So, basically, what you are saying is that the proof I (and Calrid) provided earlier holds and that this whole discussion has been a waste of everyone’s time?
Hmmm… this claim seems at odds with this:
And this.
How are we to know that “the 0.88secs does happen”? Either we have the special relativity explanation above or we have your word for it. I’ll take the SR scenario, especially since you have not given any more details and you refuse to provide your sources.
I can see that you have no control over your self-aggrandizing through opponent-demeaning speech. You would have to be barred from rational debates.
If you are accepting the frame of ship A as the inertial frame, then ship A is not “moving”. If we declare that since its clock turned, it must have been moving with respect to something, then we must accept that something moved with respect to it such as to cause the clock to turn for 0.88secs. But please don’t confuse the issue by referring to it as “the moving ship that didn’t move”. This is very relevant to the rest of your equations because the “moving ship” is actually the other ship in such a case. Your equations end up cross referencing to which ship they apply, making it all into non-sense.
- No as such is irrelevant.
- No I won’t
- No, that is your job.
- No, you are safe in accepting my word that it is within the realm of contemporary physics.
Again, the problem is not one of justifying physics, but rather trying to resolve a problem without an absolute frame. We all agree that no one really traveled at 2.27c. But the problem is that the only evidence provided to the observes says that someone must have, UNLESS they use an absolute frame to resolve the issue.
I can tell already by the way you argue that you will merely proclaim that the added frame is not absolute and use obfuscation in an attempt to disguise it. But at least get on with it.
The error of referring to the rest ship as a moving ship - the first error.
It does involve arithmetic, so I suspect it is a waste of your time to attempt a solution.
Physbang is coming close, if he would just leave out the bullshit and state it properly, we could proceed.
Don’t worry, James has scored pretty highly on the crackpot index before.
Using past behavior as a future predictor (not necessarily logically sound, I’ll admit, but as a model it often works quite well), if James is posting in NS the post actually belongs in MB if not Rant.
You’re entitled to have faith in your religion. Just try to leave the thinking to those who can and do.
I’m not yet certain that there is a rational debate here. You have avoided answering substantive questions and your starting position is a vaguely worded thought experiment. You have just now avoided discussing Galilean relativity in favour of begging for special consideration, i.e., that we should not expect you to be expected to follow the established techniques of physics.
What I have done is standard physics of the kind that one can find in a course that covers special relativity in any public school or university. One of the lessons of special relativity is that we can identify any object to be be at rest or in motion. In the scenario as I described it, I have used the names of “the moving ship” and “the target ship” because that is how we think of them in the reference frame in which they are initially introduced. But this doesn’t mean that we cannot consider either ship to be moving.
Given that you seem not to know or understand how even pre-relativistic physics works, I simply cannot take your word that your scenario has anything to do with contemporary physics. Your continued stone-walling on this issue does you no favours.
You have not shown us how the use of an absolute reference frame will resolve any issue.
Do you consider the use of the actual special theory of relativity to be obfuscation?
That is not an error, that is physics.
PS. Thank you, Xunzian.
Can you show me even one such example wherein they state that “rest ship is moving” or visa-versa?
If you cannot correct your English concerning something so trivial, I don’t see why you are even participating on any forum or in any subject.
I tried to accept your misuse and continue anyway only to see that such a thought didn’t work. I suspect additional errors of assumption. So either fix that little problem and restate it all properly or bail out.
M= moving ship
R= ship at rest
t1
R<-------->M
t2
R<----------------------->M
Looking out the window of the rest ship
t1
R--------->M
t2
R------------------------>M
Looking out the window of the moving ship
t1
M--------->R
t2
M------------------------>R
But I’m just guessing…
BTW… just out of pure curiosity… what is the rate of time dilation to relative velocity?
astro.ucla.edu/~wright/relatvty.htm
You can see a similar example when Wright writes, “The space-time diagrams above both show a rod moving past an observer. On the left the rod is moving, while on the right the same situation is shown in the rod’s frame of reference. The observer moving with respect to the rod makes a radar determination of its length, as does an observer moving along with the rod.”
Similarly, I adopted your convention of speaking of one particular ship as the moving ship, as you wrote of only one ship with a record of movement. If you would like, I will rewrite everything using the language of Ship1 and Ship2.
If you are serious about this statement, I can only accept it as an admission that you cannot actually understand the basics of special relativity.
Demanded Rewrite:
We can do the actual numbers fairly easily, assuming that the one spaceship, SHIP1, had instant acceleration at the beginning and end of its trip.
Let’s say that, in the initial reference frame A, the position of SHIP1is 0 on the x axis and the position of SHIP2 is 2 on the x axis. In this reference frame, SHIP1 went from t,x coordinates 0,0 to a,2 and SHIP2 went from 0,2 to a,2, where a is unknown.
SHIP1 turns on its magic engine and then, according to its clock, turns it off 0.88 seconds later.
