), no matter how far apart. They each maintain spin direction with respect to the tether, rather than to each other. If the tether is severed, their correlation is no longer guaranteed, an instant change in status from shared state to separate states.

This does nothing to take away from bangstrom's view that limit c should be considered a dimensionless universal constant. If time and space are both considered as separators of events then the ratio of separation/separation = 1 has no real units. That time is a unidirectional separator while space is associated with bidirectional translational freedom, does nothing to change that.

"The true constants have to be pure numbers, not quantities that have 'dimensions'" - Barrow p.36

davidm wrote:Petkov maintains that everything’s physical existence is, in fact, a world tube — that each person (and everything else) literally exists timelessly as a world tube,

I also like the term "world braid" which accommodates thermal motion of a constituent particles. The concept is one upon which I refute the existence of photons as particles. No worldline, no particle. The interval magnitude of a lightlike worldline is defined as zero. This does not deny such a "null vector" its direction but it establishes a point of contact rather than a particle.

4D Contact.png
Lightlike "null intervals" are realized in bypassing intrinsically equal separations of space and time (regardless of units). Their ratio is then a dimensionless 1, which happens to correlate to an anthropomorphic "speed" limit.


Einstein seems to have realized this in referring to separate events A & B,
"Einstein's original justification for this independence was that 'it is at once apparent that this result holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide'" from Jorrie's reference.

The context was instant acceleration, which is attributed to "photons".
Last edited by Faradave on November 12th, 2019, 1:31 pm, edited 1 time in total.
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Re: Radical Movement

Postby Faradave on November 12th, 2019, 1:14 pm 

~ Off Topic ~

davidm wrote:Petkov said that photons do not move. Neither does anything else. Everything just exists timelessly as unchanging world tubes in 4D Minkowski spacetime.

Yes and No. Petkov ignored the class of faster-than-light phenomena, which includes projections.

In frames other than Frame c ( illustrated above with interval-time coordinates), lightlike intervals are projections of contact, unrestricted by limit c. Thus, they are free to move in the 4D block! With instantaneous spin of a lightlike interval about time, a "light cone" is generated, which is coincident with an "instance" of a field (e.g. electric or gravitation).

This also explains the absolute indeterminism of light emission as the field points in all directions at once. This is a basis for free will, even in a block universe.

Image
A spinner that points in all directions at once (by instantaneous spin) is truly free in its choice.
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Re: Staying in Touch

Postby davidm on November 12th, 2019, 1:17 pm 

I also like the term "world braid" which accommodates thermal motion of a constituent particles.



Life is a braid in spacetime.

I'm pretty sure Sabine trashed Tegmark and his "mathematical universe," too, ha ha! Not that Sabine is necessarily right, but she speaks her mind!
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Re: Radical Movement

Postby davidm on November 12th, 2019, 1:34 pm 



We could do separate thread on free will in this and other contexts in the philosophy forum. There is a lot more to be said about this subject than some of the usual stuff I read online, and in moldering texts. I keep seeing how the biologist Jerry Coyne, for example, is constantly telling us that we have no free will. He even lectures on this subject, though in no way is it in his area of expertise. In one blog post he ranted and raved about how someone had dented his parked car and drove away without leaving a note. Well, Jerry, they could not have done otherwise, according to you! lol! Anyway, sorry for off-topic.
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 12th, 2019, 3:10 pm 

davidm » November 12th, 2019, 10:38 am wrote:
A world tube is a 4D generalization of world lines in spacetime diagrams. Petkov maintains that everything’s physical existence is, in fact, a world tube — that each person (and everything else) literally exists timelessly as a world tube, such that each person exists timelessly between his birth and his death. The indexical that we label now is a temporal part of a much larger whole, in the same way that, for example, the eyes are a spatial part of a much larger whole, an entire body.

Thanks for the reply. From what little I have read of Petkov so far I was beginning to get the idea that his worldtubes are not the same as worm holes which was my first impression. So would it be correct to say that world tubes are more like world lines with volume that extend both forward and backward in time?

davidm » November 12th, 2019, 10:38 am wrote:
Specifically, Petkov has argued in a number of papers that special relativity is impossible under the alternative view — that we are 3D objects that somehow “move through” time.

