Does Special Relativity contain contradictions?

[Halc]

No, there are very much two clocks.

Two sidereal clocks? Represented by the circular motions of two points on the Earth's surface? That seems odd. In that case, we must surely conclude that every point on the surface of the Earth is a different sidereal clock. The Earth is an infinite number of different sidereal clocks.

So how can the caesium clock at the top of the mountain get out of sync with the sidereal clock represented by the top of the mountain? Come to think of it, in this way of viewing things, surely the body of the caesium clock, since it's perched on the surface of the Earth (on the mountain) is itself a sidereal clock.

I have the uneasy feeling that I've completely misunderstood this particular problem.

The day is 24 hours long at sea level. The sidereal clock there ticks once every 24 hours.
The day length is 24 hours and maybe 20 microseconds on the mountain, so the sidereal clock there counts longer days, but the one at sea level is dilated more due to gravity, so the two stay in sync.

The two caesium clocks measure state oscillations of caesium, which is the same rate for both clocks, so they get out of sync due to the dilation differences.

[Steve3007]

If frame A analysis says that object A is at rest, then that frame is producing a claim that object A is at rest relative to that frame, but it is also automatically providing a theory about the speed of that object relative to a proposed fabric of space which may or may not be correct.

I think the above is one of the more unambiguous statements by David of his view of how reference frames work, without the usual imprecise use of language. And, as a result of that lack of ambiguity, the part in bold is just plain wrong. He's accidentally tripped himself up by speaking too plainly. He's made it clear that we're talking about the movement of object A with respect to frame A; as measured against frame A. The measurements made of the movements of object A with respect to frame A provide no theory, or measurements, as to the movements of object A with respect to frame E (my shorthand for the proposed ether/fabric/absolute frame), because we have made no measurements of the movements of either object A or frame A with respect to frame E. There are 3 things here (object A and frames A and E) and therefore 3 relative velocities. Only one of those relative velocities has been measured.

What is true is that if an object is measured to be moving with respect to frame A and not moving with respect to frame B (another frame) then frames A and B must be moving with respect to each other, so they can't both be stationary with respect to frame E. One of them could be. But not both. But, of course, that doesn't mean that there is any contradiction whatsoever in saying that an object is moving with respect to frame A and not moving with respect to frame B.

So this...

...if something is not moving in one frame (no change in spatial distance between itself and any other object at rest in that frame) and is moving in another (with a change in spatial distance between other objects which are at rest in that frame), then we have contradictory claims from different frames about whether the object is moving or not, and we can't tell which one is wrong.

...is wrong if the ambiguous term "something is [not] moving in one frame" means "something is measured to be [not] moving with respect to one frame".

On the other hand, if that ambiguous term means "something is theorized to be [not] moving with respect to frame E" then obviously we have a contradiction because we've thrown away frames A and B and are just talking about movements of the object WRT frame E. So we've reduced it to: "...is moving WRT frame E and not moving WRT frame E". Obviously a contradiction. But, equally obviously, that's not what anybody, with the possible exception of David, is claiming is being said.

So, just to reiterate this very, very simple pre-SR point once again: An object can be moving WRT to frame A and stationary WRT frame B. No contradictions there.

[Steve3007]

I have previously used a wording which you dislike ("frame A asserts that...."), but I told you repeatedly how it was to be understood, but you just ignored that every time and insisted that what I was saying was wrong even though it was fully sound when interpreted in the way you had been told to interpret it. That was you playing games of avoidance - there should have been no need for any dispute over this.

Unfortunately, as I explained in the post above, your use of the term "frame A asserts that..." instead of "as measured with respect to frame A..." appears to have led you to make incorrect statements. That's one of the reasons why I suggest using precise, unambiguous language as far as is practicable, which makes it clear what kind of measurement our statements relate to.

[Steve3007]

Halc, apologies in advance if I'm being a bit slow here (I often am, but I usually get there in the end), but I just want to be as precise and unambiguous as possible:

The day is 24 hours long at sea level. The sidereal clock there ticks once every 24 hours.

24 hours as measured by what clock? As measured by a clock inside the potential well at sea level, or as measured by a clock that is far away from Earth and not in a gravitational potential well? i.e. to state the rate at which one clock (the sidereal clock) ticks, we have to measure it against another clock and state which clock that is.

