Fun with spacetime diagrams

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Fun with spacetime diagrams

I was going to call this thread "Math Fun with STD's" but that would scare away 99.99% of the people on this forum. In my last S.R. thread I hinted on a variation of the Minkowski spacetime diagram where the t and t' axes were swapped. I started to fool around with this to see if any insights would fall out as a result. I got way more than I bargained for. I don't understand some of the implications. Maybe just writing this out loud will help me understand. This side-track should only take a couple of months I hope.
ralfcis
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Re: Fun with STD's

Ironically, you got your math wrong. Saying that 99.99% would be scared by the word math in the topic implies that no more than 0.01% would be comfortable with it. Given the size of our membership, that would be (ambitiously) equivalent to 1.6 people (or let's just say less than 2). However, I know at least two people here who absolutely love math and would no be scared away by it. Actually I know a lot more than just 2.

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Re: Fun with STD's

Exactly the response I was hoping for (and I was shooting for the number 2). Please, how can I get them involved outside of snide remarks?
ralfcis
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Re: Fun with STD's

I like math. I also could write a smart ass response here but instead I will simply ask, What does STD stand for and assuming SR stands for Special Relativity, Is this the thread you are referring to for future reference?
viewtopic.php?f=2&t=32807

PS: Click bate sucks and acronyms piss me off too.

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Re: Fun with STD's

yes, that is the link. yes S.R. is special relativity. STD is spacetime diagram. mSTD will be Minkowski spacetime diagram. cSTD will be the converse one.
ralfcis
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Re: Fun with STD's

I just finished the first 2 STD's of a bunch of velocities. The first is the classic Minkowski mSTD and the next is the translation into cSTD. I'm going to post them at the end because if I post them upfront people just won't see any fun in them at all; they're a little busy.

Many differences fall out as a result of swapping the t' and t axes.

1. In mSTD, he slope of every velocity line is 1/v while it's 1/(Yv) in the cSTD.

2. In the mSTD, v=c is depicted as a diagonal line separating the t' axes above and the x' axes below. In the cSTD, v=c is horizontal instead of diagonal. The cSTD has the added bonus that the slope of c will vary when relative velocity is brought in. It's near diagonal for low relative velocities (v=0) and near double that slope for high relative velocities (v=c). Hey, I don't make the math, I just report it.

Einstein arbitrarily rejected that light could adjust its velocity so that there could be no relative velocity greater than c. Instead he decided light would remain constant and spacetime would adjust itself to satisfy the max relative velocity for light. But the math shows either assumption is equally acceptable because the two STD's are mathematically the same.

If you wish to refute this mathematically, the diagonal lines going down from the t-axis in the mSTD are diagonal light message lines. Those same lines on the cSTD have varying slopes and are color coded to the velocity line that originated them. Remember, this is a math thread so no philosophical outrage to the facts presented here please.

3. You'll notice that the hyperbolas in the mSTD translate into circles for the cSTD.

4. There's more room to depict higher velocities in the cSTD, they're not bunched up against the diagonal v=c line of the mSTD.

5. The x'-axes (aka the lines of present) all take up a different slope relative to their t'-axes in the mSTD. It is a much simpler arrangement in the cSTD in that the x'axis is always perpendicular to the t'-axis. This will come in handy when we discuss the twin paradox depicted by the cSTD (the line of present can never swing into the future which is a huge difference).

I know this is overwhelming at first but if you work through some numbers you'll see that it's a simple translation. It'll get much more complicated to follow along in an example that includes a change in relative velocity.

mSTD

cSTD

ralfcis
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Re: Fun with STD's

Ralf, from the looks of it, your "cSTD" is just the Space-Propertime diagram, a.k.a. the 'Epstein diagram', which has been extensively discussed here and here.

If there is any substantial (non-philosophical) difference, would you please point it out?

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Re: Fun with STD's

When I read your reply I was super pissed. I thought you had skimmed my post and didn't see how different my cSTD was from Epstein. I spewed out a nasty retort but for some reason it would not submit no matter how many times I tried. Lucky for me because even though I had seen this diagram many times, I never really paid any attention to it. But now I see my cSTD is exactly Epstein. Sad!