This is what bothers me. SR originated as a 3D theory but it was revised by Einstein himself to include a fourth dimension of time so the “alternative” view to SR is GR. I keep waiting for the part where Petkov says, ‘Forget SR and consider GR.’ Does he ever get there?
davidm » November 12th, 2019, 10:38 am wrote:
He (Petkov) specifically discusses, in a number of papers, how the phenomenon of length contraction can only be understood (says he) on the premise that observers in different relative “motion” are observing different cross-sections, or angles, of an existent world tube that does not actually contract or change at all.

This is my view exactly. An object moving at relativistic speed is rotated counterclockwise through 4D spacetime relative to an observer giving a false impression that the object is growing shorter.
davidm » November 12th, 2019, 10:38 am wrote:
Petkov, then, is an eternalist, or block universalist, who believes that all moments in time are equally real, just are all locations in space are equally real. He also argues that this fact precludes free will, because, he says, the future “already,” in a sense, exists, and therefore cannot be changed, any more than we can change the past.

This is the unavoidable conclusion from a block world view. The block view has merit but I suspect there may be some loophole in Heisenberg’s uncertainty to allow for free will.
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 12th, 2019, 3:24 pm 

Positor » November 12th, 2019, 9:04 am wrote:
Why, therefore, is it said that information can be passed by EM radiation (which is lightlike) but not by entanglement (which is spacelike)?

If we could, and I say we can and do, send intelligible information via entanglement instantly from one remote point to another, we can never observe such communication as instant “spacelike” because the presence of spacetime itself limits our observation to being lightlike. The magnetic permeability and the electro permittivity of vacuum space make it impossible to observe simultaneous events as simultaneous whenever we see a distance between them.

Positor » November 12th, 2019, 9:04 am wrote:
If all points on a 45-degree line on a Minkowski diagram (representing a lightlike interval) are considered to be 'touching', then I do not see how all points on a horizontal line in such a diagram (representing a spacelike interval) can also be 'touching'.


If two particles act independently we say they are separate but, if two particles act in unison, we say they are touching. Entanglement is a QM effect where two remote particles act in unison by sharing a common wavefunction, in which case, the particles are touching. Entanglement only happens at the particle level so it is “impossible” only because we never observe remote touching (entanglement) at the macro level.
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 12th, 2019, 3:42 pm 

BurtJordaan » November 12th, 2019, 10:28 am wrote:
I will not comment on the entanglement aspects, but on the SR side, there is no absolute synchronization available to us humans. So if you know about an experiment, please give us the reference - it should be Nobel price worthy.

The clock synchronization used to attempt to measure the speed of entanglement should work perfectly well to measure the one-way speed of light. I would be surprised if the Noble committee is surprised to find that light signals should be much “faster than light” if measured by synchronized clocks. It is a frequently stated observation that the emission and absorption of a light signal are simultaneous events.
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Re: Picking Simultaneous Nits

Postby Faradave on November 12th, 2019, 4:43 pm 

bangstrom wrote:The magnetic permeability and the electro permittivity of vacuum space make it impossible to observe simultaneous events as simultaneous whenever we see a distance between them.

In most reference frames, yes. But in those spatially midway between (in the rest frame of the simultaneous events) and with any motion restricted perpendicular to their line of separation, we should observe the normal impression of "simultaneous". One could argue for other special cases as well.

bangstrom wrote:It is a frequently stated observation that the emission and absorption of a light signal are simultaneous events.

Some care is needed. To say that emission and absorption are the "same" event is not quite the same as saying they are "simultaneous" (literally at the same time). That's the fascinating part about "remote contact". It's 4D contact, separated by equal spans of space and time. Thus emission and absorption are the same event with different spacetime coordinates (like longitudes at earths poles).
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Re: A Personal Touch

Postby Faradave on November 12th, 2019, 5:08 pm 

Though a personal model (similar to Jorrie's cosmic heart), a curved-space, radial-time structure provides that entanglement (vx) is the shortest possible simultaneous connection that p and q can have. It is non-traversable because it is superluminal (thus, retro-temporal) but can still serve as a common reference.

entangled 2D slice.png

On the other hand, entanglement is not the shortest possible connection of any kind. That is a lightlike connection between p now and q in the future. Though light is shown as a projection, its interval span is zero. Thus, observing an entangled particle (photo-interaction) typically knocks it off (i.e. breaks) the fragile entanglement connection.
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Re: Photons: The Argument for their Existence?

