Very informative posts you've been writing in this thread. Thanks.
SR Issue
- Thread starter chinglu
- Start date
Very informative posts you've been writing in this thread. Thanks.
If you're someone who thinks you can define a common axis for two distinct frames, you're probably going to struggle to understand relative motion, never mind what Einstein was on about.
You can certainly define a common direction, and have an x axis aligned in this direction for both frames, but claiming that they have a common axis is just wrong. It's wrong if you assume the usual meaning of "common", which is "shared"; a moving frame can't possibly share one of its axes with a stationary frame.
If chinglu believes his OP describes two frames with a common x-axis, that's a big problem for him, but not for SR.
You can certainly define a common direction, and have an x axis aligned in this direction for both frames, but claiming that they have a common axis is just wrong. It's wrong if you assume the usual meaning of "common", which is "shared"; a moving frame can't possibly share one of its axes with a stationary frame.
If chinglu believes his OP describes two frames with a common x-axis, that's a big problem for him, but not for SR.
Nice job. For chinglu that is the model that gets the result he wants. Whether it describes real natural phenomena doesn't seem to be very important. Several times when I've read a post you've written I think 'here is someone' who might have fun reading a book like Taylor and Wheelers Spacetime Physics.
I've been reading through this: http://rgs.vniims.ru/books/spacetime.pdf, in which the author(s) discuss Minkowski's ideas; it includes a lecture by Minkowski given in 1908, and he goes over the length contraction thing.
Still trying to get why time is dilated, but length is contracted. Maybe it's connected to the fact that time isn't part of simultaneous space, but the space always has distances in it (time is "allowed" to shrink to a point, but space isn't).
Still trying to get why time is dilated, but length is contracted. Maybe it's connected to the fact that time isn't part of simultaneous space, but the space always has distances in it (time is "allowed" to shrink to a point, but space isn't).
arfa brane
Thanks for linking that.
From the end of pg 7 to the beginning of pg 8 the author says this.
"Minkowski’s four-dimensional physics allowed him not only to explain the physical meaning of length contraction, but to realize clearly that, exactly like the relativity principle, that effect is also a manifestation of the four-dimensionality of the world."
He's saying that length contraction is a consequence of the geometry of spacetime [the world]. It's the same for time dilation. Three components to the geometry of spacetime. One is a constant and the other two are relative. Distance and time. When you remove the metric components associated with curvature, rotation, and charge all the solutions to the EFE reduce to the Minkowski metric. It's the metric we most commonly use when the local effects of gravity are 'infinitesimal' and have no meaningful bearing on the natural phenomena being evaluated with the metric. This metric was known before the EFE were written down. Pretty good clue.
Thanks for linking that.
From the end of pg 7 to the beginning of pg 8 the author says this.
"Minkowski’s four-dimensional physics allowed him not only to explain the physical meaning of length contraction, but to realize clearly that, exactly like the relativity principle, that effect is also a manifestation of the four-dimensionality of the world."
He's saying that length contraction is a consequence of the geometry of spacetime [the world]. It's the same for time dilation. Three components to the geometry of spacetime. One is a constant and the other two are relative. Distance and time. When you remove the metric components associated with curvature, rotation, and charge all the solutions to the EFE reduce to the Minkowski metric. It's the metric we most commonly use when the local effects of gravity are 'infinitesimal' and have no meaningful bearing on the natural phenomena being evaluated with the metric. This metric was known before the EFE were written down. Pretty good clue.
They share a common x-axis.
Then, they both agree the lightning is on the positive x-axis for one frame iff it is on the positive x-axis for the other frame for this experiment. Now, if you are right prove the lightning is on the positive x-axis for one frame and not for the other.
So, your examples are meaningless for this case.
1) I proved in the OP, C' is co-located with M in M' iff they are co-located in M.
2) Therefore, if C' and M are co-located in M, then they are co-located in M'.
3) The OP prove, if C' and M are co-located in M', then the lightning is at $$(d',0,0,d'/c)$$ in M' frame measurements.
4) The OP proved, if C' and M are co-located in M, then the lightning is at $$(d'(1-v/c),0,0,d'(1-v/c)/c)$$ in M' frame measurements.
Now, combine 2, 3 and 4. If C' and M are co-located, then the lightning is at $$(d'(1-v/c),0,0,d'(1-v/c)/c)$$ and $$(d',0,0,d'/c)$$ in M' frame measurements. This is a contradiction.
