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Does Special Relativity contain contradictions?

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Halc
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Re: Does Special Relativity contain contradictions?

Post by Halc » October 9th, 2018, 1:02 pm

Steve3007 wrote:
October 9th, 2018, 11:41 am
A quick rethink of this: I still think that there would be time dilation between clocks at different radii in the centrifuge,
Of course there would. I didn't suggest otherwise. I just didn't put multiple clocks in there.
... and that therefore you are right to say that a clock that is moving at linear speed v would stay in sync with a clock that is positioned in the centrifuge such that its tangential speed is also v.
My point with that example is that they would have identical gravitational potential and identical speed, but very different acceleration. If the two clocks stay in sync, then dilation is not at all a function of acceleration since everything else is the same, but the acceleration is massively different.

Acceleration is just an indication of either a gravitational field or of change of speed, both of which have dilation effects. I found a way to cancel out both of those consequences of acceleration, or of apparent acceleration such as we experience here on the ground.

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Re: Does Special Relativity contain contradictions?

Post by David Cooper » October 9th, 2018, 3:02 pm

Steve3007 wrote:
October 9th, 2018, 4:29 am
It illustrates in detail, by way of an example, what is directly observed by A and B and what they calculate, based on both those observations and the definition of the word "simultaneous" (it means "at the same time").
You're just focusing on the unreliable measurements instead of the frame-invariant ones which provide proper facts.
Obviously if "at the same time" meant "at the same single, universally/mutually agreed, 'Newtonian' time" then this would result in a contradiction. But it doesn't mean that. Somewhere in your article on your website I vaguely remember you claiming (without appearing to say why) that Special Relativity keeps this concept of a single, universal 'Newtonian' concept of time and that it is therefore self-contradictory. I disagree that it does this and I therefore disagree that it is self-contradictory.
You misremember it then. SR denies Newtonian time and I have never said otherwise. My proof doesn't depend on me bringing it in either - the maths and experimental results do that all by themselves.

There are three ways of handling time:-

(A) If time doesn't run, then you have a static block model in which real causation is impossible, and the block depends on being created by magic to avoid generating it in order of causation, because otherwise it needs to be generated through (B) or (C), rendering (A) superfluous.

(B) If time runs and no clocks run slow, then you automatically get event-meshing failures. These failures can eventually be corrected in a block model with events changing over Newtonian time at individual Spacetime locations, but this results in far-fetched models with much greater complexity than is needed in (C).

(C) if time runs and clocks on some paths run faster than clocks on some other paths, then the contradictions come into play and force acceptance of an absolute frame. If (C), then we apply my "double twins non-paradox" thought experiment and start with the key measurements (frame-independent facts): D=S1, E=L1, D>LA and E>LS. From this we derive the rules that: if D>L1, then S1>E, and if E>S1, then L1>D. We thus prove that D>L1 and E>S1 are incompatible - to accept both at once is to accept a contradiction.

Those are your only options. All SR models are invalidated.

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Re: Does Special Relativity contain contradictions?

Post by David Cooper » October 9th, 2018, 3:55 pm

Steve3007 wrote:
October 9th, 2018, 6:00 am
For me, it really drives home the reason why General Relativity, more than Special Relativity, is often regarded as one of the most profound insights of the human mind, springing as it does entirely from a combination of pre-existing empirical knowledge and very careful thought. The whole concept of non-Euclidean spacetime, and gravity as geometry, didn't spring from nowhere, or from an overactive imagination. It is a direct result of empirical evidence, going back as far as Galileo's experiments dropping objects from the Leaning Tower of Pisa, and careful reasoning.
And yet it remains a mere mathematical abstraction which reduces all journeys taken by light to zero length. The same maths fits with a much more rational explanation which removes the need for the time dimension and non-Euclidean geometry, thereby providing a simpler account to explain the same facts. That is why GR, far from being a profound insight, is a major barrier to real insight. GR has no speed of light because light never moves at all to get from one Spacetime location to another - they are always zero distance apart. You don't tell people that though. The same big issues apply to GR as to SR in that there are three ways of handling time. Again there are three options:-

(A) Time doesn't run - this leads to a block model in which all the apparent causality is false and you rely on magical generation of the block.