Postby BurtJordaan on November 12th, 2019, 5:29 pm 

bangstrom » 12 Nov 2019, 21:42 wrote:The clock synchronization used to attempt to measure the speed of entanglement should work perfectly well to measure the one-way speed of light.

Do you perhaps know who attempted to measure it and where was it documented?
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Re: Photons: The Argument for their Existence?

Postby davidm on November 12th, 2019, 5:52 pm 

Thanks for the reply. From what little I have read of Petkov so far I was beginning to get the idea that his worldtubes are not the same as worm holes which was my first impression. So would it be correct to say that world tubes are more like world lines with volume that extend both forward and backward in time?


Yes. World tubes, or braids, are all that exist, on this view, and past, present and future are equally real.

This is what bothers me. SR originated as a 3D theory but it was revised by Einstein himself to include a fourth dimension of time so the “alternative” view to SR is GR. I keep waiting for the part where Petkov says, ‘Forget SR and consider GR.’ Does he ever get there?


No. He maintains that SR alone proves the literal existence of the block world. GR is not necessary for this proof.
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Re: Photons: The Argument for their Existence?

Postby davidm on November 12th, 2019, 6:01 pm 

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Re: Picking Simultaneous Nits

Postby bangstrom on November 13th, 2019, 5:41 am 

Faradave » November 12th, 2019, 3:43 pm wrote:
In most reference frames, yes. But in those spatially midway between (in the rest frame of the simultaneous events) and with any motion restricted perpendicular to their line of separation, we should observe the normal impression of "simultaneous". One could argue for other special cases as well.

So if an observer midway between the Earth and the moon should see a laser beam emitted from the Earth would they see the beam strike the moon at the same instant ?
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 13th, 2019, 5:45 am 

BurtJordaan » November 12th, 2019, 4:29 pm wrote:
bangstrom » 12 Nov 2019, 21:42 wrote:The clock synchronization used to attempt to measure the speed of entanglement should work perfectly well to measure the one-way speed of light.

Do you perhaps know who attempted to measure it and where was it documented?

I don’t know of any accounts of someone trying to measure the one-way speed of light with two synchronized clocks except for anecdotal reports saying that it is impossible. I interpret this as saying that someone may have tried but they didn’t like the results. Even a crude attempt to synchronize clocks should be able to detect a signal faster than c.
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Re: Photons: The Argument for their Existence?

Postby BurtJordaan on November 13th, 2019, 9:14 am 

bangstrom » 13 Nov 2019, 11:45 wrote:Even a crude attempt to synchronize clocks should be able to detect a signal faster than c.

Can you describe how such a "crude attempt" would work?
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Re: Text or Context

Postby Faradave on November 13th, 2019, 11:30 am 

bangstrom wrote:So if an observer midway between the Earth and the moon should see a laser beam emitted from the Earth would they see the beam strike the moon at the same instant ?

No. I may have missed the context.

I was referring to traditional simultaneity. A stationary observer midway between earth and moon would see synchronized explosions or two lasers (aimed at the observer) as simultaneous. He would also be in position to simultaneously receive reports on the spin states of two recently disentangled particles (on earth & moon) before parties on earth or moon receive reports from each other.

So, it would NOT work for light transmission between earth and moon (because lightlike remote contact is not simultaneous) but it would work for disentanglement (which is simultaneous).

Image
Though light transmission is interval contact, ∆x & ∆t mean it is remote and NOT simultaneous.

edit: added image & parentheses in 2nd paragraph
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Re: Photons: The Argument for their Existence?

Postby BurtJordaan on November 14th, 2019, 1:12 am 

BurtJordaan » 13 Nov 2019, 15:14 wrote:
bangstrom » 13 Nov 2019, 11:45 wrote:Even a crude attempt to synchronize clocks should be able to detect a signal faster than c.