So, your ROS disagreement for this case shows lightning must be at 2 different locations on the positive x-axis of M' if C' and M are co-located. So, no SR does not handle this correctly.
This is the simple way to understand this thread.
If C' and M are co-located, then C' uses SR to claim the lightning is at $$(d',0,0,d'/c)$$ on the M' frame x-axis.
If C' and M are co-located, then M uses SR to claim the lightning is at $$(d'(1-v/c),0,0,d'(1-v/c)/c)$$ on the M' frame x-axis.
Note that C' and M are at the same place each claiming a different position for the lightning in M' frame measurements. So, for SR to be true, the lightning must be at two different positive x-axis locations in the M' frame if C' and M are co-located.
If C' and M are co-located, then C' uses SR to claim the lightning is at $$(d',0,0,d'/c)$$ on the M' frame x-axis.
If C' and M are co-located, then M uses SR to claim the lightning is at $$(d'(1-v/c),0,0,d'(1-v/c)/c)$$ on the M' frame x-axis.
Note that C' and M are at the same place each claiming a different position for the lightning in M' frame measurements. So, for SR to be true, the lightning must be at two different positive x-axis locations in the M' frame if C' and M are co-located.
The simple way to understand where the OP went wrong:
By contrast, relativity of simultaneity is readily apparent even in the OP's algebra (which agrees with the better-labeled values which appear in [POST=3198606]Post #2[/POST]) in that line j ($$t=t_P = t_Q$$) is geometrically and algebraically distinct from line k ($$t'=t'_P = t'_R$$). Thus nowhere has chinglu performed bad algebra or arithmetic but everywhere his conclusions are damaged by the incompatible assumption of absolute simultaneity, which is not part of Special Relativity.
Assuming time-dependent facts (like the co-location of M on line $$x = x_O$$ and C' on line $$x' = x'_O - \frac{v}{c} d'$$) being universality true or false, even at locations different than the location of the fact (such as every position occupied by the flash at any time after $$t=t_O$$ or any time after $$t'=t'_O$$), is assuming absolute simultaneity and thus the OP is not a "thought experiment" within the context of special relativity but rather conflates assumptions which agree with and disagree with special relativity.
Confusion and contradiction are natural results of such a flawed approach. A [POST=3198606]better way is with geometry[/POST] and first order logic that doesn't assume absolute simultaneity.By contrast, relativity of simultaneity is readily apparent even in the OP's algebra (which agrees with the better-labeled values which appear in [POST=3198606]Post #2[/POST]) in that line j ($$t=t_P = t_Q$$) is geometrically and algebraically distinct from line k ($$t'=t'_P = t'_R$$). Thus nowhere has chinglu performed bad algebra or arithmetic but everywhere his conclusions are damaged by the incompatible assumption of absolute simultaneity, which is not part of Special Relativity.
Nope you failed here. The co-location event is universal between the two frames. Now, if this is false as you claim, then if C' and M are co-located in one frame, then they are not co-located in the other frame.
Can you prove this since this is your thesis?
The answer is no, but try anyway.
if you cannot prove it, then the event is universal between the 2 frames refuting your post above.
He left the physics out of his evaluation on purpose. 390 posts later he continues on with the intellectual dishonesty. When I said his presentation was better than his previous attempts was based on an improvement on his grasp of algebra. The 'big holiday' was leaving out the physics. Intellectual dishonesty.
OK, so you can prove if C' and M are co-located, then they are not co-located in the other frame.
Is that correct?
That is what RPenner was saying.
You failed because of your intellectual dishonesty chinglu. Your argument was over after rpenner wrote post 2. The fact you've had this explained to you in intimate detail and continue to disrespect the physics is pathetic. Idiot wind.
ps I'm flabbergasted that rpenner said anything good about your evaluation. I wouldn't. It's algebraic mathematical physics not algebra I.
From earlier posts:
chinglu, [post=3198606]Post #2[/post] has had the definitions of lines j ($$t = t_P = t_Q$$) and k ($$t' = t'_P = t'_R$$) for over a month now. Is there any event in all of space-time, other than P, where these lines intersect? If so, then calculate it and show me [post=3198606]Post #2[/post] is wrong. If not, then it is obvious that $$t=t_P$$ means something and $$t' = t'_P$$ means something else and neither is a universally agreed upon definition of "same time as event P for places not the same place as event P".