(B) Time runs but no clocks run slow. This leads to event-meshing failures where things that travel deeper in gravity wells than other objects which they were with earlier get to the Spacetime location where they're reunited with those other objects too soon to meet them there.

(C) Time runs and does so in such a way that moving clocks and clocks at greater depth in gravity wells run slower than others. The same proof as before comes into play to force acceptance an absolute frame (for those who are rational). At this point, we have objects moving through 4D Spacetime in a manner which results in the objects which take shorter routes through the time dimension travelling along those paths at such a slow rate that they gain no advantage from doing so - the speed of their travel through the "time" dimension needs to be governed by a Newtonian time not declared in the GR model. This reveals that the GR model belongs to (A) and is a magic block with fake causation.

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 10th, 2018, 3:14 am

viewtopic.php?p=321467#p321467
Halc wrote:Yes, except 450m/sec, not km per sec. I said it wrong the first time. Bob at the equator is moving at that speed, and is also going in a circle, but it takes a day to do a lap, so much lower acceleration. We should run the experiment for at least a day if we were to do this for real, so Bob's net velocity at the end is zero just like that of Alice.
OK. So Bob is the guy on the equator and Alice is in the centrifuge at the pole. (Poor Alice. I'd rather be Bob!) Bob's acceleration (towards the centre of the Earth. v2/r = 0.032 ms-2) can be taken to be near enough zero compared to Alice's acceleration towards the centre of the centrifuge = 10000 ms-2. (Assuming 1000g's.)

In SR terms, the Lorentz factor for both of them, relative to someone who is not moving at 450ms-1 with the rotation of the Earth but not in the centrifuge (perhaps Colin, standing still in the middle of the centrifuge on the North Pole) as calculated by: 1 / (1 - v2/c2)0.5 is:

1 / (1 - 202500/9X1016)0.5 = 1 / 0.999999999998874999..

So over the course of 1 day the SR time dilation between Alice and Clive, and between Bob and Clive, due to their differences in linear velocity, would be about 9.72X10-8 seconds. About 1 second every 28000 years. Perfectly measurable. I've read that caesium clocks can measure 1 second in 1.4 million years. So we could look for any time dilation between Alice and Bob and if a caesium clock can't find it, I presume we can safely say that it isn't there and you are right.

So your experiment is doable. Let's do it! :D


(Footnote: I always write square root here as "to the power of 0.5" because I can't figure out how to do a square-root symbol in here and if you try to write "1/2" as a superscript, using the "sup" tag, it doesn't seem to work, annoyingly.)
Bob is not in the box here, and the environment is very different where Alice is. Each knows which is which. I'm putting at least 1000 g's on poor Alice.
Centripetal acceleration = v2/r. If it was actually 1000g's on Alice, with her tangential speed of 450ms-1, that's about 10000ms-2. So the centrifuge radius would be 20.25 metres. It would do about 3.5 rotations per second.
Right, but we're not doing that. Only Alice, at the exact point where she has the same linear speed as Bob, and the same gravitational potential as well. <-- Pun mildly intended. There is no third clock somewhere else on the centrifuge.
Yes, understood.
I think it would be the same at exactly one point in the box: the one that moves at 450m/sec.
If we could do the experiment, that proposition is what we would be empirically testing.
Clearly it runs faster at the center (not moving at all), and slower further out (more V and more acceleration), so somewhere in between they must balance. If acceleration is not a factor, it balances at whatever RPM gives us 450m/sec. If acceleration matters, it balances at a smaller radius than that.
If we want 1000g, we need to pick an r that is about 22m I think, 290000x smaller than the r of Bob who is accelerating at about 1/290th of a g.
Yes, those are roughly the numbers that I got.
Your GR equation is useless since r is identical in both instances. It is computing gravitational dilation of something stationary, not of something moving. The SR equation you use in your program only computes a relative dilation for a clocks separated by h, and we have no h here. The appropriate SR equation is the simple Lorentz factor for 450m/sec in both cases. Acceleration (g) does not play into that equation.
The equation for the Schwartzschild solution of Einstein's GR equations is indeed useless because it's not applicable. If the rotation is equivalent to a gravitational force, then it's not a force that is inversely proportional to the square of 'r'. It is directly proportional to r. So to calculate the proposed effect of the acceleration I'd have to integrate from the centre of the centrifuge out to 22m, a series of small h's within which acceleration can be taken to be constant. (Or follow Schwartzschild and create a solution for Einstein's GR field equations, which is mathematically beyond me because I never studied Tensor Calculus.)