So I guess the only philosophical point that remains is how the slope of a speed of light message from the moving participant changes wrt the relative velocity as shown in my Epstein diagram. Is this an equally valid assumption mathematically that either spacetime alters itself to fit a constant speed of light or that the speed of light alters itself to fit the relative velocity so that no relative speed can exceed c? It should be valid because it's reciprocity. The Epstein diagram brings that out while the mSTD hides it.

I guess the rest of this thread will further explore the Epstein diagram and its revelations.
ralfcis
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Re: Fun with Epstein STD's

Ok so I guess I'm going to have to find the answer for myself in the next few posts. The following mSTD is a small portion of the mSTD in the original post. It shows the light messages passing between the participants at various relative velocities.

A light signal is sent from Alice at t'=? that will reach Bob at t=3. For the same nominal t= ?, Bob will also send a light signal which will reach Alice at t'=3.

For v=.4c (blue lines), ?=1.96 source time
For v=.6c (green lines), ?=1.5 source time
For v=.8c (yellow lines), ?=1 source time
For v=.8824c (orang lines), ?=.75 source time
For v=.9756c (red lines), ?=.333 source time

An example of this is when v=.8c (yellow lines): When Alice has aged a year on her clock (after she and Bob start at t=t'=0) she sends a light signal to Bob which reaches him when his clock says 3. Bob also sends a signal to Alice when his clock says 1 and it will reach Alice when her clock says 3.

Since atomic clocks are used, there is no need for sync'd clock networks, the implied universal accuracy of the clocks is enough to guarantee trustworthy results.

Notice the speed of light is always a 45 deg diagonal line in the Mstd but in the Epstein std (Estd) the slope of light speed changes with relative velocity (as will be seen in the next post). I need to understand what this signifies. The Mstd is converted into an Estd simply by switching t and t' axes. The next post will show the conversion of the above Mstd into its Estd and how the light lines change as a result.
ralfcis
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Re: Fun with STD's

All the best dramas - and physics is surely dramatic - interleave some light comic relief before rebuilding the tension.

I'll just mention that when I opened the thread I was greatly relieved to find it did not deal with Sexually Transmitted Diseases. It was straining my imagination to figure out how one could possibly have fun with them.
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Re: Fun with STD's

ralfcis » 28 Jul 2017, 23:46 wrote:Is this an equally valid assumption mathematically that either spacetime alters itself to fit a constant speed of light or that the speed of light alters itself to fit the relative velocity so that no relative speed can exceed c?

Neither. Spacetime looks exactly the same for every inertial observer, but the other one's spacetime looks different than one's own (so to speak). As I have shown in my thread on acceleration and space-propertime (SPT), things change under acceleration and it (sort-of) explains why "the other one's spacetime looks different than one's own".

Look specifically towards the end of that rather short thread, where the concept really comes out of the woodwork. It is in my opinion the way relativity should be introduced to newcomers, but others may differ...

BurtJordaan
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Re: Fun with STD's

Ok, I'll take a look.
ralfcis
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Re: Fun with spacetime diagrams

I've changed the last Mstd a little to alleviate confusion in the transition to Estd.

This is a small slice (around t=3) of the large Mstd. It depicts light signals between Bob and Alice at various relative velocities. Alice is depicted as the moving participant so her light speed signals originate from her velocity lines at her t' times and end up at Bob's t=3 time. These are shown as the rainbow line composed of medium thickness lines.

Bob and Alice have agreed beforehand to send out signals at the same reading on their clock for the various velocities. At .4c, they will each send out at signal at 1.96 their time after they have zeroed their clocks at the start of the journey. Relativity will make the release of their signals non-simultaneous. At .4c, Alice will release her signal 2.143-1.96= .183 yrs after Bob in Bob's time even though both clocks read 1.96 yrs. Other velocity and signal time agreements are:

.6c, 1.5yrs
.8c, 1yr
.8824c, .75yrs
.9756c, .33yrs

All were chosen because of the nice numbers they produced for easy calculation.