Can you describe how such a "crude attempt" would work?

We have a nice practical method for measuring the one way speed of light (and its isotropy) by our resident expert (Dr. Don Lincoln), posted about a decade ago. He has actually done such a test as part of his job.

Nowadays he is very busy with (on top of Fermilab duties) outreach to laypeople through talks, YouTube and other participation activities, so he rarely has time to visit us.
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 14th, 2019, 4:23 am 

BurtJordaan » November 14th, 2019, 12:12 am wrote:
We have a nice practical method for measuring the one way speed of light (and its isotropy) by our resident expert (Dr. Don Lincoln), posted about a decade ago. He has actually done such a test as part of his job.


The apparatus proposed by Dr. Lincoln is essentially the same as the question I asked Faradave where you have a emission at one point and absorption at another and an observer exactly in the middle. (In Dr. Lincoln's experiment, the observer is a clock in the middle)
I asked, would the observer see the emission and absorption as simultaneous or at light speed?

bangstrom » November 13th, 2019, 4:41 am wrote:
So if an observer midway between the Earth and the moon should see a laser beam emitted from the Earth would they see the beam strike the moon at the same instant ?


Faradave answered,
Faradave » November 13th, 2019, 10:30 am wrote:
So, it would NOT work for light transmission between earth and moon (because lightlike remote contact is not simultaneous) but it would work for disentanglement (which is simultaneous).


I had an experiment in mind where it would work by finding emission and absorption to be simultaneous but I now find it apparent that experiment would not support the theory even if it is correct so I agree with Faradave that the observer would see the events at light speed. I other words, my experiment would not work.

I find that DR. Lincoln’s experiment has the same problem. It should demonstrate that the one-way speed of light is at c exactly the same as the two-way speed of light but it does not support the theory that c is the speed of light.

The problem with any version of the experiment is that the detectors are separated by, as Faradave said, “lightlike remote contact”. In Dr. Lincoln’s experiment, the detectors are placed 10 meters apart. By modern convention, Dr. Lincoln can no longer go to Paris to borrow their platinum meter stick. The distance of a meter is now defined as the distance light travels in 1/ 300,000,000th of a second so he would need a clock and a light source to measure the distance.

This raises the question of whether he is measuring the speed of light or is he twice determining the length of 10 meters since the process is the same. The speed of light can’t be measured. Consider the impossibility of trying to measure the speed of light over the distance of a light year.

I don’t agree with Faradave about one point where he says,”... but it would work for disentanglement (which is simultaneous).” The two entangled particles are separated by spacetime so, if one particle loses energy at the same instant another gains energy, the event could never be observed as instant because they are separated by spacetime. Different observers might disagree about the timing of the events or which event came first but disentanglement can never be directly be observed as simultaneous.
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Re: Photons: The Argument for their Existence?

Postby BurtJordaan on November 14th, 2019, 5:05 am 

bangstrom » 14 Nov 2019, 10:23 wrote:The apparatus proposed by Dr. Lincoln is essentially the same as the question I asked Faradave where you have a emission at one point and absorption at another and an observer exactly in the middle. (In Dr. Lincoln's experiment, the observer is a clock in the middle)

No, his detectors were first both at the oscilloscope where the equipment was calibrated and then one cable was uncoiled and its detector moved some known distance away. There was no 'middle' detector or observation.
I know the argument could be, how did he know the distance? Maybe he called in his local land surveyor to get precise lat's, long's and alt's for the two points...
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Re: Photons: The Argument for their Existence?

Postby Positor on November 14th, 2019, 8:10 am 

bangstrom » November 14th, 2019, 8:23 am wrote:I don’t agree with Faradave about one point where he says,”... but it would work for disentanglement (which is simultaneous).” The two entangled particles are separated by spacetime so, if one particle loses energy at the same instant another gains energy, the event could never be observed as instant because they are separated by spacetime. Different observers might disagree about the timing of the events or which event came first but disentanglement can never be directly be observed as simultaneous.

But Einstein called disentanglement "spooky action at a distance". There would be nothing 'spooky' about it if it were observed to happen at lightspeed rather than simultaneously.
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Re: Photons: The Argument for their Existence?