Since our conceptual universe is the whole of space-time in special relativity, it was obvious that something that is temporary cannot be universally true, thus predicate logic is not interchangeable with first-order logic. By possibly neglecting time, chinglu seeks to obliterate space-time and replace it with slices of space taken in moments of absolutely meaningful simultaneity. Special relativity does not permit such a neglect of time.
Since the co-location event happens for only an instant, and not all time, then it is not universally true. Likewise, since it happens only in one place, it is not universally true. In fact, there is only one event in all of space and time where the two are co-located. I have called that event P, and have never neglected that time is part of space-time.
That's not what chinglu wrote previously. The co-location of C' and M only happens at one event in space-time, P, not at any other event. For C', event P only happens at one time. For M, event P only happens at one time. But the time of C', t', is not the same as M's time, t, and [post=3198449]chinglu wrote[/post] that $$t'=(t-vx/c^2)\gamma$$ so even if C' and M agree on the time at one location, they will disagree at every other location.
Event P is modeled in both coordinate frames, and the Lorentz transform connects the representations. But "universally true" means true at all events, not just at event P.
Once again you make the mistake you understand what words mean. C' and M are objects which move inertially in space-time. Frames are man-made imaginary coordinate systems used to model events and trajectories in space-time. Because event P ( the instantaneous meeting of C' and M) exists in space-time, of course it is modeled in both frames. But the models differ in that $$t = t_P$$ and $$t' = t'_P$$ mean different things at all other locations than the location of event P.
I have already proven what I set out to prove. I need not prove your mistaken interpretations of what I wrote.
What is not universal between the two frames is the concept of "same time as event P."
chinglu, [post=3198606]Post #2[/post] has had the definitions of lines j ($$t = t_P = t_Q$$) and k ($$t' = t'_P = t'_R$$) for over a month now. Is there any event in all of space-time, other than P, where these lines intersect? If so, then calculate it and show me [post=3198606]Post #2[/post] is wrong. If not, then it is obvious that $$t=t_P$$ means something and $$t' = t'_P$$ means something else and neither is a universally agreed upon definition of "same time as event P for places not the same place as event P".
OK, can you prove if C' and M are co-located in one frame, they are not co-located in the other frame. That is the logic and you failed to address it.
Why?
You did not prove if C' and M are co-located in M' or M, then they are not co-located in the other frame.
Now, you claimed the co-location event is not universal, so prove it.
Otherwise, admit C' is co-located with M in M' iff C' is co-located with M in M.
This is where you are and it is time for you to prove your assertions as I did in the Op without fear.
Are you going to prove C' is co-located with M in M' iff C' is co-located with M in M is false yes or no? It not, it is time for you to move aside.
chinglu said:
Einstein does not state or imply that two frames have a common axis here. He says they coincide; in fact he says they are all parallel. This doesn't mean you interpret what he says as meaning the two systems "share" anything, or have any axis in common. What they do have in common is a point of intersection in four dimensions.
I think this would make more sense if it said "The co-location event is common to both frames".chinglu said:
To make that more precise, you can say it's whenever (x,y,z) = (x',y',z'); you can't say t =t' unless you synchronise clocks at (x,y,z) = (x',y',z')--a "momentary" rest frame, whatever that is.
I don't know what universality has to do with a single event, or why you would bother using that term.
Anyway, obviously if both frames are co-located, they both agree they are, so that co-location as an event is something the two frames "share" momentarily. What they don't agree on is when this event occurs, so there is a separate event for each frame. Minkowski says that this means there are separate four-dimensional spaces.
Neddy Bate
Valued Senior Member
SR says the light flash is located at those two different locations at two different times. It is not a contradiction, because substituting two different times into the light postulate equation x'=ct' mathematically requires that the light flash must be located at two different locations.
All you have to say is, "At two different times," and everything will make sense.
Why would anyone claim that two different frames have a common axis? Say the two frames are moving apart, well, everyone knows that one frame can claim it isn't moving, the other one is.
In no case can either frame claim it has a part in common, i.e. shared with, the other frame; the frames are separate entities. Clinging to this obviously incorrect notion of relative motion, as chinglu is doing, means you don't understand Galilean relativity. It means you think two people walking past each other are joined together somehow; it means you must not have noticed a lot of things that happen every day of your life.
In no case can either frame claim it has a part in common, i.e. shared with, the other frame; the frames are separate entities. Clinging to this obviously incorrect notion of relative motion, as chinglu is doing, means you don't understand Galilean relativity. It means you think two people walking past each other are joined together somehow; it means you must not have noticed a lot of things that happen every day of your life.