Bob's transmissions look quite different from Alice's as they are not all bunched up in one line. They are a bunch of separated parallel lines that intersect their velocity lines at t'=3. As v-> c the lines get very much longer than Alice's signal lines to Bob. (They are the thickest color lines on the graph. They will correspond to the thickest color lines on the Estd graph. The single rainbow line gets split up into non-parallel lines that intersect the velocity lines on the t=3 quarter circle.)

This lengthening does not happen in the Estd. What also doesn't happen is the slope of the signal lines does not remain at a constant 45 degree angle. When using Estd's instead of Mstd's, c between Alice and Bob changes with their relative velocity.

So if you want to send a light signal in an Estd, it will not be a 45 deg angle. This has no physical significance, it's due to the fact that the grid of an Estd depicts dilated time while the grid of an Mstd is Bob's proper time.

Next we'll look at how the lines of present appearance changes between an Mstd and an ESTD.

P.S. Notice there is no need to invent the concept of length contraction in any part of this discussion.
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Re: Fun with spacetime diagrams

My professor gave me an STD through the mail. I had to go to her office and give her my STD in person. We understood each other much better after we exchanged STDs.

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Re: Fun with spacetime diagrams

Ralf, I haven't seen such confusion on spacetime diagrams of any type before. And the confusion in the descriptions matches the state of the diagrams.

Sorry, this can't stay in Physics, so it is moved to Personal.

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Re: Fun with spacetime diagrams

ralfcis » 04 Aug 2017, 17:44 wrote:So if you want to send a light signal in an Estd, it will not be a 45 deg angle. This has no physical significance, it's due to the fact that the grid of an Estd depicts dilated time while the grid of an Mstd is Bob's proper time.

No, horizontal lines in Epstein diagrams are the lines of simultaneity for the reference frame, not 'dilated time'. Frames moving relative to the reference frame, also have lines of simultaneity at right angles to their time axes, as you correctly depicted before.

Remember, Epstein diagrams are really 'space-propertime diagrams' and they are all about propertime. The fact that they can be used to illustrate time dilation and Lorentz contraction is just coincidental and is just confusing the issue of the real purpose if the diagrams.

As you may have noticed, I have not mentioned the latter two terms in my writings about them - they are quite irrelevant when we are dealing with propertime.

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Re: Fun with spacetime diagrams

Jorrie I can only assume you've had a bad week and didn't actually read any part of this thread before you responded. So take the weekend. Maybe take a look at what I've posted; it's just basic algebra. I've seen no evidence there's someone here who's familiar enough with that to come to my defense but maybe you can point out the math that backs up any of what you said. Then, feel free to re-instate this thread back on the physics forum where it belongs. Thanks
ralfcis
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Re: Fun with spacetime diagrams

Ralf, you have probably succeeded in scaring everyone here off spacetime diagrams forever. :( You have surely taken the fun part out of it...

I have read and understand what you are attempting, but this is not the way to explain relativity using spacetime diagram. Up to this post, it was still reasonable, despite somewhat objectionable prose, but nothing fundamental.

After that, everything degraded into a confusing mess. I put it to you that the Minkowski diagram that you posted here, with its text, is likely to be incomprehensible to most people, including me. And I think I understand spacetime diagrams.

You said something like "show the math" - well I have not seen any math in your posts to criticize, but please spare us that. If the math is anything like the diagrams and their descriptions, it may drop this thread further than just "Personal".

My suggestion to you is to rather read up on what Epstein Space-Propertime diagrams really entail and what their limitations are. I have not seen you ask any questions on any of the threads that discussed such diagrams, but do you really think you have enough understanding to write threads in our Physics section about them?

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Re: Fun with spacetime diagrams

Yes I do and I'll tell you why. I don't know how Epstein came up with his STD but I know how I derived it. I simply swapped the t and t' axes in the Minkowski STD and out popped Epstein. I am just exploring the ramifications of that swap. I find it too much effort to ask questions because I find your answers are more about semantics than understanding. Very rarely do you provide a definitive answer to my specific questions so I stopped asking.

I can just do a simple example of how an mSTD at .8c transforms to an Estd. That has far fewer lines than considering 5 relative velocities on 1 graph. You'll see all I'm considering in this first part is the exchange of birthday messages between Bob and Alice; absolutely unrelated to what you think I'm saying. In subsequent posts I will consider how the transform affects lines of present, same-age lines and the doppler effect ratio.

