Re: Time: is time a concept or a physical force and can we prove the arrow of time
Posted: September 10th, 2018, 2:08 am
David Cooper wrote: ↑September 9th, 2018, 6:56 pmThat speed is very frame dependent. In your preferred frame, it varies around the circle as the disk spins, sometimes slower and sometimes faster than c. Both beams of light exhibit this variance.Yes, this has been verified. That's what the Sagnac effect is. You act surprised by it. The light goes further one way than in the other, so the long way takes more time. Relativity does not predict otherwise, as you have asserted.I'm not in the least bit surprised by it, and I never said that SR or any other kind of relativity predicts otherwise. The point that you should be focusing on is the speed of the light relative to the material of the ring that it's passing (when it's at the closest point of approach to each bit of that material).
I'm using a single frame of reference, though the whole thing can be thought through from the perspective of any other frame with the same finding coming out of it in every case. The easiest frame to imagine to begin with is the one with the centre of the ring stationary in it while the disk rotates. The ring is divided into lots of sectors, but let's keep it down to 100 of them, and we can name them s0, s1, s2, etc. all the way up to s99.You never specified a frame. Now that you have, the ring need not be divided up. Each one of them yields the same delta-speed value for the red beam and a different one for the blue beam, but dividing up is necessary to express the varying delta-velocity value around the ring.
The emitter/detector is on the boundary between sector s0 and s99. That's how I described the experiment in the threads linked to on the other forum. I have the ring rotate anticlockwise (because I started off describing it as being set round the equator of the Earth and viewed it from over the north pole, while the sector numbers go up as you move eastward round the ring [faster than the ring is rotating]).Yes it is. Don't even need to invoke relativity yet. Newton would have agreed with this. Cutting up the ring makes no different to that.
The point of introducing these sectors is simply to uncover something that would be hidden otherwise by averaging out the effect that we're trying to see. I want the speed of the clockwise light relative to the material of the ring as it's passing that material at close range and not when it's at the far side of the ring, so it's added up on a sector by sector basis. We have the speed of the clockwise light relative to the material of s99 while it's passing through s99, the speed of that light relative to s98 while it's passing through s98, etc. all the way round. This produces the finding that the speed of light relative to the material to the ring that it's passing while it's right next to it is higher clockwise than it is anticlockwise.
If we rotate the ring at a suitable speed, e.g. 0.6c, we can ensure that both lots of light return to the detector/emitter at the same moment after a few laps but with the clockwise light having passed all the material of the ring more times than the anticlockwise light.OK, we have parted company with Newton. That's fast. You have a ring dilation of 4/5 to contend with. Either the ring got smaller or you will need to add more material to it. Maybe it doesn't matter. Either way, the one beam hits the detector 4 times as often as the other, same as what Newton says.
It has, on average, passed through the sectors of the ring at a higher speed relative to them than the anticlockwise light, and it has done so at a speed greater than c relative to them (on average). [The wording "on average" isn't actually necessary in this case where the centre of the ring is at rest in the frame we're using, but it is needed for other frames where the centre of the ring is moving through them.So far so good. Yes, the rate of both beams is the same all the way around in the frame where the axis is stationary, as you proposed.
Now you're switching frames mid-example. One frame has become 100 of them now, despite your lack of use of the plural. But I see in the rest of this post that you don't do anything with these little measurements. You just sort of let it drop, so I don't so the point in bringing it up in the first place. Yes, these little local frames have both beams moving at c through the momentarily stationary material.This statement makes no reference to a frame, so I presume you mean that each little sector has light moving at c in the frame where the material is stationary.Yes - each sector is moving through the frame that we're using, and light always moves at c through this frame, as the rules demand.
The mathematics is all there for you to extract and run through your head,Yes, they were pretty trivial so far. The movement of the transparent material is (pun intended) immaterial. It is the movement of the emitter/detector that matters.
and you can easily supply your own numbers to test it. I've suggested rotating the ring at 0.6c because it produces a convenient amount of length contraction for the ring - this speed contracts things to 0.8 of their rest length, so you'd need an extra 0.25 of ring material to complete the ring (which actually means it has to shrinks down in size once it's up to speed).OK, that answers the issue I brought up. You're letting the ring contract. I still think it doesn't matter since we never specified the radius or lap time in the first place.
