Age Relative? Time, Speed and Paradox Explored

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The discussion centers on the paradox of time dilation as described in the Special Theory of Relativity, particularly in the context of the twin paradox. A traveler on a spaceship moving near the speed of light ages slower than their counterparts on Earth, leading to a contradiction about whose clock runs slower. The conversation highlights that while both observers perceive the other's clock as running slow, the acceleration experienced by the spaceship traveler complicates the equivalence of their frames of reference. The relativity of simultaneity is crucial in resolving the paradox, as the shift in inertial frames during acceleration alters the perception of time. Ultimately, the paradox remains a topic of debate, emphasizing the complexities of time, speed, and observation in relativity.
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We well know that time is relative according to the Special Theory of Relativity. So, a person on a spaceship close to the speed of light (~c) could go on a trip for some years, return and find out that he is still young, while his friends or relatives are already very old or gone. This happens because the observers on Earth see the clockticks on the spaceship go slower. Now, speed is relative, so the observer on the spaceship sees the Earth frame of reference move away with the same speed. So he reaches a similar conclusion, that clocks on Earth go slower so that he would expect to find his relatives younger than usual. Now this is the contradiction or paradox as we may say: time is relative, ok, but is grey hair relative? Certainly not. Only one of them could be younger than usual.
When I was discussing this paradox in 33rd IPHO, Indonesia, some said that the two frames of reference are not equivalent. One accelerates, while the other stays at constant velocity. So the laws of physics are not valid for the observer on the spaceship while it accelerates. I agree. But what happens when the spaceship ceases to accelerate and is in constant velocity? It is an inertial frame of reference as good as the Earth is, the physical laws hold. So the observations of the guy on the spaceship are correct and the observations of the persons on the Earth are correct as well. Both parties observe that the clocks on the other frame of reference run slower. Isn't this now a paradox? I've thought long about it. If somenone has any idea, I would appreciate their opinion.
 
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Time is relative, the speed of time is not. Every observer is traveling to the future at 1 second per second, each one with its second length depending on the speed.
 
ramollari - You're initial analysis of the situation is correct, the fact that at some point in the journey the twin in the rocket has to undergo an acceleration to change direction to come back allows us to determine that with respect to us here on earth, he is the one really moving, so it's his clock that actually runs slow.

Another interesting discussion of this paradox which uses the relativity of simultaneity can be found in "A First Course in General Relativity" By Bernard Shutz. To paraphrase: If you draw a two dimensional space-time diagram, with one axis being time, the other being space, you notice that on the outward journey the rocket twin's line of simultaneity includes the the departure event and so you can't say whose clock is really running slowly. But, once the rocket twin changes direction, she changes inertial frames and her line of simultaneity shifts to the return event, and she sees the Earth twin age incredibly quickly.
 
geometer said:
ramollari - You're initial analysis of the situation is correct, the fact that at some point in the journey the twin in the rocket has to undergo an acceleration to change direction to come back allows us to determine that with respect to us here on earth, he is the one really moving, so it's his clock that actually runs slow.

Another interesting discussion of this paradox which uses the relativity of simultaneity can be found in "A First Course in General Relativity" By Bernard Shutz. To paraphrase: If you draw a two dimensional space-time diagram, with one axis being time, the other being space, you notice that on the outward journey the rocket twin's line of simultaneity includes the the departure event and so you can't say whose clock is really running slowly. But, once the rocket twin changes direction, she changes inertial frames and her line of simultaneity shifts to the return event, and she sees the Earth twin age incredibly quickly.

I don't quite understand your second argument, i'd need to consider it more closely. Regarding the first argument, I think that you're correct in that we can make a difference between the two frames of reference: they are not equivalent. Maybe there's some more detailed theory behind this paradox. But the the way time dilation is generally explained is too simplistic. It doesn't take any factors like acceleration into consideration.
 
ramollari said:
I don't quite understand your second argument, i'd need to consider it more closely. Regarding the first argument, I think that you're correct in that we can make a difference between the two frames of reference: they are not equivalent. Maybe there's some more detailed theory behind this paradox. But the the way time dilation is generally explained is too simplistic. It doesn't take any factors like acceleration into consideration.

The relativity of simultaneity resolution of the twin's paradox is much easier to understand graphically. It basically uses the fact that relativity did away with the idea of absolute simultaneity also.

The equation for time dilation falls right out of the definition of proper time if you differentiate proper time with respect to coordinate time.
 
The relativity of simultaneity resolution of the twin's paradox is much easier to understand graphically. It basically uses the fact that relativity did away with the idea of absolute simultaneity also.

