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#201 |
Penultimate Amazing
Join Date: Jun 2003
Posts: 48,034
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You can't stick with a single topic, and *I'm* the one mixing sub-discussions?
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I'm not going to bother double-checking your math right now, but it looks plausible. In which case, the traveler went 3.46 cs distance in the unprimed reference frame, and experienced 2 seconds of proper time in doing so. So where's the conflict? You still haven't produced one. |
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#202 |
Muse
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#203 |
Penultimate Amazing
Join Date: Jun 2003
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It's where the line of simultaneity for the outbound prime reference frame would intersect both the 4 second mark for the earthbound twin and that outbound journey, if the traveling twin hadn't turned around.
But he did. And that changed everything. This is really, really basic special relativity. I don't know what to tell you if you still can't get it. |
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#204 |
Penultimate Amazing
Join Date: Mar 2009
Posts: 17,729
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Well, what I could say as a hint is what I've said before: don't forget that t' = γ(t - vx/c2), not just γt. That seems to account for pretty much every confusion about the twins paradox I've seen so far.
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Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand? |
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#205 |
Penultimate Amazing
Join Date: Apr 2004
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#206 |
Muse
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#207 |
Muse
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#208 |
Penultimate Amazing
Join Date: Apr 2004
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#209 |
Penultimate Amazing
Join Date: Apr 2004
Posts: 12,881
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__________________
The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#210 |
Muse
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#211 |
Muse
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#212 |
The Clarity Is Devastating
Join Date: Nov 2006
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Posts: 17,293
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A zømbie once bit my sister... |
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#213 |
Penultimate Amazing
Join Date: Jun 2003
Posts: 48,034
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#214 |
Muse
Join Date: Jul 2018
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So now we cannot simplify, right.
So no simplification. There is a train car with L0=3.4641cs and the platform frame. Front of the train car is x'=0 and t'=0 and it is align with the platform origin x=0 and t=0. ![]() So the green B is platform origin and train car front (the train origin) aligned. There is no motion at the beginning, the motion starts at t=t'=0. The acceleration, then the deceleration as per the diagram. It takes 4s of the platform time. Then everything stops again. The back of the train car is aligned with the platform origin. There is a time dilation so the front train clock and the back train clock have both 2s on them, agreed? How did the platform origin crossed 3.4641cs of the train frame in 2s of the train frame? |
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#215 |
Penultimate Amazing
Join Date: Jun 2003
Posts: 48,034
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We can simplify, if you understand the simplification. You aren't comfortable with the results of that simplification, but so what? Your discomfort doesn't matter. So what if there's a time jump? It's a coordinate effect. As I explained previously, there is no discontinuity in what the traveling twin sees. Even if he reverses direction instantly, what he sees is still continuous. So why do you care if there's a coordinate time jump at a location outside his light cone? Why does it matter?
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You changed reference frames. |
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#216 |
The Clarity Is Devastating
Join Date: Nov 2006
Location: Betwixt
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This effect of special relativity has been a trope in science fiction for a hundred years. A
Disregarding the acceleration and deceleration times, a trip at a relative velocity greater than .707c (c/sqrt(2)) will be "faster than light" in subjective time. The traveler's subjective time can be arbitrarily short if arbitrarily high fractions of c are reached (as in e.g. Poul Anderson's Tao Zero). Of course, from the traveler's frame, the distance traveled is shortened, so the traveler never observes the ship traveling faster than light either. |
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A zømbie once bit my sister... |
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#217 |
Penultimate Amazing
Join Date: Apr 2004
Posts: 12,881
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#218 |
Penultimate Amazing
Join Date: Apr 2004
Posts: 12,881
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__________________
The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#219 |
Penultimate Amazing
Join Date: Mar 2009
Posts: 17,729
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Deleted.
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Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand? |
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#220 |
Philosopher
Join Date: Jun 2008
Posts: 5,279
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We don't want good, sound arguments. We want arguments that sound good. |
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#221 |
Muse
Join Date: Jul 2018
Posts: 959
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These are your couple of last posts.
When I read them my understanding is that you claim the time dilation is a function of acceleration and not velocity. What do I miss? If I look at the sun and the sun is in +x direction then I turn 180 degrees I am facing -x direction and the sun stayed in the +x direction. What are you talking about? Even if I change frames + is + and - is -. The relative velocity is +v and -v between two moving frames, isn't it? ![]() Does this work for the Lorentz transformation? |
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#222 |
Penultimate Amazing
Join Date: Jun 2003
Posts: 48,034
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Time dilation is different than the jump in time due to the change in reference frames.
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But again, this isn’t a problem. Rotating frames are not inertial. What you don’t understand is that Lorenz boosts (accelerating frames) are just 4D Minkowski space rotations. They aren’t fundamentally any different than you facing the sun and then turning around. You think it’s wrong to change frames when you rotate in Euclidean space, but you insist on changing frames when you rotate in Minkowski space. That there is your contradiction.
