[guest4091]

It may be simple, but I can't map the description to the diagram. It would be a lot easier to follow these things if you'd describe the scenario in ordinary words and if the things in the description also exist in the diagram.

Here's the new and improved version.
Fig.1 is the U frame description.
A moving at .5c, sends a signal (blue) to mirror M at Ux=2.00. The signal reflects at R, and is detected by A at Ut=2.67. U observes the A-clock running slow. The hyperbola (red) is a line of constant time, and transfers At to the Ut scale.
Fig.2 is the A frame description.
M is moving at .5c in the -x direction, reflects the A signal, which A detects at At=2.31.
A assigns the time of reflection to R', per the SR simultaneity convention (half of round trip time). A calculates the distance to M as 1.73 at At=0, i.e. length contracted.
In fig.1, U observes light speed relative to A as .50 outbound and 1.50 inbound. The path 0RD is overlaid in fig.2 for comparison. The round trip time is the same for A.
This is the justification for Einstein's simultaneity definition, with equal path lengths out and back. Since there is no means or need of determining the absolute A-time for the reflection, consistency of the theory is the priority.
Using the coordinate transforms CT:
x' =  γ(x-vt) = 1.15[2.00 - .5(2.00)] = 1.15
t' =  γ(t-vx) = 1.15[2.00 - .5(2.00)] = 1.15
A check to support the fact that the spacetime graphics are a geometrical  representation of the CT.
A 2nd example is shown with the event off the diagonal.
x' =  γ(x-vt) = 1.15[1.50 - .5(1.00)] = 1.15
t' =  γ(t-vx) = 1.15[1.00 - .5(1.50)] = .29

p&r reflection.gif (9.5 kB . 1044x505 - viewed 2415 times)
p&r reflection2.gif (6.49 kB . 797x548 - viewed 2409 times)

[guest4091]

@phyti You could actually come down off your high horse and help others.
https://en.m.wikipedia.org/wiki/Postulates_of_special_relativity

I don't ride horses!.
If you want more references, I can do that.
I'll repeat, that most here seem to know the basics of SR, and some like pmb, know the whole theory.
I'll also admit that someone who works with an idea more than others, may forget that others need more detail for understanding. I may not agree with other opinions, but I don't insult them, just offer an alternate explanation.. My advice is the standard, "if you don't understand, ask".

[yor_on]

Phyti , I kind of like you, but I also think you hide. What is more is that you present it in such a way that it makes little sense to those not having a background in the mathematics you push for. Neither of those things impress me
=

don't get mad now :)
The point I'm making is that if you want to push for something you think someone else is arguing about, better ask first, and then define the terms you're using to define where they go wrong. Keep it clear and don't overwhelm the reader. It's at that time you lose them. If you're as good as you think you are, you should be able to do this

[yor_on]

I know, for you the mathematics speaks :)
But it doesn't for all of us Phyti

so simplify, find that reason why the mathematics must hold. and then describe it

[David Cooper]

Here's the new and improved version.

Much better - thanks.

This is the justification for Einstein's simultaneity definition, with equal path lengths out and back. Since there is no means or need of determining the absolute A-time for the reflection, consistency of the theory is the priority.

It's simply assuming that A is at rest and that the two light paths are of equal length, so the real justification for that synchronisation is that light is taken to be travelling at c relative to A. In the first case, where you took M as being at rest instead, the speed of light relative to A was not c. If you put a mirror with A and bounce the signal back to M, you can justify imagining that M is at rest when thinking things through for someone travelling with M on the same basis of assuming that both light paths (this time the ones starting from and then coming back to M) are of equal length. You thus have two contradictory accounts of events (one for A and one for M) which cannot both be true accounts of the action, but either one of them could be true, and no one will ever know. The inability to tell what speed light is actually going at relative to either A or M is not justification for claiming that there is no single right answer. The only way you can make the speed of light relative to both A and M equal to c is by changing reference frame in between looking at them, and you're then failing to recognise that you're having your cake and eating it by changing frame between measurements rather than sticking to a single inertial (i.e. genuine) frame for both. Using the frame in which A is at rest automatically asserts that the speed of light relative to M is not c, and using the frame in which M is at rest automatically asserts that the speed of light relative to A is not c, but what do you do: you selectively prune out all the things that aren't moving at c relative to light and deny that those relative speeds (that aren't c) count for anything, asserting that you have to change frame until they are moving at c relative to the light before that relative speed magically becomes the valid one for them, and in this way you make the one-way speed of light c relative to all objects.