The day length is 24 hours and maybe 20 microseconds on the mountain, so the sidereal clock there counts longer days, but the one at sea level is dilated more due to gravity, so the two stay in sync.

And, similarly, what clock do we look at to decide that the day length on top of the mountain is slightly longer?

[Halc]

The day is 24 hours long at sea level. The sidereal clock there ticks once every 24 hours.

24 hours as measured by what clock?

By the sea-level sidereal clock actually, but using our own sun, not some distant star, as our reference.
I made a mistake about the duration of the sidereal day as measured by the sea-level clock synced to a distant star: It ticks about every 23 hours and 56 minutes, and the one on the mountain about 20 microseconds longer than the one at sea level.
That's the standard, which we arbitrarily decided to cut up into 24 equal pieces, eventually defining minutes and seconds from that.
The year is more strangely defined as the duration from one winter to the next. For all the other planets, it is defined as the time to do one orbit. The seasonal definition is about 20 minutes different than the time to go around. I digress....

As measured by a clock inside the potential well at sea level, or as measured by a clock that is far away from Earth and not in a gravitational potential well? i.e. to state the rate at which one clock (the sidereal clock) ticks, we have to measure it against another clock and state which clock that is.

As measured by a clock inside the potential well at sea level, that clock being the sidereal clock, synced to the sun.
We calibrate the caesium clocks to count off exactly 24 hours worth of seconds for each tick of that standard. The one on the mountain is similarly calibrated.

And, similarly, what clock do we look at to decide that the day length on top of the mountain is slightly longer?

The caesium clock we brought with us measures it nicely. If we don't have one, we can figure it out by computing the difference in gravity and velocity up there. From up there, the Earth is in a relative gravity well, and runs slower just like it would if it was considered in a frame where it was moving at I believe the same speed that a rock would achieve if it fell from the mountain to sea level.

[Burning ghost]

DC -

There's nothing weird about it - the car (that's moving along the road) and the road cannot both be stationary relative to the aether.

You are assuming you know the nature of the aether here. Is this your proposition, that the aether is the term to,be used for the “underlying reality” of the universe?

[David Cooper]

If frame A analysis says that object A is at rest, then that frame is producing a claim that object A is at rest relative to that frame, but it is also automatically providing a theory about the speed of that object relative to a proposed fabric of space which may or may not be correct.

I think the above is one of the more unambiguous statements by David of his view of how reference frames work, without the usual imprecise use of language. And, as a result of that lack of ambiguity, the part in bold is just plain wrong. He's accidentally tripped himself up by speaking too plainly. He's made it clear that we're talking about the movement of object A with respect to frame A; as measured against frame A. The measurements made of the movements of object A with respect to frame A provide no theory, or measurements, as to the movements of object A with respect to frame E (my shorthand for the proposed ether/fabric/absolute frame), because we have made no measurements of the movements of either object A or frame A with respect to frame E. There are 3 things here (object A and frames A and E) and therefore 3 relative velocities. Only one of those relative velocities has been measured.

My use of language is almost always sufficiently precise for the point being made (and all you need to do is ask for clarification in cases where it might not be) - it isn't my fault if people repeatedly twist what I've said according to their own biases. The part in bold is fully correct. A frame of reference is always providing a theory as to the nature of the underlying reality whether or not that is the intention of the person using that frame. There is no frame E being dragged into this - the theory that frame A automatically provides about the underlying reality is that frame A is the absolute frame. One measurement serves for both frame A and the proposed absolute frame because they are the same frame.

So this...

...if something is not moving in one frame (no change in spatial distance between itself and any other object at rest in that frame) and is moving in another (with a change in spatial distance between other objects which are at rest in that frame), then we have contradictory claims from different frames about whether the object is moving or not, and we can't tell which one is wrong.

...is wrong if the ambiguous term "something is [not] moving in one frame" means "something is measured to be [not] moving with respect to one frame".

The part you keep quoting simplifies down to the original form: "If something is not moving in one frame and is moving in another, then we have contradictory claims from different frames about whether the object is moving or not, and we can't tell which one is wrong." (The rest of it was only added solely to show that your objection to my use of the word "moving" made no difference to the meaning whatsoever, and the result is a long wording which is not easy for the reader to make immediate sense of, which appears to be why you keep quoting it as part of your objective to muddy the waters.) There is nothing ambiguous about something not moving in one frame and moving in another, and there's nothing ambiguous about the issue of whether it's actually moving or not in the underlying reality. You just don't want there to be an underlying reality.