After the ring has completed three rotations, both lots of light have done five laps by this point from the point of view of a stationary observer standing by the ring who is not rotating with it, but the clockwise light had passed through each sector eight times while the anticlockwise light has only passed through each sector twice. This means that the clockwise moving light has passed through the sectors of the ring at a speed four times higher relative to them than the anticlockwise light did. The speed of the clockwise light relative to those sectors while passing through them is 1.6c, while the speed of the anticlockwise light relative to those sectors while passing through them is 0.4c.As I said, pretty trivial arithmetic. Except for the shrinking unspecified ring circumference, we have yet needed to open the relativity book on this one.
Oh. I thought I did. The OP posted a list of things that refuted relativity, and your initial response was that most of them do no such thing. However the Sagnac experiment ... "I found your first post and discovered that you assert that SR and LET make the same predictions, but that only one of them predicts the Sagnac effect.I made no such claim, so you must have read a meaning into something that wasn't there.
That wording carried an implication that the effect was some sort of falsification of SR since it doesn't predict it, that it perhaps denies this relative speed of two moving things at > c. It doesn't. You put this up against relativity's claim that that relative speed is different in different frames. Yes, SR claims that it is measured thus, but no further. The 3D interpretation of the geometry of the universe for instance says that measurements in non-stationary frames are not actual values, and the Minkowski interpretation says all the values are actual.
The reference to it not being Minkowski Spacetime is there simply because if you use that you're dealing with different models where light has no speed because it reduces all paths to zero length.If I parse this statement correctly, that is the straw man that steve is talking about.
A 3D theory that asserts that all frames are equally valid necessarily generates claims from different frames that contradict each other.Hence steve asking you to define what you mean by 'valid' in this context. The 3D interpretation of SR makes no assertions that events in a moving frame are simultaneous with the current time. That such frames are valid or not I suppose depends on one's definition of valid. I've seen you use the phrase 'corresponding to reality', so no, those other frames do not correspond to the ordering of events in reality. The 3D interpretation requires two things: A preferred frame (which GR has, so it is actually pretty hard to avoid), and a preferred moment, which not even LET asserts. The 3D model simply asserts that physics works unchanged in these other frames.
People typically assert that the speed of light relative to object A is c in all directionsStraw man. This is false in any frame where said object is not stationary. If they say this, they're implying the frame where the object is stationary, as I have previously assumed you've been doing when leaving frame references off your statements like you did just there.
and then they switch frame to assert that the speed of light relative to object B is c in all directionsAgain, only relative to that different frame, not to object B, and only that light will be measured thus in that frame. The Minkowski interpretation would say that objects are worldlines and their speeds are just slopes of their worldlines in various frames, all of which accurately reflect reality.
and they insist on the frame B claim about the speed of light relative to object B being the correct one for frame A too while rejecting frame A's measurement for the speed of light relative to object B.Do you even know what a reference frame is? It is a relative reference, not an objective one. Any statement about frames is a relative one. It simply is not contradictory for me to be stationary relative to my laptop here yet be moving relative to a bird flying by, but you seem to be asserting exactly that here. I make no claim about actual objective speed of anything when saying those things. Yes, different frames order events differently, and that makes the relative speed between any two things (not just in relation to light) a frame dependent thing. You are comparing different events when making delta speed assessments, not the same events, so of course the separation between them is going to be different.
Your simulation shows this. Play with the +/- button and the relative speed between the two planets is the same in the frames at either end of the range of the frame selection, but that relative speed is greater between them in the frame half way. It can be seen better if you let that button go all the way to the frames of either of the ships.
Any frame that represents that material as having the speed of light relative to it as c in all directions is misrepresenting realityIt 1) No theory claims that all light moves at c relative to a moving object, and 2) SR theory makes no claims about the geometry of reality, but interpretations that do make claims about the geometry need to be consistent within the chosen geometry.