Let's play the same kind of silly game with light itself. In some frames of reference, some photons are moving at 2c relative to other photons, but others are moving in the same direction with a relative speed of zero. What about all the values in between? Well, if they aren't moving on parallel paths we can always select a frame of reference in which we can assert that they're moving apart at 2c, so we can play the frame-switching game and make the claim that light always travels at 2c relative to other light unless it's co-moving, and any case where that doesn't appear to be the case is irrelevant because we should only analyse it by switching to a frame which makes it a relative speed of 2c. Only frauds would play such a game.

[alancalverd]

Alan, you can't use rotating discs for it

Agreed. See my reply #55, which also points out that as c is a scalar, not a vector quantity, it is independent of any direction, so the one-way speed must equal the two-way speed.

[jeffreyH (OP)]

Why is c a scalar? What are the historic reasons? Is it because it is considered a constant? A vector can certainly be defined for a photon.

[Colin2B]

Why is c a scalar? What are the historic reasons? Is it because it is considered a constant? A vector can certainly be defined for a photon.

Because it is the general case before a direction is defined? So just the magnitude.

[jeffreyH (OP)]

Yes for a locally measured magnitude.
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

[alancalverd]

No.

ε₀ and μ₀ are measured in entirely separate, static experiments.

If the value of c depended on direction, at least one of these would have to be a vector so you would always get different values for either ε₀ or μ₀ depending on the polarity of the applied electric or magnetic field. You don't.

For anyone with a real interest in experimental physics it is worth noting that the relative values of ε_xyzand μ_xyz for some materials are indeed anisotropic tensors and the magnitude of c does indeed vary with the orientation of the material. The fact that the resulting birefringence effects are independent of the orientation of the material with respect to the fixed stars, phase of the moon, or anything else, strongly suggests that there is no aether or other universal frame of reference, so c₀ is independent of direction.

[David Cooper]

ε0 and μ0 are measured in entirely separate, static experiments.

They aren't static if the experiments are moving. How are you calculating them? Are you using any distance measurements? If so (clue: you are), then you are supplying those measurements on the basis that the experiment is stationary, even though it may not be. You therefore fool yourself into imagining that there's no aether because you only have a simplistic understanding of what you're doing. It is the phenomenon of relativity itself that hides all the differences from you - that's precisely what allows you to carry out experiments on a naive basis and still get answers that work.

[guest4091]

Yoron#62;
Thanks for sharing your thoughts.
I do think if many words do not impart understanding, your effort is wasted. I remind myself to keep it simple and clear for the reader, but am not always successful. When reviewing papers I've written in the past, if they seem faulty, they go in the trash. I'm my worst critic, so it's not a question of 'how good you think you are', but how well you convey understanding to others. I'll work to improve.

[guest4091]

David C #64;
The 1st observer is actually U, and M is in his frame. Fig.1 is drawn according to his description/perception of events. The U frame is randomly selected from a multitude of frames with a velocity different from A, i.e. with a relative motion. U is not special in any way. The light path 0RD is associated with U only.
Returning to the 'train' example, the passenger on the moving train extends his hand forward and releases a stone. The path he sees is a straight vertical line to the floor. For  the bystander on the platform, the path is a curved line from the hand to the floor.
The path, the planetary orbits, missile trajectories, and even the light path, are histories of position, that reside in the mind, and have no physical objectivity outside the mind. As it is with the train example, so it is with the reflection example. The perception depends on the motion of the observer. 
In fig.2, A cannot observe himself as in an 'out of body experience'. A is present at At=0 and At=2.31, but not at the remote reflection. A does not know the local time of the reflection. As Einstein stated, it's not about the propagation of light, but a simple solution that resolves the issue of the remote event while in agreement with the constant c.
I know you are an advocate of LET from previous exchanges.
I added the relative light speeds, .5c outbound and 1.5c inbound, from U's perception to show, there is no difference. If you have read the 1905 paper, you would be aware that Einstein used relative speeds c+v and c-v to develop SR, which implies an absolute reference frame as an initial assumption, but disappears when the theory is simplified to one depending only on the relative speeds of the observers.
Lack of math skills or graphical interpretations will be a handicap for some.
There is nothing contradictory about two observers in relative motion having equivalent perceptions, such as reciprocal time dilation, or simultaneously different perceptions of an object in motion. It's not just about matter, light and motion. It's about knowing the difference between objects in motion and images of objects as processed by the mind.
SR was never presented as a theory of perception by it's author or those who modified it, but it should be, since it has the qualifications.