That means that in another reference frame, A’, SHIP1 went from t’, x’ coordinates 0,0 to 0.88,0 and SHIP2 when from t’, x’ coordinates of b,c to 0.88,0, where b and c are unknown.
We have three unknowns in this scenario. Fortunately, as this scenario involves a translation from one system to another, the unknowns are coordinated through the relative velocity of the reference frames and the frames are chosen based on the relative motion of the ships. So we really have four unknowns: a, b, c, v.
We know ds^2 = - dt^2 + dx^2 = - dt’^2 + dx’^2 . (NB: We are using a “d” here to represent a delta.)
So - dt^2 + 2^2 = - (0.88)^2 + dx’^2 .
Therefore dt^2 + dx’^2 = 4 + 0.7744 = 4.7744
dt^2 = (a - 0)2^2 = a^2
dx’^2 = (0 - 0)^2 = 0
So, a^2 = 4.7744 and a ~ 2.185.
The standard Lorentz transformation in our coordinate systems (where the speed of light = 1) to t’ is:
t’ = [1/(1 - v^2 )^1/2 ](t - vx)
This gives us
b = t’ = [1/(1 - v^2 )^1/2 ](0 - v2) = -2v/(1 - v^2 )^1/2
for the t’ coordinate of SHIP2 at the start of movement in the second frame.
Also useful to us is the inverse transformation:
t = (t’ +vx’)[1/(1 - v^2 )^1/2 ]
We can get from that,
a = t = (0.88 + v(0))[1/(1 - v^2 )^1/2 ], so t = 0.88[1/(1 - v^2 )^1/2 ]
for the coordinate in the initial reference frame when the two ships collide.
And the translation for the x’ coordinate is:
x’ = [1/(1 - v^2 )^1/2 ](-vt + x)
This gives us
c = x’ = [1/(1 - v^2 )^1/2 ](-v0 + 2) = 2/(1 - v^2 )^1/2
If we shorthand g = [1/(1 - v^2 )^1/2 ], then a = 0.88g, b = -2vg, c = 2g.
We know right off the bat (ignoring the approximate value for a) that g = 2.185/0.88 = 2.483.
Some algebra gets us that v = 0.917 (approximately) and that (approximate values) b = -4.554, c = 4.966.
So we know that according to the reference frame in with the two ships were originally (and finally) stationary, SHIP1 travelled for 2.185 seconds at a velocity of 0.917 light seconds/second. We also know that in our chosen second reference frame, SHIP2 moved from time index -4.554 to time index 0.88 (5.434 seconds) to move the distance from 4.966 to 0, a speed of approximately -0.914. Given the rounding of the figures used throughout, we can see that these cases are symmetrical, i.e., that the motion for one frame is the opposite for the motion of the other.
In no case does this reasoning appeal to a reference frame in which there is an absolute speed. We chose reference frames that were easy to work with, but we can use the Lorentz transformations to work with any inertial reference frames.
This should do away with any linguistic problems that people have in understanding the scenario. Only problems understanding the relevant physics should remain.
That would convey “a moving ship” and “a rest ship”, but not specify which… so okay…
Okay. That seems to merely point to t2 being larger than t1
No one in the scenario actually looked out any windows, so this should be mere supplementary information.
As I stated earlier for a single velocity (and why don’t these posts have ref. numbers?);
For 2 velocities to be compared;
df = 1 / (1-((v1-v2)/c)[3]2[/size])[4]1/2[/size]
…depending on the direction of the velocities.
To less tempt ambiguity;
?? What reference frame were you intending to refer to? The 0.88 time was measured by a moving clock inside SHIP1. The distance of 2 was measured in the rest frame A.
That has become meaningless as it seems to be using 2 different frames of reference for its values.
What is “delta-speed”? I am using ds^2 to refere to an invariant interval between two points of spacetime.
The interval ds^2 is an invariant; in this case it is the spacetime distance traversed by SHIP1. After one realizes that, one merely needs to follow the algebra. In frame A, dt^2 is (0-a)^2, the square of the interval of the time coordinate, and dx^2 is (0-2)^2, the square of the interval of the spatial coordinate. In frame A’, dt’^2 is (0-0.88)^2, the square of the interval of the time coordinate, and dx^2 is (0-0)^2, the square of the interval of the spatial coordinate. Special relativity assures us that these intervals must be the same in every frame, specifically, ds^2 = ds’^2. This is a fundamental part of SR.
No, it does not when one used the values properly: ds^2 is the same value in every reference frame. This allows us to use algebra to solve for the unknowns in the equations.
Okay, so you actually intended to mix frames yielding a temporarily meaningless number, so let’s proceed;
So if for SHIP1 alone using frames A (initial frame) and A’ (SHIP1 moving frame); ta = 2.185
Of course “ta” originally meant the time elapsed according to the initial rest frame. It has lost meaning now, but okay…
tb is the initial time stamp of SHIP2. How did you get tb into all of these equations for SHIP1? Or have you jumped into talking about SHIP2 now?