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But B is NOT where that line intersects the t axis. B is located at the point where the t axis intersects with the horizontal line given by t=8s. So what are you trying to say with this graph? |
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#223 |
Penultimate Amazing
Join Date: Apr 2004
Posts: 12,881
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Still saved from the last time we had this discussion:
A=(0,0,0,0) A'=(0,0,0,0) B=(4,3.464,0,0) B'=(2,0,0,0) C=(4,0,0,0) C'=(8,-6.928,0,0) |
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#224 |
Muse
Join Date: Jul 2018
Posts: 959
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The discussion is getting better, thank you, Ziggurat!
There is so much going on in just this one sentence, here is why. ![]() The first couple of milliseconds of the acceleration. The back train car observer accelerates more yet stays back and the front observer moves 'ahead'. The last couple of milliseconds of the deceleration. The back train car observer decelerates less yet moves 'ahead' now and the front observer is already 'ahead' and waits for the back observer to catch up. Isn't this like the equivalence principle? The accelerated frame undergoes different acceleration at the back and the front? Where is the time dilation coming from? Is it really relative motion that is causing the time dilation or it is the delta in the acceleration/deceleration? |
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#225 |
Penultimate Amazing
Join Date: Jun 2003
Posts: 48,034
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Depends which reference frame you want to work in. In a frame which is accelerating with the train observer, yes, they will observe that the front of the train gets stretched out compared to the back of the frame. In the platform frame, they remain the same distance apart at all times.
I keep telling you, accelerating frames are strange.
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#226 |
Muse
Join Date: Jul 2018
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It all depends how we define our frames, if they are inertial or not.
If i turn around and my frame has +x where I look, what I face, then no problem. We have a discussion about inertial frames and that's why I said the sun would stay behind me. Changing, 'jumping' frames is not easy. It involves 4-momentum, mass and energy of the bodies that are 'jumping' frames and there are limitations.
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Do you agree with how the right diagram is drawn? |
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#227 |
Penultimate Amazing
Join Date: Mar 2008
Location: New Zealand
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Read the SR part of time dilation. You changed reference frames so time dilated. This is textbook SR.
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NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist! |
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#228 |
Penultimate Amazing
Join Date: Mar 2008
Location: New Zealand
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This is wrong, SDG. Frames of reference in special relativity are inertial (but see below). It is GR that deals with non-inertial frames. We do not really define frames as inertial or non-inertial. It is the physical situation being considered that defines this. For example you have a train moving at a constant speed and a platform, thus inertial frames.
This is irreverent. Changing (jumping between) frames is extremely easy. You just write that you have changed frames! There are no bodies "'jumping' frames", there are observers in their respective frames. There are no imitations. This question is irreverent if you are getting the physics wrong. You have an impossible scenario. An theoretical train moving at a speed v cannot have cars that "accelerate more" or "accelerate less". Every car is moving at the same speed v. If the theoretical train accelerates than every car will accelerate equally and we have a general relativity scenario. If you want to make this into a hideously complex GR scenario then include the flexibility of the train (couplings) and the finite speed of the acceleration being applied to each car. There is one way that acceleration can be included in SR - make it instantaneous. This is one resolution of the twin paradox. The travelling twin makes an instantaneous change in direction to return to Earth which puts them into a inertial frame with an opposite velocity. |
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NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist! |
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#229 |
Muse
Join Date: Jul 2018
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As pointed out by Ziggurat,
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The traveling twin did not turned around, just stopped motion in the outward direction, to be precise, nevertheless there is no C' with t'=8s. This is the question, where is C/C' in the right side diagram of this figure? ![]() |
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#230 |
Penultimate Amazing
Join Date: Mar 2008
Location: New Zealand
Posts: 27,671
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This is nonsense, SDG. The twin paradox requires that the clocks of each twin be compared. What you have is a scenario where Alice stays at home, Bob travels some distance and then stops relative to Alice. Alice and Bob end up in the same inertial frame of reference. This leads to the trivial situation where Alice and Bob's clocks tick along at the same rate but have different times from GR acceleration effects. Nothing to do with your attempt to do special relativity.
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NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist! |
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#231 |
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#232 |
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#233 |
The Clarity Is Devastating
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Ziggurat and Robin have both given you the clear and correct answer to this question. What don't you like about it? Everyone and everything exists in every reference frame all the time. Observers don't pop "into" and "out of" reference frames like the TARDIS. The measurements attributed to the primed reference frame, whether made directly by observers stationary with respect to that frame or inferred from Special Relativity via Lorentz transformations, don't become invalid when the train stops. |
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A zømbie once bit my sister... |
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#234 |
Penultimate Amazing
Join Date: Mar 2009
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Hear, hear. SR doesn't even have the event horizons that an accelerating frame would have, so there is no time where any point exists in one frame but not in another. If they are SR frames, that is.
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Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand? |
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#235 |
Muse
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#236 |
Muse
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Confused enough?
![]() How about this? ![]() The axes ct and ct' are out of sync. |
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#237 |
Penultimate Amazing
Join Date: Mar 2008
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I did: This is nonsense, SDG.
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NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) Electric comets still do not exist! |
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#238 |
Penultimate Amazing
Join Date: Apr 2004
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The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#239 |
Penultimate Amazing
Join Date: Apr 2004
Posts: 12,881
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__________________
The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" |
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#240 |
Muse
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