[David Cooper]

I added the relative light speeds, .5c outbound and 1.5c inbound, from U's perception to show, there is no difference.

No difference to what? Only to the illusion that each observer is stationary.

If you have read the 1905 paper, you would be aware that Einstein used relative speeds c+v and c-v to develop SR, which implies an absolute reference frame as an initial assumption, but disappears when the theory is simplified to one depending only on the relative speeds of the observers.

It doesn't disappear because the attempt to remove it leads to an infinite number of contradictions as soon as you assert that there is no absolute frame.

Lack of math skills or graphical interpretations will be a handicap for some.

Indeed, and the acceptance of contradictions is one of the worst failures you can make in maths.

There is nothing contradictory about two observers in relative motion having equivalent perceptions

There is something contradictory though when you assert that both accounts of events are true in terms of what has actually happened. Things would be fine if this stuff was just being pushed as a theory of perception, but it isn't - it's being pushed as an absolute account of reality in which contradictions are generated by the business of having one's cake and eating it.

[jeffreyH (OP)]

No.

ε₀ and μ₀ are measured in entirely separate, static experiments.

If the value of c depended on direction, at least one of these would have to be a vector so you would always get different values for either ε₀ or μ₀ depending on the polarity of the applied electric or magnetic field. You don't.

For anyone with a real interest in experimental physics it is worth noting that the relative values of ε_xyzand μ_xyz for some materials are indeed anisotropic tensors and the magnitude of c does indeed vary with the orientation of the material. The fact that the resulting birefringence effects are independent of the orientation of the material with respect to the fixed stars, phase of the moon, or anything else, strongly suggests that there is no aether or other universal frame of reference, so c₀ is independent of direction.

This is exactly why this is the best science forum. Is everyone taking this in? This is a very unique opportunity to learn. Don't waste it. No tuition fees!

[guest4091]

David C.#73;

There is something contradictory though when you assert that both accounts of events are true in terms of what has actually happened. Things would be fine if this stuff was just being pushed as a theory of perception, but it isn't - it's being pushed as an absolute account of reality in which contradictions are generated by the business of having one's cake and eating it.

If 10 people form a circle around a house, each will have a different view of the house.
There are 10 simultaneous views, each different from the others.
Who has the true/real view if there is only one house?
This simplest of cases shows the question is meaningless. If there were x people, all x  views would be correct, relative to each person. The statements are true concerning the images, but each image is incomplete regarding the house. All the images collectively are incomplete since they only provide information about the exterior of the house. The statements are about perception, not about the house.

In science, information is verified by measurement. Experiment has demonstrated that motion affects measurement and perception. There is no expectation that two observers moving at different velocities will make identical measurements or receive identical images of events.
In the last example, U makes measurements from his location and assigns local times to events. In the U frame, A is moving at v and light is moving at c.
A makes measurements from her location and assigns local times to events. In the A frame, U is moving at v and light is moving at c.
Each can say light is moving at c-v or c+v relative to the other, but not relative to themselves. They have no means of that type of measurement.
All an observer has is measurements and perception.
 
"it's being pushed as an absolute account of reality"

FALSE, since 'RELATIVITY' makes no such claim, and has no need for the concept 'absolute'. Why is the 1905 paper titled "On the Electrodynamics of Moving Bodies", and not some variation of "Relativity"?
The common phenomenon of induction was one example that didn't need an absolute reference. Move the magnet or move the coil, there was still current flow. Which object was 'really in motion' was irrelevant.

You miss the point of the principle of relativity.
Time dilation: (the most often misinterpreted)
The 1st postulate states physical processes occur the same way in any inertial frame.
1. If A observes the B-clock moving past him at high speed, it's perceived to run slower than the A-clock.
2. If B observes the A-clock moving past him at high speed, it's perceived to run slower than the B-clock.
It would be a contradiction of postulate-1, if both observing the same process, got different results. It would also be a strange world with no predictability. 
The math (algebra and geometry) consists of equations that are symmetrical with respect to A and B. It's as simple as swapping A and B in the 1st statement to form the 2nd statement.
What you call contradictory is actually reciprocity

[David Cooper]

If 10 people form a circle around a house, each will have a different view of the house.

And each view maps to the same model of the house rather than to ten incompatible models of the house which contradict each other, so your analogy doesn't fit.
 

Who has the true/real view if there is only one house?

They all map to the same one. In SR, you only have that if you go to an extreme model in which light reduces all the paths it follows to zero length and zero time, and with such a model you get event-meshing failures unless you go to a block universe model, and even if you go there, you get stuck because you can't account for the generation of that block without creating it under different rules (i.e. not SR).