Postby BurtJordaan on November 14th, 2019, 10:37 am 

Positor » 14 Nov 2019, 14:10 wrote:But Einstein called disentanglement "spooky action at a distance". There would be nothing 'spooky' about it if it were observed to happen at lightspeed rather than simultaneously.

I expressed the hope before that someone knowledgeable in particle physics could correct some of bangstrom's misconceptions, e.g.
bangstrom » 12 Nov 2019, 10:05 wrote:The electron in one atom can jump to a higher orbital at the same instant that the electron in the other drops to a lower orbital and the electron with the higher energy level can be found in either of the two atoms. The two atoms share a common energy level and their energies are in superposition.

I know about Schrödinger wave functions, but I've never heard of such a superposition before. AFAIK, if an electron drops to a lower energy level, the event emits an energy packet (a photon or two, if you wish). It travels at light speed and some time later a distant atom can absorb the energy packet and an electron can jump to a higher energy level there.

To insinuate that this has anything to do with is entanglement is missing the point by a light year, IMO. But I'm open to be corrected by someone who knows this stuff.

I have heard of energy-time entanglement, but this is also something very different.
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 14th, 2019, 2:02 pm 

BurtJordaan » November 14th, 2019, 4:05 am wrote:
No, his detectors were first both at the oscilloscope where the equipment was calibrated and then one cable was uncoiled and its detector moved some known distance away. There was no 'middle' detector or observation.

This experiment sounds much different from the one I recall which was only in the planning stage. Do you have any more details?
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 14th, 2019, 2:21 pm 

Positor » November 14th, 2019, 7:10 am wrote:
But Einstein called disentanglement "spooky action at a distance". There would be nothing 'spooky' about it if it were observed to happen at lightspeed rather than simultaneously.

Right, there is nothing spooky about photon theory so Einstein's objection was not about a lightspeed interaction.

The idea of a simultaneous exchange of light energy was popular with a group of physicists known at the time as the “Vienna School.” Some of the members were the originators of quantum mechanics. These were the objects of Einstein’s objection to spooky action.

The oldest reference I know of to a spooky action where two atoms share a common Schroedinger wavefunction is from Hugo Tetrode’s article in Zeitschrift fur Physik. 10, 317 (1922).

This is from Tetrode’s 1922 article translated by A. F. Kracklauer
Suppose two atoms in different states of excitation are located near each other, normally it is to be expected that they would have little influence on each other; however, under special conditions with respect to positions and velocities, possibly also in the vicinity of a third atom, it might be that strong interactions occur, Such a situation could well lead to an energy transfer between atoms such that their excited states are exchanged. The energy loss of one and the gain of the other could occur in a time interval corresponding to their separation; that is, we would have an instance of emission from one atom and absorption by the other. While according to classical understanding, emission is a random event leading to radiation that also randomly might somewhere at some time be adsorbed; here in this theory, the source and sink of a radiative interaction are a virtually predetermined paired events.
That is, in effect, the sun would not shine at all were there no other charged bodies in the universe to adsorb its radiation.
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Re: Photons: The Argument for their Existence?

Postby BurtJordaan on November 14th, 2019, 2:47 pm 

bangstrom » 14 Nov 2019, 20:02 wrote:This experiment sounds much different from the one I recall which was only in the planning stage. Do you have any more details?

I gave the link to Don's quick description in this reply to you above. Do you really need more than that?
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Re: Nothing but Net

Postby Faradave on November 14th, 2019, 3:59 pm 

bangstrom wrote:The idea of a simultaneous exchange of light energy

An octopus glides over a coral reef feeling in nooks for prey. It receives information form its surroundings through nerve fibers running back through its arms to its brain. That's feedback information.

It's different if I cast a net in an area that usually has fish. When I pull it back I get a fish, but I never had information on its particular location. The net acts as a field, capturing a fish that happens to be in its range.

I adhere to the notion that exchange of a light quantum is exactly that, requiring both emitter and future absorber. But that doesn't mean the emitter knows of the absorber's existence. The absorber happens to occur on an that instance of the emitter's electric field (which coincides with its light cone). If there are multiple such absorbers, exchange is absolutely random (especially if a field is modeled as a field element pointing in all directions at once because of chronaxial spin). The field acts as a net which qualifies absorbers as in range but it provides no feedback to inform the emitter about that.