On the other hand, if that ambiguous term means "something is theorized to be [not] moving with respect to frame E" then obviously we have a contradiction because we've thrown away frames A and B and are just talking about movements of the object WRT frame E. So we've reduced it to: "...is moving WRT frame E and not moving WRT frame E". Obviously a contradiction. But, equally obviously, that's not what anybody, with the possible exception of David, is claiming is being said.

You keep starting in the wrong place. If you want to get to grips with reality, the place to start is with the relative tick rates of clocks. Once you've found the need for an underlying reality there, you can see how it relates to other issues like the business of whether things are moving or not. However, you don't want to look at the relative tick rate issue because it shows you to be wrong, so you keep diverting it back to a case that's less obvious where you hope to go on fooling people.

I have previously used a wording which you dislike ("frame A asserts that...."), but I told you repeatedly how it was to be understood, but you just ignored that every time and insisted that what I was saying was wrong even though it was fully sound when interpreted in the way you had been told to interpret it. That was you playing games of avoidance - there should have been no need for any dispute over this.

Unfortunately, as I explained in the post above, your use of the term "frame A asserts that..." instead of "as measured with respect to frame A..." appears to have led you to make incorrect statements. That's one of the reasons why I suggest using precise, unambiguous language as far as is practicable, which makes it clear what kind of measurement our statements relate to.

There's nothing wrong with my "frame A asserts that..." wording. You've been told how to interpret every single occurrence of it and there is no ambiguity involved when you do that. The simplest transformation is to convert to "frame A analysis says..." but you can transform it further from there into a long-winded form containing "as measured with respect to frame A" and a long description of how there are many standard questions which can be asked with any frame which you're using which will force you to make measurements that claim the exact same thing that I say the frame asserts. You're attack on my wording is nothing more than a diversion tactic using language games - it has no impact on the argument at all other than to waste everyone's time.

[Steve3007]

If frame A analysis says that object A is at rest, then that frame is producing a claim that object A is at rest relative to that frame, but it is also automatically providing a theory about the speed of that object relative to a proposed fabric of space which may or may not be correct.

The part in bold is fully correct. A frame of reference is always providing a theory as to the nature of the underlying reality whether or not that is the intention of the person using that frame. There is no frame E being dragged into this - the theory that frame A automatically provides about the underlying reality is that frame A is the absolute frame. One measurement serves for both frame A and the proposed absolute frame because they are the same frame.

Please may I refer to "the absolute frame" as frame E.

Please will you tell me and Burning Ghost whether "underlying reality" and "absolute frame" are in some way related to a reference frame in which the ether is stationary.

There is no contradiction in saying that I am moving with respect to frame A and stationary with respect to frame B. See my previous post for the simple reason why. If you don't accept that, then you're effectively telling me that black is white. I don't know how I can help you any further, and while you continue to do that I see no point in discussing clocks, "event meshing failures" (which Halc explained to you a very long time ago are due to your misunderstanding of the concept of a world line) or any of the rest of it.

[David Cooper]

DC -

There's nothing weird about it - the car (that's moving along the road) and the road cannot both be stationary relative to the aether.

You are assuming you know the nature of the aether here. Is this your proposition, that the aether is the term to,be used for the “underlying reality” of the universe?

Only in the context of set 2 and set 3 models. (I have in a multitude of places put in a line saying something along the lines of, "Remember - this applies only to set 2 models and that other models are invalidated in different ways".) We only have three non-magical proposed types of underlying realities for different models, but if we're restricting things to set 2 and set 3 models, then we can show that an absolute frame is required there to eliminate contradictions (and that absolute frame is a manifestation of the fabric of space or aether). The contradictions that invalidate set 2 models are the ones that show up in the happening and unhappening of events (when you change frame - this is shown in mode 2 of the simulation), but an alternative way of reaching the same conclusion without needing the simulation is to think about the relative ticking rates of clocks instead and the impossibility of clock A and clock B both ticking faster than each other at the same time. These things both demonstrate the incompatibility of set 2 models with any non-magical underlying reality. We can also eliminate them by thinking about the speed of light relative to objects where again contradictions emerge - there are multiple ways of proving the case. It would be best though for anyone who wants to go on objecting to this if they would just state categorically that they believe that clock A can tick faster than clock B while clock B ticks faster than clock A in the underlying reality - that way we'll know that we're dealing with a magical thinker who tolerates contradictions. Alternatively, they can state categorically that they believe such a thing is impossible and accept that the set 2 models are not viable. And if they can't make up their mind, then it means that they're open to the possibility of magic mechanisms where contradictions are allowed, so that's no better than the first option.