I strongly suspect that you still misunderstand what this integration process is doing and what the various values in the GUI of the application represent. But I could be wrong. Perhaps I'll post an annotated version of the GUI.
I still stand by my assessment of that. Every locally measurable way, yes, but not every measurable way. My Uranus/Earth thing bears that out. Both locally detect a similar g, but the one with the slightly higher g has considerably less actual dilation.
I explained the reason for this, when calculated using the numerical integration method, in an earlier post. And I ran the simulation to show that both methods (SR and GR) yield the same result for Uranus.
There is no local test for actual dilation or for r (the r is what differs between Earth and Uranus). David would be ecstatic if there was such a test, since it would prove that his is the only correct view.
In terms of the relationship between r and g, the difference between Earth and Uranus is that on Uranus the value of g reduces more slowly, with respect to r, than it does on Earth.

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 10th, 2018, 3:20 am

Error: I mixed up two names: Colin and Clive. They're supposed to be the same person. Let's call him Colin and stick to that.

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 10th, 2018, 6:42 am

viewtopic.php?p=321470#p321470
The rocket has no decreasing gravity as it moves. Your calculation compute a new different g at every point. The rocket has a fixed g. Alice at the top measures the same g as Bob at the bottom, not 30000 times less like in the Earth numbers. You seem not to realize that you're not simulating that.
As I've said, I'm simulating a whole series of rockets/boxes each with small but finite height such that acceleration can be regarded as approximately constant within each one, but it varies across them all. In the example screenshots that I've posted here the value of 1 metre was chosen for h in all except the example of the sun, in which I chose 10 metres to see what happened. The height - the "step size" as I've called it in the GUI - can be chosen by the user.

I've said this lots of times now, so it seems odd to me that you think I seem not to realise it!
It is in an accelerating rocket. Both Alice and Bob measure 1g (9.8m/sec2) for all of the 100 (subjective?) years.
There are lots of Alices and Bobs in the software. Lots of accelerating boxes. Typically just under a billion (you can see the number in the GUI).

The 100 year value shown in the GUI is calculated by simply taking the time dilation value and multiplying it by the number of seconds in 100 years. If you look up the values in other sources it seems to give reasonably accurate numbers. But I guess it would because it's a simple function of the value returned by the GR Schwartzschild solution. It sounds like you might have got confused about what that 100 year box in the GUI represents.
The actual dilation would be much more than the dilation on Earth because the rocket would really be moving after that much time, but it is the relative dilation between Alice and Bob we're trying to compute here. You're not doing that.
"That much time"? How much time? Are you referring to the 100 years shown in the GUI of my application? If so, I think you might still be confused as to what the application does.

Relative time dilation between all of billion or so Alices's and Bob's is precisely what I am computing. See the code. The equation used in that part of the code is taken directly from the results of the mathematical analysis, using SR, of the accelerating rocket/box.

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Halc
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Re: Does Special Relativity contain contradictions?

Post by Halc » October 10th, 2018, 7:15 am

Steve3007 wrote:
October 10th, 2018, 3:14 am
So to calculate the proposed effect of the acceleration I'd have to integrate from the centre of the centrifuge out to 22m, a series of small h's within which acceleration can be taken to be constant.
Why are you integrating this? Alice doesn't move from the center to the 22m point. She's at the same point the whole time and speed and g and r are all fixed. Only v changes, but dilation isn't a function of v. I don't see why you find integration to be a useful thing for this example.
But you had already done the mathematics above. Speed gets you this dilation factor that makes them both 1e-7 seconds. You figured that out without integrating anything. Doing it some other way implies that you have a way to do it using 'a', which is different between Alice and Bob.
I explained the reason for this, when calculated using the numerical integration method, in an earlier post. And I ran the simulation to show that both methods (SR and GR) yield the same result for Uranus.
I didn't say otherwise. My beef is that they're both Uranus, or both Earth. Never a rocket, whose g does not fall of with changing r. Rockets don't have an r.
In terms of the relationship between r and g, the difference between Earth and Uranus is that on Uranus the value of g reduces more slowly, with respect to r, than it does on Earth.
I know that. Alice and Bob do not since that isn't something you can figure out locally. Detection of a non-uniform field like that requires significant separation. A long way away from the planet (you put them at 10e9 meters) the g is much less. 10e9 meters into the rocket trip and the g is unaltered and Alice and Bob's clocks are dilated a much different value.