If you don't understand what I'm saying you can ask for clarification. You don't accept graphical representations as valid math then I'll present algebraic equations. Math is not a personal theory or a philosophical theory. I think kicking me off every time you or I don't understand something is beyond the power that a forum moderator should have. You seem to have far more patience with word-salad and brain-salad posts than you do with mine and those posts are far more damaging to the integrity of this forum..
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Re: Fun with spacetime diagrams

ralfcis » 05 Aug 2017, 12:50 wrote:You'll see all I'm considering in this first part is the exchange of birthday messages between Bob and Alice; absolutely unrelated to what you think I'm saying.

So what do you think I think you are saying?

Actually, do not bother, because I find your answers equally enlightening, somewhat like you said:
Ralf wrote:I find it too much effort to ask questions because I find your answers are more about semantics than understanding.

You are welcome to develop your understanding here on Personal Theories and just maybe some other views will help you. Do not expect much from my side, because it is not necessary to protect the Forum from private theories. In fact, on the science side it seems to be the most popular section - maybe this tells us something...

BurtJordaan
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Re: Fun with spacetime diagrams

No, this does not belong in the personal theories section as it is pure physics. If I show you the simpler example at .8c, you will understand it. If you're banning me on the basis of complexity then your recent posts are no walk in the park either.

This is what you think I'm saying:

ralfcis » 04 Aug 2017, 17:44 wrote:
So if you want to send a light signal in an Estd, it will not be a 45 deg angle. This has no physical significance, it's due to the fact that the grid of an Estd depicts dilated time while the grid of an Mstd is Bob's proper time.

No, horizontal lines in Epstein diagrams are the lines of simultaneity for the reference frame, not 'dilated time'.

I'm talking about the 45 deg light message lines and you're talking about horizontal lines of simultaneity. I was exploring why the light lines are not 45 deg in the Epstein diagram; a question I asked up front and another question that went unanswered. I mean relativity is all about translation between coordinate systems and you are convinced this does not apply between Minkowski and Epstein. I'll show you the simpler translation example on Monday when I have time.
ralfcis
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Re: Fun with spacetime diagrams

ralfcis » 05 Aug 2017, 16:51 wrote:I'm talking about the 45 deg light message lines and you're talking about horizontal lines of simultaneity.

I was commenting on a false statement that you made. I repeat: horizontal lines in Epstein diagrams are the lines of simultaneity for the reference frame, not 'dilated time'. The problem is not just semantics - it is about incorrect interpretations and/or statements.

It so happens that light signals in the reference frame also move along the horizontal lines and this is one of the weak points of the Epstein and probably the main reason why physicists don't use them. It makes figuring out the how your "greeting signals" will look like a little difficult and quite unintuitive, but I'll leave you to puzzle that out.

I mean relativity is all about translation between coordinate systems and you are convinced this does not apply between Minkowski and Epstein.

Nonsense. Relativity is about transformation between inertial frames, not between coordinate systems. One can obviously also convert values from one coordinate system to another, so where did get the idea that I'm "convinced" of something silly like you stated?

In any case, I'm out of here, but please stop making false statement as if they are facts.

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Re: Fun with spacetime diagrams

BurtJordaan » August 5th, 2017, 12:00 pm wrote:
I was commenting on a false statement that you made. I repeat: horizontal lines in Epstein diagrams are the lines of simultaneity for the reference frame, not 'dilated time'. The problem is not just semantics - it is about incorrect interpretations and/or statements.

It so happens that light signals in the reference frame also move along the horizontal lines and this is one of the weak points of the Epstein and probably the main reason why physicists don't use them. It makes figuring out the how your "greeting signals" will look like a little difficult and quite unintuitive, but I'll leave you to puzzle that out.

I agree that Ralf’s diagram could use some clarification but, that said, I am inclined to agree with Ralf about the other diagrams. I read the horizontal lines in the Epstein diagrams as lines of simultaneity and equivalent to the 45 degree lines in the Minkowski diagrams and, in both diagrams, the lines represent time dilated to the point of instanteneity.