Just as a fish knows someone through a net, before the fisher knows he got the fish, information flows only forward in time along an emitter's lightlike field.
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Re: Photons: The Argument for their Existence?

Postby TheVat on November 14th, 2019, 4:33 pm 

So if a star were shining in an otherwise empty universe, would there just be a field but no exchange? The star, without external absorbers, would be a black blob?

edit: ah, i see Tetrode posed this conundrum. Sorry i didn't read all the posts.
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Re: Oh! I see.

Postby Faradave on November 14th, 2019, 8:58 pm 

It's a preposterous proposition on its face. Of course, stars at any given moment have more internal light than that which is radiating away. An allowance is needed for that or it's not a star.

Also remember it's not the existence of external absorbers now that matters. It's the existence of future particles, on the light cones of the emitters that is critical. That shouldn't seem strange, since every quantum of light ever directly detected by anything, anywhere, anytime has occurred on the future light cone of an emitter.

So, if the sun is calculated to be unleashing enormous numbers of yet undetected quanta, take that as assurance of the future.
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Re: Photons: The Argument for their Existence?

Postby bangstrom on November 14th, 2019, 11:26 pm 

BurtJordaan » November 14th, 2019, 1:47 pm wrote:
I gave the link to Don's quick description in this reply to you above. Do you really need more than that?

I don’t need any more information. Sorry, but I was looking through citation for the YouTube videos and didn’t notice the other citation.

The question remains of whether Don was measuring the speed of light or measuring the distance between the detectors in units of time. The constant c works as a conversion factor for converting between units of distance and units of time so the distance can be expressed as either value. The experiment doesn’t rule out the possibility that the object it claims to be speeding is totally imaginary at any point between the detectors.
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Re: Text or Context

Postby bangstrom on November 14th, 2019, 11:32 pm 

Faradave » November 13th, 2019, 10:30 am wrote:

I was referring to traditional simultaneity. A stationary observer midway between earth and moon would see synchronized explosions or two lasers (aimed at the observer) as simultaneous. He would also be in position to simultaneously receive reports on the spin states of two recently disentangled particles (on earth & moon) before parties on earth or moon receive reports from each other.

So, it would NOT work for light transmission between earth and moon (because lightlike remote contact is not simultaneous) but it would work for disentanglement (which is simultaneous).

Image
Though light transmission is interval contact, ∆x & ∆t mean it is remote and NOT simultaneous.

Shouldn’t interval (d) be simultaneous where it wormholes from one light cone to another while not moving either up or down on the space-time axis?

All light signals we emit are signals into our future and all light signals we receive are signals from our past but I don’t see that represented on your diagram.

Perhaps, since all recipients of our light signal exist in our past, their light cones should originate farther down on the common space-time axis so that the interval (d) intersects the other light cones in their future while all incoming light signals to our own light cone must originate from pinhole points above ours on the space-time axis.
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Re: Photons: The Argument for their Existence?

Postby Faradave on November 15th, 2019, 12:34 am 

bangstrom wrote:All light signals we emit are signals into our future and all light signals we receive are signals from our past but I don’t see that represented on your diagram.

Good question. I recently answered in another thread.

I see interval-time coordinates available at every location in a curved-space, radial-time model of the universe. That model specifically provides two independent paths to the future, one aging along a radial time coordinate and another path perpendicular to time and tangent to curved space. Two paths are demanded by SR in that light undisputedly gets to the future without aging (i.e. experiencing full time dilation).

Image
Two views of the same reflection.
Left: In frame c, where space is completely contracted in the direction of motion, incident light originates and terminates at the same event (yellow dot) p despite different spacetime coordinates for emitter and absorber. That light appears to jump (without aging) to event q. From there it reflects to a future event in contact with q.
Right: In the cosmic rest frame, light transmits tangent to curved-space (thus, independent of aging) from emission event p and incident upon spatially-remote future event q. From there, light is reflected tangent to space at the reflector. Both paths are perpendicular to the aging coordinate of their origin, yet destined for spatially-distant future events.
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