Einstein used simultaneity to prove relativity.
In his experiment he used two simultaneous light flashes equal distant from an observer at rest with respect to the sources of the light. If the speed of light is constant, then all points equal distant from the observer are simultaneous. The simultaneous condition of the source may be established by synchronizing the two sources at the observer then moving them away each in the same manner to points that are equal distance.

You now have established a circle or sphere of simultaneity. If the observer moves the two sources are not influenced by his change of position and therefore remain simultaneous. The observer however no longer sees the flashes of light simultaneously but will see all points that are now equal distance from his position as simultaneous, thus establishing another circle or sphere of simultaneity. It must follow then that if the two simultaneous circles intersect both circles must be simultaneous.

Since an infinite number of circles may be simultaneous in both cases then all possible points in the universe must be simultaneous. You may also move the observer to an infinite number of positions with also the same results.

Einstein’s theory not only does not disprove simultaneity but it requires it. Einstein’s theory is a theory of relative observation not reality.

Einstein’s theory using simultaneity resolves the problem of time travel. If all things in the universe occur at the same time, then it is impossible to arrive before an action takes place even if you exceed the speed of light.
 
Einstein used simultaneity to prove relativity.
In his experiment he used two simultaneous light flashes equal distant from an observer at rest with respect to the sources of the light. If the speed of light is constant, then all points equal distant from the observer are simultaneous.

OK if your observer is at rest, in relation to the light sources one in front of him/her and one behind, but traveling a say 90% of the speed of light. how do you get the idea that the light from both arrives at the observer at the same time?

Twistedseer
 
4Newton said:
Einstein’s theory not only does not disprove simultaneity but it requires it. Einstein’s theory is a theory of relative observation not reality.

The failure of simultaneity is an inescapable aspect of Relativity. Consider two space-time coordinate systems A and B. We'll condense the space axes down to one, the x-axis. And, we will call the speed of light 1 just to make things simpler. Now, assume B is in motion with respect to A with some velocity v. Now, let's look at what B's axes look like with respect to A when A and B's origins coincide.

Since B is in motion with respect to A, B's clock is running slower than A's so B's time axis is inclined at some angle with respect to A's time axis (the tangent of the angle will give you B's velocity).

Now, to find where B's x (space) axis lies with respect to A's x axis, we switich for a second to B's frame. Consider a beam of light emitted from an event at x = 0, t = -a in B's frame. This beam will reach B's x-axis at x = +a since in our coordinate system, c = 1, which means light travels at a 45 degree angle with respect to where it is emitted or reflected. If it is reflected back to the t axis, it will arrive at t = +a. So, we can consider B's x-axis as the locus of all events that reflect light rays in such a manner that they return to B's t axis at +a if they left it at -a.

Drawing B's x-axis to satisfy this property, remembering the fact that the velocity of light is constant for all observers regardless of the state of motion of the source, (in other words we need to maintain the 45 degree thing) we find B's x-axis makes some angle with A's x axis. In other words, the two x axes don't coincide. What this means is that events that are simultaneous in A's frame are not simultaneous in B's frame.
 
Twistedseer:
OK if your observer is at rest, in relation to the light sources one in front of him/her and one behind, but traveling a say 90% of the speed of light. how do you get the idea that the light from both arrives at the observer at the same time?
This is the Einstein experiment. His first condition was in a rest frame, no velocity. This is the proper time frame. This was Einstein’s starting point. He showed that two light, or all light, sources at equal distance reached the observer at the same time.

The second condition of his experiment is your description of a moving frame. He showed that the time of the arrival of the two flashes is dependent on the velocity of the moving frame. That is relativity of observation and action. Since no action or light can reach another point faster than the speed of light.

Change of position or velocity has no effect on the two sources of light, if they were simultaneous they remain simultaneous no matter the action of the observer.
 
  • #10
4Newton said:
Change of position or velocity has no effect on the two sources of light, if they were simultaneous they remain simultaneous no matter the action of the observer.

Not so. Any events that appear simultaneous to frame A, will not appear simultaneous in any frame in motion with respect to A.
 
  • #11
geometer:
Not so. Any events that appear simultaneous to frame A, will not appear simultaneous in any frame in motion with respect to A.
The key word in your reply is “appear” relativity only applies to observation or actions at a distance, the condition of the limitation of the speed of light.

If you have two lights flashing at the same time in the same place you of course consider their action to be simultaneous. Their action of simultaneous flashing does not change with your change of position. If you now move the two lights just a few feet apart their flashing will stay simultaneous again your change of position has no effect on the flashing lights only your observation changes. This is the difference between real and observed.

In Minkowski space-time all frames of zero velocity, proper time, have clocks that tick at the same rate independent of position. SR only considers moving frames. You can not take a proof that started from a zero reference frame, proper time, then take your results and change the source of your proof.
 