I have a distrust of diagrams because there is the always the danger of mistaking the map for the territory but, in the case of the E-sdt and M-std, I think the diagrams are valid when compared to observations and they are telling us that the proper time for light is instant between signal and receiver. This has some important implications and I would not dismiss it as a “limitation” of the diagram.

The diagrams are telling us that it is possible to jettison the concept of c as being a speed and treat it as a Pythagorean representation of Einstein’s formula; that is, c can be derived simply as a geometric constant ratio of units of distance and time. This makes the use of c fundamentally different from Einstein’s axiomatic interpretation of c as the speed of light.

Also, I can’t fault the logic of Dave O’s comments in the “Experiments” thread. He is describing the way light should work if photons have a velocity through space. The problem with this view is that it is not consistent with observation. The std’s are consistent with observation but they are not consistent with the use of c as a speed. Dave's views provide an interesting comparison.

The horizontal line in the E-std is telling us that a light signal has no “proper” time interval but there is another aspect to time known as “relativistic” time and that is what we see as observers. Relativistic time is found in both SR and the std’s as a dimensional constant where every interval of space includes a constant interval of time amounting to one second for every 300,000 km of distance. This is the delay all observers see in a light signal.
bangstrom
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Re: Fun with spacetime diagrams

As Ralf progresses in his effort to show Alice an Bob's reciprocating greeting signals, the limitation of having the signal path of light on the line of simultaneity will become apparent. Not insurmountable, but, let's say, awkward...

BTW, Einstein did not invent the speed of light as 'c', Maxwell did so long before the era of Einstein. Einstein just discovered how to use it in the rel world.

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Re: Fun with spacetime diagrams

BurtJordaan » August 6th, 2017, 2:51 am wrote:
BTW, Einstein did not invent the speed of light as 'c', Maxwell did so long before the era of Einstein. Einstein just discovered how to use it in the rel world.

The constant c appears in Maxwell’s equations as the ratio of the magnetic permeability and electric permitivity of free space which was previously calculated by Weber and Kohlrausch in 1857 and, it was noted at the time, that numerical value was the same as the so called ‘speed of light.’ However there is no implication of a ‘wave theory’ in Maxwell’s equations where c is interpreted merely as a constant. And, since Maxwell’s equations apply equally to all inertial observers independent of their relative velocities, it makes no logical sense to regard c as a speed rather than as a dimensional constant.

It was also counter-intuitive for Einstein to postulate the value of c as a speed appearing to be the same for all observers independent of their own velocities but he likely did so from consideration of Maxwell’s laws and continued the error.
bangstrom
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Re: Fun with spacetime diagrams

Bang, evidently you have missed out on some piece of classic scientific history:

"With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. Maxwell proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena.[6] The unification of light and electrical phenomena led to the prediction of the existence of radio waves."

https://en.wikipedia.org/wiki/James_Clerk_Maxwell

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Re: Fun with spacetime diagrams

BurtJordaan » August 6th, 2017, 3:06 pm wrote:Bang, evidently you have missed out on some piece of classic scientific history:

"With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. Maxwell proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena.[6] The unification of light and electrical phenomena led to the prediction of the existence of radio waves."

https://en.wikipedia.org/wiki/James_Clerk_Maxwell

I am well aware of the history of Maxwell’s c but his c has all the characteristics of a spacetime dimensional constant and none of the characteristics of a speed with the exception of being a ratio of distance to time. I don’t consider each and every ratio of distance divided by time to necessarily be a speed and the ratio c appears to be a dimensional constant having nothing in common with what we understand as a speed. Also, Maxwell’s proposal of light as electric and magnetic fields traveling through space as waves in a medium ran into difficulty with the null result of the M-M experiment which failed to demonstrate the existence of such a medium.

For a speed to be a speed it has to be the speed of something that is physically observable and all speeds correctly identified obey the rule of the composition of velocities where velocities can be added or subtracted from other velocities relative to differently moving observers but light does not qualify by this definition.