The statements are about perception, not about the house.

Your analogy doesn't fit, but if it's all about perceptions, let's see SR being discussed in such a way that it only deals with those and stops making incompatible assertions about the actual house.

"it's being pushed as an absolute account of reality"

FALSE, since 'RELATIVITY' makes no such claim, and has no need for the concept 'absolute'. Why is the 1905 paper titled "On the Electrodynamics of Moving Bodies", and not some variation of "Relativity"?
The common phenomenon of induction was one example that didn't need an absolute reference. Move the magnet or move the coil, there was still current flow. Which object was 'really in motion' was irrelevant.

Stop pretending that SR makes no such claims. SR claims that there is no aether, and in doing so it ceases to be a mere theory of perceptions. We have armies of experts going around laying down the law as to how there is no aether and that the one-way speed of light is always c relative to any object it passes, and they attribute this to SR. SR is a theory of reality. Physics is an attempt to explain what reality is. If you want to take issue with the things people are saying here, you need to go and jump on all the ones who are asserting those things (about the non-existence of aether and the speed of (unslowed) light always being c relative to whatever it passes) and tell them they're out of line, bringing science into disrepute.

You miss the point of the principle of relativity.

I haven't missed the point at all. You are the one who has missed it, and it's because you're blind to contradiction.

What you call contradictory is actually reciprocity

No - it's plain contradiction. If its true that light passes A at c relative to A and that it also passes B at c relative to B while A and B are moving relative to each other along the same line, you must have light overtaking itself as it travels between A and B because it's moving faster than itself. In reality though, it is not moving at c relative to both A and B along that line. You've sabotaged your own thinking so extensively that you're incapable of recognising this kind of contradiction. For that reason, it would be best for you to look carefully at MGP instead (where it's harder to hide from the truth) and to let it help you unshackle your mind, but I'll say more about that in my next post because it's aimed at everyone who believes in SR. I want them to stop hiding from the truth by spelling out where they stand on the questions that it raises.

[David Cooper]

A challenge to all those who haven't yet seen the light:-

The Michelson-Gale-Pearson experiment showed what happens when you rotate a circuit and send light round it in opposite directions. I've pointed to this before from this thread, but the SR fans have failed to commit themselves to any pronouncements on it because it proves that the one-way speed of light is not always c in all directions relative to the things it passes and by extension that there must be an absolute frame. It's time for them to stop running away from this and to state their position on each question that I ask them to answer.

Imagine a ring of empty tube lined with a mirror coating. We will label it with a hundred sectors (or a million, or any big finite number you like), each sector being the same size. When we send light round the circuit, it is sent out from S0 (sector zero) and travels either through S1 next or S99 depending on which way it travels round the circuit. We will rotate the ring anticlockwise (as if it's sitting round the Earth's equator with us looking down at it from over the north pole [or it could be in orbit over the equator to make it perfectly circular and so that the tube contains a vacuum rather than air]). We will send pulses of blue light round the circuit in the anticlockwise direction too (S0, S1, S2, etc.), while pulses of red light will be sent clockwise (S0, S99, S98, etc.).

If we rotate the ring at a particular speed, we can observe pulses of blue and red light being emitted simultaneously from S0 in opposite directions and then travelling round the ring thousands of times before arriving back at S0, again simultaneously, after the ring has completed a single rotation. The red light will have passed through S0 (and every other sector of the circuit) one time more than the blue light has.

For each sector, the red light has passed through it at an average speed of R relative to that sector while it was passing through that sector.

For each sector, the blue light has passed through it at an average speed of B relative to that sector while it was passing through that sector.

The same amount of time has passed for each sector, and this can be measured by clocks local to each sector. Each sector has also travelled the same distance, regardless of which frame of reference you use to measure that.

So, is R=B, or is R>B?

If your answer is R>B, you are necessarily agreeing that the average speed of the red light relative to each sector it passes through while it's passing through that sector is >c and that the average speed of the blue light relative to each sector it passes through while it's passing through that sector is <c.

If your answer is R=B, then you need to deny the result of the MGP experiment and assert that the red light cannot have passed through each sector of the circuit an extra time.

Where do you stand? Are you in the R=B camp or the R>B one? Who here has the courage to post their answer to this simple question?

