Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: TyroJack on 16/08/2016 10:10:48
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Thoughts upon Special Relativity.
Take the Frame of Reference of an observer in Spacetime.
The observer's location is permanently (0,0,0,t) in that Frame of Reference.
To that observer Spacetime is at rest, as it is mapped from his location and the rest of spacetime moves relative to him.
Now, if that observer were to be holding a perfect clock, then that clock would, in effect, measure (provide, form) the time axis.
Therefore, would it not be the case that the time coordinates in that frame constitute Proper Time, being time measured on a clock at rest, that is accompanying the worldline of that observer?
To summarize: is the time measured by an observer, 'locally' in their own Frame of Reference, an instance of Proper Time?
(while time in any other Frame of Reference, relative to them, will be coordinate time?)
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You are giving, roughly, the definition of proper time. As long as that "observer" only has inertial motion, then this is OK for Special Relativity.
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Thoughts upon Special Relativity.
Take the Frame of Reference of an observer in Spacetime.
The observer's location is permanently (0,0,0,t) in that Frame of Reference.
To that observer Spacetime is at rest, as it is mapped from his location and the rest of spacetime moves relative to him.
Now, if that observer were to be holding a perfect clock, then that clock would, in effect, measure (provide, form) the time axis.
Therefore, would it not be the case that the time coordinates in that frame constitute Proper Time, being time measured on a clock at rest, that is accompanying the worldline of that observer?
To summarize: is the time measured by an observer, 'locally' in their own Frame of Reference, an instance of Proper Time?
(while time in any other Frame of Reference, relative to them, will be coordinate time?)
That is correct.
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Just to elaborate further any observer with a momentum that is constant in both magnitude and direction can be considered at rest in their own frame of reference. If all frames of reference everywhere had identical momentum then the universe would not exist. Since it would contain no energy. Therefore inertia alone is not enough to guarantee a well functioning universe. Ultimately this describes heat death.
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Just to elaborate further any observer with a momentum that is constant in both magnitude and direction can be considered at rest in their own frame of reference. If all frames of reference everywhere had identical momentum then the universe would not exist. Since it would contain no energy. Therefore inertia alone is not enough to guarantee a well functioning universe. Ultimately this describes heat death.
It appears strangely that this is possible how the gravitational field works. A spaceship moving at a constant speed near C and constant direction has a gravitational field that travels with it. To the people aboard the spaceship everything appears happy to them. To another spaceship which is stationary in space, the moving spaceship appears very distorted to them. To me this is possible if the gravitational field of the moving spaceship moves at near infinite light speed otherwise the spaceship itself would become terribly distorted relative to its gravitational field.
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It confuses me when one refers to a body having momentum or "moving at a constant speed, near c"; for I feel that is implying that there is an absolute state of rest in Spacetime, yet is not all motion relative to the observer? So a spaceship may be moving near c relative to the "spaceship stationary in space" yet the reciprocal is also true, so moving at any speed cannot be a property of either spaceship (can it?). Is it not but an effect of the relative motion, perceived by the observer?
If a body accelerating relative to Spacetime and approaching the speed of light, then if gravity moves at the speed of light, would there not be the equivalent of a sonic boom (a 'gravitic' boom, creating a black hole, perhaps? hehehe) as it passed reached the speed of light?
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Therefore, would it not be the case that the time coordinates in that frame constitute Proper Time, being time measured on a clock at rest, that is accompanying the worldline of that observer?
No. The proper time between two events refers only to the time as measured by a clock which passes through both events. The time coordinate in a frame is determined by a collection of clocks located throughout an observers frame of reference.
It confuses me when one refers to a body having momentum or "moving at a constant speed, near c"; for I feel that is implying that there is an absolute state of rest in Spacetime, yet is not all motion relative to the observer?
When someone speaks of the speed of an object without mentioning the frame of reference with which that speed is measured then frame of reference is merely implied to exist. The person writing such a statement is just omitting it. It's sloppy language but there's never any confusion if one understands that the frame of reference is implied because otherwise the statement is meaningless. Its just easier to speak and write that way.
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No. The proper time between two events refers only to the time as measured by a clock which passes through both events. The time coordinate in a frame is determined by a collection of clocks located throughout an observers frame of reference.
And are those clock not synchronised with the clock at the origin?
And is the clock at the origin not travelling along its worldline? And therefore displaying Proper Time?
Or is it that Proper Time is not a measure of time at all but, perhaps, a measure of the motion (in 4D) of a body?
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And are those clock not synchronised with the clock at the origin?
No. Not in general. They're only synchronized in the rest frame of the clock at the origin. In any frame S' moving in the x-direction relative to that frame, clocks with different values of x' are not synchronized with that clock. So there are differences in the time readings.
And is the clock at the origin not travelling along its worldline? And therefore displaying Proper Time?
The clock at the origin reads its own proper time, not the proper time of the other clocks. But which the clocks have different readings in S' they will still run at the same rate. The text Spacetime Physics - 2nd Ed. by Taylor and Wheeler explains all this very nicely as I recall, as does the glossary in their text Exploring Black Holes. However I have to admit to being a bit prejudice since I proof read the text and was the one who wrote the glossary of terms. :)
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I have a time question that may suit this thread or the correspondents in it.
I am almost totally ignorant about physics, so i'd appreciate some gentleness if it is a totally stupid question.
I understand that special relativity predicts that measured time is relative to the observer and to speed etc and that this is real and used in technology.
If an observer were "God" and the entire universe were observed as a whole, it seems to me the case that in any given instant, everything must have a location. And in the next instant, everything must have a location. Everything everywhere must have a location in the universe, from leptons to galaxies at any given instant. The timing of instant to instant is the true forth dimension (0,0,0,t). I fail to see how this can be relative to anything, such a dimensional time must be a definition of time. Does this mean that measured/perceived/(proper?) time is different from dimensional/coordinate time? One is relative and one is not?
