Hi Nereid, 'c' never varies, irrespective of the relative velocity of the object emitting the light or the observer receiving it.

Massless entities, e.g. photons.

Perhaps, but I have no idea how it could be achieved. We are getting into the cosmology here. I've been thinking of starting the next thread anyway, but held off in deference to your kindness in undertaking this TE. Do you have any objection to my starting the thread? I would, of course, be happy to continue the TE in parallel.

Oddly enough, this is not far from the situation in the rest frame of the muons. In this rest frame the mountain is hurtling up towards them at 0.998c, but the distance to the ground is Lorentz contracted, and hence in the muon rest frame the distance to be travelled doesn't take as long to go past the muon.

This is explained on the webpage that we have both referred to.
In the rest frame of the Earth the muon has a lifetime of 34.8 x 10^-6 which allows it to travel the 10,400 metres with no difficulty.

As long as you are consistent with the frame that you are working in there are no problems for SR here.

You either work in one rest frame and time dilation is the important thing, or in the other rest frame and it is now Lorentz contraction that does the job. You could even work in an intermediate inertial frame and then you would have to use the full Lorentz transformation to make sense of the scenario. What you can't do, however, is explain this scenario using the standard Gallilean transformation, i.e. it is extremely non-Newtonian.
As I point out above, SR has no problem in explaining this. Can you identify where you think the problem lies?
'fraid not.

How fast do the photons travel in the rest frame of the astronauts? Note that these are internal to the clock and are not the means by which the astronauts observe the time recored by the moving clock.

If the photons employed within the moving clock photons have to move further between "ticks" in the rest frame of the astronauts, then it is clear that the time between ticks, as measured using clocks in the astronauts' rest frame must be have increased. If this is not the case, then the photons must be travelling greater than c.
My point here was to show that once you have the effect with one type of clock, in this case one that uses photons for its internal time-keeping then the effect must apply to all clocks, and hence must also apply even in the absence of photon clocks.
You're welcome. Hopefully we will be able to generate more light than heat.

Certainly, see below...

I'm not. We've barely touched on my scenario. We're just discussing SR and it's implications.

Agreed. I take it that you agree that the equivalence of rest frames means that in it's rest frame the high energy muon has a lifetime of 34.8 x 10^-6 which allows the Earth to travel 10,400 metres (as measured by clocks and rulers at rest in the muon's rest frame)? If you do not agree with this, please give your figures for the lifetime of the muon and the distance travelled by the Earth (both as viewed in the rest frame of the muon)? Also, I'd be grateful if you could also explain how you arrive at these figures?

With respect, you appear to have mixed the frames of reference. The distance to the ground is not Lorentz contracted in the rest frame of reference of the muon. My understanding is that the Lorentz effect in SR only affects the view of clocks and rulers at rest in one frame of reference when viewed from a different rest frame. It does not, and cannot, affect what takes place in a rest frame when viewed from that frame.

Of course, in GR the Lorentz effect has an actual effect on the passage of time in a rest frame of reference. So a clock lowered into a gravity well actually runs slower than a clock outside the well. So if they were initially sychronised, when the clock is removed from the well, the two clocks are no longer sychronised, even when viewed in their rest frame. Quoting Wikipedia:

"In contrast, gravitational time dilation (as treated in General Relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree. Thus gravitational time dilation is agreed upon by all stationary observers, independent of their altitude."

But that is not my understanding of SR. In SR, the effect is symmetrical, and only affects the view of the passage of time in one frame of reference when viewed from another. There is no actual difference in the passage of time in any frame of reference, when viewed from the same frame of reference. That's my understanding of the "official" interpretation of SR. If you believe that it has changed, I'd be grateful if you could explain your reasons and give the sources supporting your view?

My understanding is that the high energy muon has a lifetime of 34.8 x 10^-6 in its own rest frame. The low energy muon has a lifetime of 2.2 x 10^-6 in its own rest frame. How can SR account for this? It is a real difference, not one that is merely apparent when observing clocks and rulers from a different rest frame.

By the way, this is really nothing to do with my scenario. But it is important to agree what SR says the relationships are, and we clearly differ on that.

Regards, Terry.

I've never disputed that (at least, not intentionally). What I disagree with is the conclusions you seem to draw from it. Please see #244 for more details.

Agreed.

I think we are getting there.

Regards, Terry.

You agree the distance measured by the astronauts is greater than the distance measured by an observer in the clock's rest frame. Is this correct? Do you agree that this difference in distance is "real"?