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Halc
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Re: Does Special Relativity contain contradictions?

Post by Halc » October 10th, 2018, 7:43 am

Steve3007 wrote:
October 10th, 2018, 6:42 am
As I've said, I'm simulating a whole series of rockets/boxes each with small but finite height such that acceleration can be regarded as approximately constant within each one, but it varies across them all.
I know what you're doing with the small step sizes. Pretend for a moment that I see the need for that in your planet example. My point, which you never seem to get, is that with a rocket, it (g) doesn't vary across them all. It's the same the whole way. It isn't an elevator lifting slowly off a planet. It is a rocket out in deep space with no gravity anywhere. Just constant local acceleration, and local is all that Alice and Bob see from their positions at either end of the rocket.
In the example screenshots that I've posted here the value of 1 metre was chosen for h in all except the example of the sun, in which I chose 10 metres to see what happened. The height - the "step size" as I've called it in the GUI - can be chosen by the user.

I've said this lots of times now, so it seems odd to me that you think I seem not to realise it!
I know how you're using h in the planet integration.
Relative time dilation between all of billion or so Alices's and Bob's is precisely what I am computing. See the code. The equation used in that part of the code is taken directly from the results of the mathematical analysis, using SR, of the accelerating rocket/box.
I want one Alice and Bob in one rocket experiencing 1 g. Not a billion Alice/Bob pairs, each experiencing a different g.

Your point was to demonstrate that GR equations derive from SR equations, and you've done that. The integration was necessary for that goal.
My point was to demonstrate the equivalency principle that Alice and Bob, in the one small box the whole time, cannot tell if they're parked on a small planet, a larger planet, or in a rocket accelerating the whole time, despite the fact that their actual dilation is significantly different in all three cases (showing that equivalency principle does not assert that what is true of one situation is true of the other). One box on the planet surface, not a billion of them in a tower. You can't consider a different box at 1e9 meters. Alice and Bob will definitely measure that their g is less up there and know that they're not in the rocket.

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Re: Does Special Relativity contain contradictions?

Post by Steve3007 » October 10th, 2018, 8:19 am

Halc wrote:I know what you're doing with the small step sizes. Pretend for a moment that I see the need for that in your planet example. My point, which you never seem to get, is that with a rocket, it (g) doesn't vary across them all. It's the same the whole way. It isn't an elevator lifting slowly off a planet. It is a rocket out in deep space with no gravity anywhere. Just constant local acceleration, and local is all that Alice and Bob see from their positions at either end of the rocket.
Yes, I know that. My point, in the simulation, was to demonstrate that an equation for gravitational time dilation from General Relativity yields the same results as an equation from SR for a bunch of boxes/rockets accelerating out in deep space with no gravity anywhere.
I know how you're using h in the planet integration.
Good.
I want one Alice and Bob in one rocket experiencing 1 g. Not a billion Alice/Bob pairs, each experiencing a different g.
Yes, I know that. And we have both now used the Lorentz factor (Special Relativity) to calculate the time dilation due to linear motion: The linear motions of Alice at a tangent to her circular motion around the centrifuge and the linear motion of Bob as he sits on the Earth's equator. Good. That's fine.

But the proposition of yours that we are testing is that if those linear motions are equal (450ms-1) then their clocks will stay in sync. In other words, your proposition is that the only effect is due to their linear motion. Your proposition is that Alice's high acceleration towards the centre of the centrifuge is not relevant to this experiment. In other words, your proposition is that the acceleration of objects moving in a circle is not equivalent to a radial gravitational field in which the field strength is directly proportional to r, instead of being inversely proportions to r2, as it is for the gravitational fields of massive bodies like the Earth.