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I have a time question that may suit this thread or the correspondents in it.
I am almost totally ignorant about physics, so i'd appreciate some gentleness if it is a totally stupid question.
I understand that special relativity predicts that measured time is relative to the observer and to speed etc and that this is real and used in technology.
If an observer were "God" and the entire universe were observed as a whole, it seems to me the case that in any given instant, everything must have a location. And in the next instant, everything must have a location. Everything everywhere must have a location in the universe, from leptons to galaxies at any given instant. The timing of instant to instant is the true forth dimension (0,0,0,t). I fail to see how this can be relative to anything, such a dimensional time must be a definition of time. Does this mean that measured/perceived/(proper?) time is different from dimensional/coordinate time? One is relative and one is not?
You're not incorrect. At any instant everything in the universe has a location. For simplicity I'll speak only of point particles. Every particle has a location in the universe. "God" could even label those locations uniquely. What God can't do is provide a unique distance between particles located at different locations. If I were religious I'd say that it was the way he chose to design the universe.
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Thanks for the reply.
It raises the question, for me, why can't a distance be determined?
I understand that, from any particular "snapshot", velocity cannot be determined, but would have thought that particle A (a,b,c,t1) has a determinable distance from B (x,y,z,t1). A straight line can be drawn between 2 points.
The question may raise "curved space time", but predictably, I'm unclear why gravity should affect a dimension grid. Certainly it affects how particles relate to each other, and a warped dimension grid is useful to visualise this. But I fail to see how this affects where everything is at an instant and why a distance between two points could not exist.
Btw, I'm also not religious and merely used "god" to give the problem a better view than man. I'm not suggesting that we should be able to magically determine a distance, but that a distance between the two particles must exist, none the less
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It raises the question, for me, why can't a distance be determined?
I didn't mean that distance can't be determined. I meant that distance depends on the frame of reference in which the observer is located.
I understand that, from any particular "snapshot", velocity cannot be determined,...
That's not exactly true. There are methods in which the velocity of an object []can[/i] be determined. Consider a car or motorcycle which has an electric generator attached to the wheels. The angular motion of the rotor moves conductors through a magnetic field. Such motion creates a current in the wires and that current can be used to move a magnetic needle. The displacement of the needle determines the instantaneous speed of the moving object. The velocity is then determined by multiplying the speed to a unit vector pointing in the instantaneous direction of motion.
The question may raise "curved space time", but predictably, I'm unclear why gravity should affect a dimension grid.
Because a gravitational field can alter the distance relationships in an observers frame of reference. That is the prediction of general relativity (GR). As to why gravity does this is not something that GR can answer. Theories tell us what happens. In many case general physical laws cannot tell us why this happen, only what happens.
Btw, I'm also not religious and merely used "god" to give the problem a better view than man.
I'm sure that most of use understand that. The 'God' character that you mentioned has been referred to in the physis literature as Maxwell's Demon. See: https://en.wikipedia.org/wiki/Maxwell%27s_demon
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many thanks for the reply
Maxwell's Demon (I like it already) is outside any observers frame of reference - so the dimension grid lines can/should be straight, unaffected by gravity. Time also.
is this "perfect grid" (straight, non bending, perfect time) scenario something that has been examined and dismissed as wrong or not useful/pointless? i wouldn't dream of dismissing GR and SR as pointless. we are observers of stuff relative to us and the theories work.
edit...i read that Maxwell's Demon is more related to energy systems and equilibrium, 2nd law etc, but has been coopted to be magic elsewhere, so I'm happy to have it as a magic, frame of reference free, observer of the universe
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Maxwell's Demon (I like it already) is outside any observers frame of reference - so the dimension grid lines can/should be straight, unaffected by gravity. Time also.
That is incorrect. While Maxwell's demon is outside of he universe spacetime is within the universe and is affected by matter which is also in the universe.
is this "perfect grid" (straight, non bending, perfect time) scenario something that has been examined and dismissed as wrong or not useful/pointless?
Yes. It's been "examined" and as such its been verified. Its not wrong, its not useless and its not pointless. GR and its predictions of curved spacetime was used to calculate the deflection of starlight by the sun. The predictions of GR and its curved spacetime were consistent with the observed deflection of starlight. If spacetime wasn't curved then the amount of deflection predicted would be half the observed value. GR predicts the observed amount of deflection. Another experiment was done to measure the curvature of spacetime by Irwin Shapiro in the 60's. His team at MIT Lincoln lab bounced radar waves off the surfaces of Venus and Mercury. The time delay was consistent with the results predicted by GR.
edit...i read that Maxwell's Demon is more related to energy systems and equilibrium, 2nd law etc, but has been coopted to be magic elsewhere, so I'm happy to have it as a magic, frame of reference free, observer of the universe
That's correct. However the concept and term has been used for different purposes such as the one you mentioned. That's why I said that its be referred to as Maxwell's demon and not defined as Maxwell's demon.
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Thanks again for the reply. You are being very informative
I fear that I may have not been clear when I asked whether a perfect grid, straight grid had been examined.
I know that GR and a "curved grid" has been thoroughly examined and proved etc, gravitational lensing etc etc.
My question was more whether the Demons non relative view had been examined from a theoretical perspective (as it is unobservable). I have been reading briefly about proper time and proper distance which assumes, as I understand it, a relational consistency, unaffected by gravity and relative speed. This is more what I was trying to ask. Is there any merit in applying proper time and distance to the universe as a whole....like a map grid, straight lines, regardless of the topography of the land (in such a metaphor, gravity could be contour lines on the grid)
(The grid lines a straight because the earth is flat 😆)