Previously you have stated that in your SR alternative there is no time dilation (more specifically, that it is an "illusion"). Does the above quote indicate a change in your position on that? There's nothing wrong with that. I just want to know if I'm understanding you correctly.

It's as "real" as refraction. I.e. It occurs, but what occurs is only apparent. When you poke a stick at an acute angle into a pool of water, the underwater part appears to be bent away from you with respect to the part out of the water, Of course the stick is not really bent, it just an effect of the refraction of light.

So it is with distances measured by rulers that are at rest in a frame of reference that is moving with respect to you. They seem foreshortened.

Time dilation in SR is similar to the effect on rulers. The passage of time as measured on any clock in its rest frame of reference is never dilated. It's only when you look at a clock that is moving in your rest frame that the time displayed appears to be dilated. And the effect is reciprocal. With two clocks moving with respect to each other, observers at rest with both clocks would see the time in the other clock dilated, but would assert that their own clock was not. Neither clock is actually dilated, but both appear to be to observers at rest in the other frame of reference. That is why I referred to it as an "illusion".

Note: This applies to SR and my alternative. See post #244, GR is different and causes an actual time dilation.

I hope that clarifies what I'm saying.This may prompt a question "So what is different in my scenario?". My scenario differs principally in the concepts, and leads to a different cosmology (which I've not covered yet).

Regards, Terry.

I would argue that we are discussing the consequences of an invariant speed of light. That this looks like SR is no coincidence as that is the only really new assumption that SR makes. The rest follows from this and it is very difficult to see how you can avoid it. Hopefully when the mathematics for your model is better developed we will be able to see if your model can be consistent with an invariant c and the rest.
Not at all. In the rest frame of the Earth, the muon has a lifetime of 34.8 x 10^-6 which allows the muon to travel 10,400 metres. How did you arrive at these figures?
Let's see. In the rest frame of a muon, which by definition will have zero kinetic energy, the lifetime is 2.2 x 10^-6, as I said in my previous post. I know this because I have personally measured the lifetime (or decay constant) of a muon in its rest frame. (This was a standard undergraduate experiment in my youth. )

As to the distance travelled by the earth in the rest frame of the muons, I cannot make a direct measurement, but assuming SR (which to all intents and purposes is really just assuming the invariance of c) the height 10,400 m is Lorentz contracted.

So L_{muon rest frame} = L_{earth rest frame}*sqrt(1-v²/c²)

which for v=0.998c gives the distance in the muon rest frame as 657 m.

Hope that this helps.
Again, I mean no offence, but I really do recommend reading a decent introductory text on SR as the maths is very straightforward and it would help to clear up misunderstandings like this.

The distance to the ground, i.e. the height of the mountain, is clearly Lorentz contracted. The height of the mountain that we are using is the height as measured in the rest frame of the mountain, not the rest frame of the muon. If we want to consider what is happening in the rest frame of the muon, then you need to carry out a Lorentz transformation from the mountain's rest frame to the muon's rest frame. This will give you a Lorentz contracted mountain.
But the mountain is not at rest in the rest frame of the muon, and therefore measurements made in the rest frame of the mountain need to be transformed.
Agreed. Happily we need not consider GR, though it does require SR to be valid (in a local inertial frame) for it to work. What may be confusing you is that though it is non-symmetric, one observer will see the other clock ticking clower than his "correct" clock, while the other observer will see the other clock ticking faster than his "correct" clock. Neither observer can say if his own clock has been made slower or faster by the effect. In other words there is no actual difference in the passage of time in any frame of reference, when viewed from the same frame of reference.
I hope that my comments above explain better what is going on here.
My understanding is that the high energy muon has a lifetime of 34.8 x 10^-6 in its own rest frame.
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Note correct.
Correct.
It doesn't need to account for this because one of the two statements is incorrect. Hope this helps.

Ok. To recap, the experiment is a light clock, which consists of two mirrors and a beam of light bouncing between them in a spacecraft traveling at some high velocity with respect to some astronauts. Up until now, the mirrors have been at rest with respect to the spacecraft. Imagine instead that we rerun the experiment but this time leave the top mirror at rest with respect to the spacecraft, but remove the bottom mirror and place a mirror or mirrors at rest with respect to the astronauts below the path the spacecraft is traveling with the intent to bounce the light off of those mirrors.