In my simulation, I have demonstrated two ways to measure gravitational time dilation. One uses an equation created by Schwartzschild from Einstein's GR equations for a radial gravitational field that varies as 1/r2. The other uses the equivalence between a radial gravitational field like this and the results for a set of boxes/rockets that are accelerating in zero gravity space.

If the rotating centrifuge were to be considered as a radial gravitational field in which the force is directly proportional to r, then I do not have access to an equivalent of that Schwartzschild (GR) equation for that type of radial gravitational field. That is why I proposed using the same integration method used in the simulation. The calculation for a 1/r2 radial field means considering the difference between a point in the field and a point of zero gravitational potential (infinite distance away). The analogue here would be to the centre of the centrifuge, because if this rotational motion were equivalent to a radial gravitational field whose strength is directly proportional to r, then r=0 would be the point of zero potential. Whereas when the field strength goes as 1/r2 r = infinity is this zero gravitational potential point.

That's why I proposed the integration.

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Re: Does Special Relativity contain contradictions?

Post by Halc » October 10th, 2018, 11:59 am

Steve3007 wrote:
October 10th, 2018, 8:19 am
But the proposition of yours that we are testing is that if those linear motions are equal (450ms-1) then their clocks will stay in sync. In other words, your proposition is that the only effect is due to their linear motion.
And that both are in a gravity well, but since we're not computing absolute dilation here, only relative dilation, both the identical gravitational potential and the identical speed can be discounted. So the only effect is due to their different acceleration, and since acceleration is proposed to not have an effect, the two clocks will stay in sync.
In other words, your proposition is that the acceleration of objects moving in a circle is not equivalent to a radial gravitational field in which the field strength is directly proportional to r, instead of being inversely proportions to r2, as it is for the gravitational fields of massive bodies like the Earth.
No, I had no concept of equivalent r. It isn't necessary. Alice can be accelerating randomly in all different directions like military evasive maneuvers. I just want her to keep up the 1000g and stay close to the average of 450m/s, returning to the starting point after the duration of the exercise. The circle is the easiest way to do that, but r never figures into it.
In my simulation, I have demonstrated two ways to measure gravitational time dilation.
They both measure delta-dilation, not dilation. They both express the difference between Alice and Bob, piled atop each other at separation h. Nobody is piled up like that in my experiment. The equations are inappropriate for this situation.
You can compute actual dilation from 450m/s speed and about 1.1e6m/s escape velocity, but that's the same for both of them, so why bother when the two computations are going to be identical. If you want to use a meaningful r, you can put a tiny black hole at the pole that has a gravitational pull of 1001g at 20.25m and have Alice wing around that at that same RPM, but the dilation in that case will be different than Bob. Alice won't enjoy that experience either, so it's not like Alice won't be able to tell which box she was put in.
One uses an equation created by Schwartzschild from Einstein's GR equations for a radial gravitational field that varies as 1/r2. The other uses the equivalence between a radial gravitational field like this and the results for a set of boxes/rockets that are accelerating in zero gravity space.
Well, both of those equations are going to be pretty useless in this case. We don't have a set of boxes. Just one box.
If the rotating centrifuge were to be considered as a radial gravitational field in which the force is directly proportional to r, then I do not have access to an equivalent of that Schwartzschild (GR) equation for that type of radial gravitational field.
There wouldn't be one since gravity doesn't do that.
That is why I proposed using the same integration method used in the simulation. The calculation for a 1/r2 radial field means considering the difference between a point in the field and a point of zero gravitational potential (infinite distance away). The analogue here would be to the centre of the centrifuge, because if this rotational motion were equivalent to a radial gravitational field whose strength is directly proportional to r, then r=0 would be the point of zero potential. Whereas when the field strength goes as 1/r2 r = infinity is this zero gravitational potential point.

That's why I proposed the integration.
OK, I think you're going to integrate from Alice at 1000g to the center at 0g where Clive sits, using the AccelerationalTimeDilation() computation for delta dilation over a tiny H (we're only going 22 meters) and see if that figure matches the figure that you get just plugging 450m/s into a Lorentz calculation. From a GR standpoint, you have trouble. There is no equivalent radius or mass involved. Alice is going around due to a different force than Gravity. The tiny black hole provides both m and r, but it significantly changes the local situation for Alice, so any number that comes from that doesn't really demonstrate anything.

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