For the record, my answer is R>B, and this is the case for all inertial frames of reference. If you want to try to explain how the problem can produce R=B by using a non-inertial frame instead, feel free to set out your analysis for that, and then I'll show you why it isn't valid. (Clue: every non-inertial frame of reference has to be compatible with an inertial frame so that an inertial observer co-moving with the apparatus doesn't have light moving at different speeds relative to him in the same direction at opposite parts of the circuit.)

[guest4091]

David Cooper#30;
In fig.1, U describes a fiber-optic cable (ring) at rest, with light emitted in opposite directions from a device at A, which reflects from a mirror M at the other end of the diameter. The signals travel one complete revolution and return simultaneously.

In fig.2, the ring rotates ccw. The cw light arrives at the mirror before the ccw light as seen by U.

With the device A serving the role of moving observer, the center of the ring remains fixed relative to U and A, but A is moving relative to U. The time axis is perpendicular to and centered on the ring.
The light paths are spirals around the time axis, as if on the surface of an invisible tube, 0-R2-D ccw and 0-R1-D cw. For simplicity the tube is unfolded to a flat surface as in fig.3. The minus signs on the x axis indicate small lc. The 3rd blue signal ending at At = 6.28 is the round trip time for both signals.
The round trip times will be equal for A, with a measured constant light speed of c.
Per the equivalence principle, A would experience a weak g-field from the rotation.
Fig.3 represents the description by an observer who is NOT rotating with the ring.
As with the inertial frames, you are imposing the description by U (the rest frame) onto the perception of the moving frame A. Both cannot have the same perception if there is relative motion between them. U may have an advantage of observing all 3 events, 0, R, and D, which are not local for U, and also modified by his motion, which is also relative.
Note a rotating frame is considered absolute motion in Relativity.

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[David Cooper]

In fig.1, U describes a fiber-optic cable (ring) at rest, with light emitted in opposite directions from a device at A, which reflects from a mirror M at the other end of the diameter. The signals travel one complete revolution and return simultaneously.

I don't understand part of your experiment's description. How can the signals travel one complete revolution when they're bounced back at M and don't get to go the rest of the way round? You appear to have designed an experiment where both lots of light go from A to M and then back the way they came, and they both arrive back at A simultaneously precisely because neither of them do a circuit, but they instead do half a circuit each way and spend equal amounts of time going anti clockwise as each other, plus equal amounts of time going clockwise as each other. This avoids the entire issue put to you by my experiment where the two signals don't arrive back at A simultaneously (unless A has completed a full revolution, by which time one lot of light has done an extra circuit compared with the other lot).

The minus signs on the x axis indicate small lc.

Not sure what you mean by lc. It would be worth explaining now in case this comes up again.

As with the inertial frames, you are imposing the description by U (the rest frame) onto the perception of the moving frame A.

Not so, and this is not my experiment either, but yours - you have the two lots of light getting back to A simultaneously and thus we are in agreement about A's perception. The question now is whether we're in agreement about S0's perception in my experiment (which is its closest equivalent to your A).

So, what is S0's perception in my experiment? If I'm moving with S0 throughout, what do I see? I see the red light go off westwards and blue go off at the same moment eastwards. The red light comes back from the east and heads out westwards again, then the blue light comes back from the west and heads out eastwards again. This happens many times with the time gap between the returns of the two lots of light growing greater each time, but eventually I see them both arriving simultaneously and note that red has done an extra lap. I determine from this that because the red light has done an extra lap, it must have moved faster on average relative to each sector it passed through, while passing through that sector, faster than the blue light did. I am A in this case (with a non-inertial frame of reference as my measuring standard), and I have just given you A's perception that R>B, just like all the other observers regardless of which inertial or non-inertial frame they're using for their analysis.

So, S0's observer A (in his non-inertial frame) determines that the average one-way speed of light relative to each of the hundred sectors while it's passing through it is greater than c in one direction (anticlockwise) and less than c in the other (clockwise). What kind of voodoo do you have to resort to to turn his perception into something that agrees with SR (given that SR denies the ability of unslowed light to move at any speed relative to anything than c)? The only fix is to move to one of the SR variant models in which light reduces all paths to zero length in zero time, at which point you can hide the problem in an infinity by removing the property of speed from light altogether (though that too has unpalatable consequences for you).

[Note my careful wording: "average speed of light relative to each of the hundred sectors while it's passing through it" - if you ignore the "while it's passing though it" part, you will get a different result which would mask the truth of what's going on. My careful wording is there to force you only to consider the speed of light relative to any sector that it is passing through at the time while it's passing through it and not when the light is elsewhere in the circuit. It is only when you respect this wording that you force the truth out from the experiment.]