Having eliminated the set 2 models (I'm assuming that we all want to do physics rather than magic), we still have more than one proposed underlying reality in play, but we have simplified things down to sets zero, 1 and 3, and we can simplify them further. With set zero models, nothing is moving at all, so the idea that we can't tell if we're moving or not is plain wrong for those models. However, we can eliminate the set zero models on the basis that they can't contain real causality (as they were never built in order of causation), so they become an irrelevance - they cannot be the underlying reality. We can also see that set 1 models suffer from event-meshing failures, so the non-block versions of those are eliminated from the enquiry too. In the set 1 4D block model, everything is a strand of infinite length and is moving all the time through the block like a one-way conveyor belt, but it's only moving through the time dimension - there is no movement whatsoever through the space dimensions. This means the issue of whether things are moving or not doesn't really apply there, but this model, while still viable, is so contrived and far-fetched that it has never been claimed as SR, not least because it requires an additional Newtonian time to function (but it does conform to the requirement that no clocks actually run slow, and that is a claim of SR). No one normally thinks about this model though, as is clear from the fact that practically no one out there in the wild is even aware of the event-meshing problem - they only hear about it when I tell them. The set 1 3D block model's geometry produces problems during the construction phase, generating contradictions in a similar way to the set 2 models, and these show up when you change frame in the simulation, although they're subtle. Again though, no one even tries to use that model for SR (or anything else).

We are left with two set 3 models in play (because the block ones in that set are superfluous) and one set 1 model which no one wants to claim - the rest have been invalidated (apart from the two superfluous set 3 block ones which can simply be ignored as they add nothing). The only serious choice left is between set 3's 3D and 4D non-block models, both of which have an absolute frame. So, is it wrong to assume that there's an absolute frame? Yes, but the only alternative to that is a model that no one rates at all.

Be aware too that we normally assume that the speed of light is c, but the only surviving model in which that is the case is LET - the other two both have 4D geometry in which light reduces all paths to zero length and it covers those paths in zero time through the time dimension (though it takes longer in the Newtonian time which both those models also contain - notice too that both of these models contain two kinds of time, and that's more than a little contrived). Given that we normally say the speed of light is c, we are already talking the language of LET, but it's only right that we should, because LET has always been the only option that isn't contrived in the extreme.

[Steve3007]

Let A = a reference frame.
Let E = the absolute reference frame against which the proposed ether/fabric, if it could be measured, would be found to be stationary.

The statement "I am moving relative to frame A" neither states nor implies anything about my movement relative to frame E, or any frame other than A.

It would be best though for anyone who wants to go on objecting to this if they would just state categorically that they believe that clock A can tick faster than clock B while clock B ticks faster than clock A in the underlying reality - that way we'll know that we're dealing with a magical thinker who tolerates contradictions.

"while" = at the same time.
Time is the thing that is measured by clocks.

The question of whether clock A is measured to be ticking faster than clock B while clock B is measured to be ticking faster than clock A depends on which clock is being used to make this measurement of simultaneity. That has not been specified.

It is found that if two observers, A and B, are receding at non-zero constant velocity from each other, and if each one receives signals - "ticks" - from both their own clock and the other's clock, and if they count those ticks, they count fewer from the other clock than from their own.

[David Cooper]

Please may I refer to "the absolute frame" as frame E.

You can if you like, but when frame A is automatically serving as a proposed absolute frame, it means that it's proposing itself to be frame E, so a single measurement is a measurement for both frames at the same time (frame A and the frame that it proposes to be the absolute frame).

Please will you tell me and Burning Ghost whether "underlying reality" and "absolute frame" are in some way related to a reference frame in which the ether is stationary.