With the refraction analogy (which may be imperfect, I suppose), if you attempt the grab the end of stick where it appears visually you will miss it. The end of the stick is not really where it appears to be. With our experiment, we are attempting to determine the path the light actually follows by arranging the experiment such that actual, physical processes occur. In other words, the light either hits a mirror or it doesn't...in all frames. In the first flavor of the experiment (both mirrors at rest with respect to the spacecraft), an observer inside the spacecraft sees the light bounce straight up and down. The astronauts see the light bouncing in a saw tooth pattern. So for one back and forth trip they observe that the light travels farther than it did in the rest frame of the clock. If I understand you correctly, you are saying the distance the light appears to travel in one bounce in the rest frame of the astronauts is an illusion. To test this claim, I'm suggesting that we place the bottom mirror(s) at rest with respect to the astronauts. I don't see any way for this experiment to work (ie: the light to continue bouncing back and forth) other than for the astronauts to place a series of mirrors at rest with respect to them to reflect the light as it bounces up and down in a saw tooth pattern.

So I'll simply ask you this: The top mirror is at rest with respect to the spacecraft. Knowing the velocity of the spacecraft, where would the astronauts place the bottom mirror or mirrors, at rest with respect to themselves, in order to allow the light to continually bounce back to the top mirror as the spacecraft flies by?

Perfectly true.

This is not true of SR. It is true that clocks are not dilated (and objects are not length contracted) in their own rest frame. But according to SR, time dilation (and length contraction) that is observed is real. There are many thought experiments and real experiments that demonstrate this (the muons you have been discussing with Fortis is a real observation that demonstrates this). One of the more famous thought experiments, that deals with both length contraction and the relativity of simultaneity is the Barn and Pole Paradox. According to you, the pole should not fit in the barn. According to SR, it does indeed fit inside the barn.

Hi Tassel, I did not say that. Please re-read the post.

To recap briefly, the point is not the distance the light travels when viewed in a "moving" frame of reference, it is what deductions you make from this. The deduction that a "real" time dilation and distance contraction is obtained does not stand up to scrutiny. The effect is symmetrical, and observers in different frames see different clocks and rulers dilated or contracted. There is no consensus as to which clocks and rulers are affected:
Observer A (at rest with clock A), sees the time displayed by "moving" clock B dilated.
Observer B (at rest with clock B), sees the time displayed by "moving" clock A dilated.
Observer C (at rest with neither clock) sees both clocks dilated, but by a different amount.

That is a "real" time dilation? I think not.

I've given as full a reply as I can. If you disagree with it please point out the illogicalities in what I have said. You appear to be ignoring what I've said, and repeating variations of the same ideas.

Regards, Terry.

Hi Fortis, well I'm glad that we agree on that much.

There has to be a logic flaw in your argument, because you are deriving an assymetric result from a symetrical effect. I will think more on this and let you know my conclusions. If I come to the conclusion that I am wrong I will openly admit it.

Regards, Terry.

Well, yes and no. According to special relativity, an observer stationary with respect to the barn will see the pole entirely contained within the barn with both doors closed at the same time, for at least a moment. But also according to special relativity, an observer moving with the pole will claim that the doors of the barn were nver both closed at the same time, and the pole was never contained entirely within the barn. And both observers are correct, as far as their own frames of reference are concerned.

__________________
Conserve energy. Commute with the Hamiltonian.

Possibly this might help you with the symmetry issue.

We take the same example of the muons hurtling past the mountain to the ground and add the following elements.

a) An inverted mountain that is stationary w.r.t. the original beam of muons, i.e. one that is hurtling towards the earth at 0.998c in the rest frame of the earth.

b) A column of muons that is at rest relative to the original mountain.

The setup is now symmetric and the results are also symmetric, i.e. two different groups of muons hitting two different patches of ground.

As an aside, due to the Lorentz contraction, you will find that the density of the moving column of muons is greater than the column of stationary muons (in the rest frame of one of the mountains.) Surely, you ask, doesn't that change the electrostatic forces between the two columns of muons? The answer is yes, but moving charge also creates a magnetic field, and this allows reality to continue to function.

This does make me wonder, however, if you consider the magnetic field in an inertial frame to be real. After all, if we have a column of electric charge, and we are at rest in its rest frame then there is no magnetic field, but if we are in a frame moving relative to it, there is a magnetic field. What do you think?

(By the way, the quantity that is frame invariant is the electromagnetic 4-tensor. Electric fields and magnetic fields are just the components of this field expressed in the coordinate system of a particular inertial frame.)

You wrote the following:

The word "apparent" is a synonym for "illusory" so I think you can understand my confusion. How should I have interpreted your statement?