The diagrams you have been using were not derived by tracking the path of a light beam as it moves through space and likewise they can not be used to plot the position of a light beam on the way from source to receiver. They only work for plotting the departure and arrival times of a light signal. This is because the diagrams are based on the use of c as a dimensional constant with a fixed geometrical relationship between space and time and the ‘speed of light’ lies on the lines of simultaneity where travel times are instant and ‘instant’ is not a speed.

Some of Einstein’s contemporaries, mainly from the Copenhagen school, noted this disconnect between the value of c and whatever the true ‘speed of light’ might be. The ‘speed of light’ from the perspective of light, appeared to take place in terms of pure proper-time-instantaneous action-at-a-distance but we can only observe light as described in SR where otherwise simultaneous events separated by space are also separated by a time interval of one second for every 300,000 km of space.

Niels Bohr, among others, proposed that when we see a distant star, an electron on the star drops to a certain level while an electron in one’s eye simultaneously goes up by an equal amount and we see the star with no energy loss and no energy is lost to ‘hang time’ as a photon waits for a place to land. We may see a vast distance to that far away star but both electrons ‘see’ none of the time or distance that we see. Einstein dismissed this possibility as “spooky action at at distance” and insisted that light propagated through space with a measurable speed but there is nothing speed-like about his view where c is the speed of light. The constant c appears in SR as a true dimensional constant independent of any speed so c can not be a speed.
bangstrom
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Re: Fun with spacetime diagrams

Bang, have you read the Maxwell paper, available on http://rstl.royalsocietypublishing.org/content/155/459?

He has shown unequivocally that electromagnetic waves have a theoretical constant propagation speed through space, which he labeled v, not c. In the paper, c was used for an electrical current parameter. He then commented that since the (then) observed speed of light is close to this value, it suggests that light may also propagate as an electromagnetic wave, something that has been confirmed since.

In general, science considers anything that has the dimensions of distance/time as a speed. Einstein/Minkowski replaced the "medium" of early times by spacetime and we never had to look back since.

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Re: Fun with spacetime diagrams

BurtJordaan » August 8th, 2017, 1:15 am wrote:
In general, science considers anything that has the dimensions of distance/time as a speed.

This appears to be so broad a definition of the word ‘speed’ as to include even jargon uses of the word that differ from ‘velocity’ such as the ‘speed’ of a trip to the store or the operating ‘speed’ of a computer. The speed of an airplane is not measured by its departure and arrival times but this is the way the speed of light is measured and it only works for round trip measurements with the one-way speed of light remaining unknown. Some who have looked into the matter of the speed of light have found its speed to be something far from the classical understanding of speed as a ballistic velocity and, in model form, much more like the operating speed of a computer.

As for the “constant propagation speed through space,” this has never been anything more than conjecture because light can’t be observed between source and sink. In the old Wheeler-Fynman Absorber Theory, light travels at every possible speed including all speeds in reverse and who can say they were wrong? The theory worked despite its whimsical explanations.

Jim Walker has this to say about the problem:
“How can it (light) travel through space? If it exists in space, what describes its shape, size, and boundary limits within space-time? How does this mysterious "action-at-a-distance" occur? No one has yet come close to accurately describing the alleged corporal substance of this ethereal phenomenon, and certainly not without also producing insurmountable paradoxes. Needless to say, the inconsistent descriptions present epistemological problems as well as ontological. Can we actually know anything about sole photons? Perhaps, even in principle, there occurs a quantum barrier to forever prevent knowledge of them. Or perhaps there exists nothing for us to know about; maybe light does not exist at all between emission and detection!

In this treatise I have no intention to show that the phenomenon of light does not exist. On the contrary the vast experimental data provides ample evidence that something occurs at the events. By "event" I mean something happening. For example the source (emission) of light and the detection of light act as measurable events. But where else does it occur? Our descriptions of light forces us to think of light as traveling through space, either as wave, particle or a union of both. But in doing so, we come up against insurmountable logical problems when we try to apply these descriptions to the double-slit experiment or the three polarizer problem. Can we describe light in another way that upholds the data yet eliminates the paradoxes without contradicting the mathematical models?” http://nobeliefs.com/light.htm
bangstrom
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Re: Fun with spacetime diagrams

The source that you have quoted says it all. No further comment needed.

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