Every initial t and t’ is 0 in this scenario. SHIP2’s initial time stamp of tb = 0.
I don’t think anyone is bothered who gets what its just the question is nonsense that people have a problem with. if he does get it he’s applying the equations incorrectly as if there was not relativity, in which case any answer can be ignored as being out of kilter with reality. The answer is that if the normal laws of physics apply then you could not come up with a measurement of 2.27x the speed of light given length contraction and time dilation effects at speeds approaching c. Any other answer is specious.
You might say you are travelling towards each other at .98 c and that thus in theory the relative speed you must be approaching would be 1.96 but this isn’t in fact true neither would measure the actual clocks passage of time to be in accordance with this nor would relatively such a measure ever happen, nor would they agree when speaking in relative terms it did.
Realize that in this scenario, I know what actually happened, so it is easy for me to verify the end result of any equations you use (although jumping into matrix algebra makes following them a little tough).
All the participants in the scenario know is;
A) Nothing can travel faster than light
B) Ship1’s travel clock reads 0.88secs
C) The original distance between them was 2Ls
But if you simply divide distance and time traveled, as with any speed calculation, you get that something traveled at 2.27c. So the question becomes one of how the observers who experienced what seemed to be faster than light travel resolve what actually took place without assuming an absolute frame of reference.
No, I intend to use known physical quantities to determine unknown quantities. Your response seems to indicate that you have never taken a class in relativity theory nor have you ever worked through a problem in relativity theory. Do you have difficulty understanding the invariant spacetime interval? I can explain it in some detail if you would like.
The equation has nothing to do with either SHIP1 or SHIP2. It is simply the Lorentz transformation for the time coordinate of any one spacetime point from one reference frame to another reference frame that differ by movement along the x axis. I include these calculations for the completeness of the description in the second reference frame; determining the coordinates of that spacetime point gives the trajectory of SHIP2.
One can stipulate this, but then one is not doing special relativity. The the set of spacetime points that correspond to t=0 is not the same set of spacetime points as those that correspond to t’=0. The point (0,2) in A is the same point as (-4.554, 4.966) in A’.
This is a very disturbing statement, because as far as a reasonable person could tell, nothing like this scenario has ever happened. Do you have a source for this actual event, complete with measurements? Or do you have some source for this scenario? Or do you simply have some kind of psychic sense that lets you understand the nature of the universe despite scientific and mathematical results? (Note that there has been no matrix algebra in this thread yet. Does your source use matrix algebra?)
And are we supposed to simply trust that you did this experiment with two astronauts correctly, or that you read your source correctly, or that your psychic sense is correct? You write that you can “verify the end result of any equations you use”, but how are we supposed to trust that assessment?
This is correct, but in relativistic scenarios, we know from empirical results that doing this does not produce correct results.
Yes, and this was done above.
I’m gonna take a whack at this and say:
Assuming the clock is measuring the movement of particles that are moving at (close to) the speed of light, traveling a distence of 1Ls for each second registered on the clock… they would need to pay the speed traveled in the distence it takes to run their course, since they can’t increase their speed. They tick 0.88 after having added 2Ls of distence to their standard course…
Or think of it this way: I run at my max speed in laps around a given circle, which happens to take me exactly 1 second per lap… But now the circle starts moving! So not only do I have to keep up with the circle, I also have to do my laps, but am unable to increase my max speed… Given that I manage to not only keep up with the circle but also cover 88% of a lap around it by the time it has moved twice the distence of a lap around itself, how long did this take me?
2.88 seconds… Which means it took me 2.88 seconds to do what would otherwise take me 0.88 seconds… which means i was operating 3.27 times slower due to the speed of the circle!
using the tools you gave me
1 / (1-(v/c)^2)^1/2 = 3.27
Then just do the math.
v = c * (1-(1/3.27)^2)^½
or
v = 0.95c
That’s remarkably close to PhysBang’s numbers… so I’m assuming I’m not totaly off track, and that I merely forgot to take contraction into consideration and assumed the particles in the clock were moving at c when in fact they would likely be slightly slower ect.
They can’t its not going to happen in reality. End of story.
If they had of applied the correct equations they would of come up with a result which was less than c in m/s, relatively speaking, the fact that they came up with what you have stated means either they have used the wrong equations or non relativistic assumptions and conditions, or they exist in a universe where the laws of nature are different.
You already say we can’t assume an absolute frame of reference so that rules out any explanation of perceived time in one frame of reference as opposed to the perceived passage of time in another, so the answer must be relatively correct, if that is so and your assertion is true, then reality is broken. Short of a hyperspace jump or a wormhole (both completely hypothetical assertions) there is not other solution. The answer is that the question is wrongly worded so as to avoid taking account of actual special relativity.