It is related to them for some sets, but not for others. As I keep saying though, the arguments about contradictions are only important to set 2 models where the clocks are actually ticking and where they are not ticking at the same rate as each other. [They are also relevant to one of the set 1 models, but no one takes that model seriously, so arguments about it can wait until someone makes the mistake of pinning their fading hopes on it.]

There is no contradiction in saying that I am moving with respect to frame A and stationary with respect to frame B. See my previous post for the simple reason why. If you don't accept that, then you're effectively telling me that black is white.

I've told you plenty of times that I have no problem with that - it is not a contradiction. You've been shown where the actual contradictions are, but you just ignore them and keep producing things that aren't contradictions which you claim I class as contradictions. Your inability to tell the difference between the two things shows that you simply aren't getting your head around the subject.

I don't know how I can help you any further, and while you continue to do that I see no point in discussing clocks,

You're the one who needs help - I've told you that the best place to see the contradictions is with the relative ticking rates of clocks, but you keep running away from that because you don't want to admit you're wrong. If you were actually up to this stuff you would have no difficulty in selecting one of the following options and tying your name to it:-

In the underlying reality...

(1) clock A can tick faster than clock B while clock B ticks faster than clock A.

(2) clock A cannot tick faster than clock B while clock B ticks faster than clock A.

Pick one of those options if you're a serious participant in the conversation.

... "event meshing failures" (which Halc explained to you a very long time ago are due to your misunderstanding of the concept of a world line)

Event-meshing failures automatically arise out of any attempt to run time under the rule that no clocks run slow. Anything Halc may have said about a set zero model has no bearing on what happens in set 1 models - with set 1 we try to generate the block in a manner that gives causation a role, and event-meshing failures are absolutely unavoidable there. You are simply arguing against something that goes beyond your limited knowledge and understanding.

or any of the rest of it.

Well, of course you don't want to discuss something that systematically throws SR in the bin.

[A new reply came when I was about to post the above, so...]

Let A = a reference frame.
Let E = the absolute reference frame against which the proposed ether/fabric, if it could be measured, would be found to be stationary.

The statement "I am moving relative to frame A" neither states nor implies anything about my movement relative to frame E, or any frame other than A.

It does if A is proposing to be E, and when you're working with at set 2 model in mind, all frames are making that proposal whether you intend them to or not.

"while" = at the same time.
Time is the thing that is measured by clocks.

They can measure each others ticks on approach and after passing each other, and there's a guarantee that they've done part of that at the same time. They can correct for Doppler shift to get a constant tick rate for the other clock.

The question of whether clock A is measured to be ticking faster than clock B while clock B is measured to be ticking faster than clock A depends on which clock is being used to make this measurement of simultaneity. That has not been specified.

Each is measuring the other (and measuring itself). Clock A is measured by clock A to be ticking more quickly than clock B while clock B is measured by clock B to be ticking more quickly than clock A. No contradiction in that. However, there is only one underlying reality, and in that underlying reality it cannot be the case that both clocks are ticking faster than the other clock. If you disagree with that, you should say so. And if you agree with it, again you should say so. This will reveal whether you are doing magic or physics.

[Steve3007]

You can if you like, but when frame A is automatically serving as a proposed absolute frame, it means that it's proposing itself to be frame E, so a single measurement is a measurement for both frames at the same time (frame A and the frame that it proposes to be the absolute frame).

Let B, C and D be more reference frames.

Reference frame A is not proposing itself to be either B, C, D or E.

[Steve3007]

There is no contradiction in saying that I am moving with respect to frame A and stationary with respect to frame B.

I've told you plenty of times that I have no problem with that - it is not a contradiction.

You have told me that precisely that sentence is a contradiction. Therefore you are contradicting yourself.

You've been shown where the actual contradictions are, but you just ignore them and keep producing things that aren't contradictions which you claim I class as contradictions.

You assert contradictions by incorrectly stating that frame A is proposing itself to also be another frame.

[Steve3007]

In the underlying reality...

(1) clock A can tick faster than clock B while clock B ticks faster than clock A.

(2) clock A cannot tick faster than clock B while clock B ticks faster than clock A.

Pick one of those options if you're a serious participant in the conversation.

Please re-frame this question in terms of a potential measurement. If you cannot do so, then you are not discussing physics. See my earlier post for definitions of the words "while" and "time".

[Steve3007]

It does if A is proposing to be E

A is not proposing to be A, B, C, D or E.