« on: 31/07/2020 23:19:26 »
Several problems here.I didn't state otherwise, in the quote of mine to which you responded or in post 3. Given a spinning radius of 1, it has a contracted circumference of 6.283 and a rest circumference (proper circumference) of 8.796. That's contracting due to spin. Either the spokes get shorter (reeled in??) as it spins, or the thing perhaps needs to be manufactured already spinning.
In the Ehrenfest paradox, the circumference contracts, not expands, since the wheel is moving.
Of course, the spokes experience Lorentz contraction. They are moving too. Because they are in motion, and the light from the outer portions takes longer to reach the observer in the center, they appear curved. That is, the observer does not need to look along the length to notice Lorentz contraction. Yes, the spokes get shorter as the rim contracts. Since the rim is moving along with the blocks, it will experience exactly the same Lorentz contraction as the blocks. No increasing gap sizes.
QuoteFrom the viewpoint of a non-rotating observer at the center of the circle, the blocks would be seen to shrink along with any gaps between them.Given fixed length radius, the blocks would have no gaps between them when stationary, and as they shrink, gaps would form, allowing more blocks to be inserted in them if you like. You seem to suggest that the gaps shrink as well, which is wrong. Picture a bunch of roller coaster cars, touching each other while parked in a circular track. As they speed up, the track doesn't change size at all, but gaps must form between the cars as they contract. That's what the recent diagram depicts. The ring circumference will contract if there's no track and the cars are bolted together. In that case there never are gaps, but the radius goes down as the ring circumference contracts.
But as we have seen, the radius does shrink because the spokes also experience Lorentz contraction and that is visible to the observer in the center.
QuoteThis could be seen by comparing the observed length of the blocks compared to their width. An observer riding on the rim would not notice any difference in the size of the blocks or the gaps.He'd very much notice the gaps forming, which were not there at all before. I agree that he'd not notice the ratio of length/width of his own car changing. We're talking about fixed radius here. Fixed spokes or a track or something.
Sorry, no fixed radius when the wheel is spinning.
QuoteWhy are you making the circumference larger?I'm not.QuoteAnd why are the gaps larger?Different example. Don't mix them. The text of mine you quoted is about gaps forming with blocks moving at a fixed radius. Post 3 talks about a solid ring contracting as it rotates, reducing the radius. Nothing gets larger with speed.
The increasing gap size points to the blocks shrinking but the rim not shrinking. That is equivalent to the rim expanding relative to the blocks. But the rim will contract as much as the blocks. No gaps.
QuoteThe radius is assumed to be constant.Only in the example in post 29, where the radius is held constant with detached objects moving around that fixed path at ever increasing speeds.
Detached objects following a circular track requires an additional force to keep them on track. That is, there must be something comparable to a rim to exert that inward force. This changes nothing. Whatever is keeping the blocks on track will be subject to the same Lorentz contraction.
If you want something that holds the blocks on track but is not itself moving, you are introducing all sorts of complications. For one thing, from the viewpoint of the blocks, the whatever it is outside will be the thing that is moving and will therefore be Lorentz contracted and have a smaller circumference/radius. For another, the force holding the blocks in place will result in the outside influence thing being set in motion and the blocks slowing down. (Newton #3)
QuoteThe size of the radius can only be determined with a measuring rod.We have one. You can't measure a stationary track or fixed length spokes moving only perpendicular to their length? Post 29 shows a sort of track. No spokes. The grey boxes seem to be the track, not spinning with the red stuff.
The spinning disk (grey) and the red boxes on it will all undergo Lorentz contraction along the direction of motion. This will reduce the circumference and therefore the radius. No broken strings.
If you photograph the whole thing from a distant point. You will see something different from what an observer at the center sees. But it will still exhibit Lorentz contraction since it is moving with respect to that distant observer. Lorentz contraction is relative. It is not real.QuoteIf we use the rotating stick as the measuring rod, we will see something interesting. It will not appear to be rigid. Light coming the rod from near the rim will take longer to reach the observer in the center and will show the stick at an earlier time in its rotation. The stick will appear to curve and have a length greater than the expected radius.Appearances or no, the stick (spoke) is in fact straight in an frame where the axis of rotation is stationary. Light 'appearing' to curve is Coriolis effect that you get in a rotating frame. Light does not move in straight lines in a rotating frame. If you photograph the thing from a distant point on the axis, the spoke-stick will appear straight since light takes about equal time to get from any location of the stick to the point of view.
QuoteBut if the observer in the center holds a measuring rod out to the circumference until sparks fly when it touches the rim, the measured radius would be as expected for a non-rotating wheel. (Actually, the measurement will be a bit too long as it would take time for the light of the sparks to reach the center. But since the speed of light is known, an adjustment could be made for this.)If the radius is 1, then the light will take time 1 to reach the observer in the center despite it not moving along the spoke. No adjustment is needed.
The observer in the center will not know that contact has been made until a light signal comes back from the rim. In the meantime, the observer is still pushing the rod out beyond the point of contact. The length of measuring rod that has been pushed out is too much. An adjustment needs to be made to the measured length.
QuoteThis result contradicts the radius implied by the observations made of the blocks on the spinning wheel.The blocks are not making any measurement of the radius. They measure proper circumference.
No, the blocks are measuring Lorentz contracted circumference because they are in motion. No gaps.
QuoteLength contraction is not real. It is relative.You're denying that gaps form between the blocks? By your posts above, it seems so. Let me know how that works for you. I stand by my statement that contraction is objectively real and is well illustrated by the Ehrenfest scenario. There is no frame in which those gaps do not form.
I am denying that gaps form because the circumference is contracting along with the blocks. There is no frame in which the gaps do form.
QuoteIt is impossible to synchronize separated clocks. The two spaceships cannot start at the same time. There is not such thing as the same time.This is nonsense.
The ships are initially stationary, and begin identical proper acceleration at the same time relative to the frame in which they are stationary. Are you in denial now that clocks can be synced in a given inertial frame? Einstein gives some nice examples of ways to do exactly that.
As I explained in a prior post, the clocks are out of sync when the engines start because each space ship sees a delay in the start of the other space ship’s engine. As a consequence, each space ship sees the other one going slower than itself because it has not been accelerating for as long. No common frame of reference. It is not possible to start the engines at the same time. Distance = time delay.
You appear to be searching for cop-out excuses to avoid explaining a scenario that you apparently don't understand. The ship at the rear could even start out a little before the other, putting initial slack in the string. As the ships and the string gain speed and contract, the string will eventually break, but it takes a bit longer due to that initial slack.
No cop outs going on. I understand the scenarios perfectly. You are the one being inconsistent in the application of Lorentz contraction. It applies to the circumference as much as to the blocks.
As I described in the previous post, even starting at the same prearranged time on previously synchronized clocks, each spaceship thinks the other one is going slower with opposite expectations. Even if you manage to get them agreeing that they are both going at the same speed, the two spaceships and the string would all be in a common inertial reference frame and they would see no Lorentz contraction and no broken string.
As I pointed out in my prior post, an observer in a different inertial reference frame would see the entire complex of ships and strings equally Lorentz contracted and no broken string.
If a string was tied inside a spaceship along the direction of travel, and the spaceship accelerated (slowly) to a high speed, would the string break? It is not material objects that get contracted, it is space itself by appearing to be at different orientations in Minkowski spacetime to different reference frames. This is the point you are missing.
Lorentz contraction is relative, not real.