  • #12
The twin paradox continues to be a paradox - it is not resolved by acceleration, either at the beginning of the outward bound journey, nor at the turn around point. The triplet version of the event eliminates any acceleration (outbound traveler simply transfers his clock reading to an inbound traveler without slowing down) - moreover, even if acceleration forces were experienced, they have no effect upon local time except to the extent they modify the velocity), and any shift that is experienced by the distant twin as he observes the Earth clock cannot actually add time to the Earth bound twin's clock... this time shift if it is actually observed can only be apparent, and for the two twins to have different ages, the time difference(s) must be actual - which presumes some physical cause.
 
  • #13
Follow up - I think it was Michio Kaku in one of his recent popular treatise on SR that he posed the question of what happens if the traveling twin never turns around - could we live in a universe where each twin continues to be younger than the other?
 
  • #14
The twin paradox is not a paradox. SR is very clear about what actually happens. Both twins will see the other aging more slowly, but when the spaceship has turned around the astronaut twin will be in another inertial frame than he was before, and in that frame his twin on Earth is (still) aging more slowly than him, but is much older than him to begin with.

This may be difficult to understand, but it's not a contradiction, and not a paradox.

I'm surprised that no one in this thread has mentioned that there are lots of other threads about the twin "paradox" in this forum. It seems like a new one is opened up once a week. My suggestion to those of you who are interested is that you read those. This is one of them. You can find the others by using the search feature.

geometer: I agree with your recommendation of Schutz's book, and most of what you said. But please don't say things like "he is the one really moving". It hurts my eyes. :smile:
 
  • #15
Geometer and yogi:
If again you look at Minkowski space-time you find that clocks do not measure time. In Minkowski space-time proper time is the same everywhere. In Minkowski space-time diagram all vertical lines are proper time transition lines and all horizontal lines are spatial transition lines. Light is on a line that is 45 degrees to both lines. This is because light must travel at the speed of light in the spatial dimension and all things are also transitioning in the time dimension at the same rate as the speed of light.

In Minkowski space-time light starts from source S on proper time line A and transitions to proper time line B. light then returns back to proper time line A and arrives at proper time line A at the same point where source S has transition to on time line A.

You now have a condition that source S has moved only in time from S0 to S1. Light has transition from S0 to B1 and back to S1. Both the transitions of S0 to S1 and the transition of light occur in the same amount of time. The transition of light must then be faster that the speed of light in space-time. The products of space and time do not vector add to a limited transition to the speed of light.

If you now take the two twins and one twin again takes off from Earth at S0. Twin 1 then travels at a rate a little less than the speed of light to some point B1. Twin 1 then turns around and heads back toward Earth at the same speed and reaches Earth when Earth is at point S1.

Twin 1 must exceed the speed of light in space-time to arrive back on earth. If he did not exceed the speed of light in space-time he would never be able to return to Earth at the location that he left. He would drop behind the proper time of Earth and disappear from our universe forever.

All frames therefore must stay in proper time and as we have proved before in posts 6,9,11 all actions in proper time are simultaneous.

At the same time that twin 1 is on his trip his clock slowed down. On returning to Earth he finds his clock is way behind proper time. Clocks therefore do not control real time. Clocks do have a relation with real time but that is another thread,

There is no twin paradox of SR. Minkowski space-time is based on SR. As you can see Minkowski space-time is the correct interpretation of SR. It does clear up many misconceptions about SR. there are rest frames in SR Anything on the proper time lines is in a rest frame. The speed of light does not limit transitions in space-time, and clocks do not indicate real time. Real or proper time is absolute. Real actions, simultaneity, is the same everywhere in the universe under all conditions.
 
  • #16
4NEWTON - that is an interesting analysis - but if clocks don't measure real time - what do they measure? Reminds me of the comment by William Randoff Hursh: if "burd" doesn't spell "bird" what the hell does it spell ?

The explanation of the TP is almost always resolved by postulate - not by any physical evidence - we have no reason to suspect that simply changing from one reference system to another causes any physical event to occur that is going to result in an age difference when the twins are reunited. You as well as all those who rely upon this assumption do not have an evidenciary basis - what we do know is that decaying particles live longer when they are traveling at a high velocity with respect to the Earth frame (the one way twin paradox with no turn around) - we have never done the twin experiment although we have flown clocks around the Earth and measured that they log different times with respect to each other and the Earth centered reference frame in which they were synchronized - this looks to be a real time dilation consequence.

For those who wish to read the many hundreds of articles dealing with the twin paradox with an open mind, they will be surprised find some very intelligent, educated and thinking persons in universities all over the world, who believe the issue is unresolved. The successes of SR are legion, but the explanations that attempt to resolve this particular aspect of the theory are not at all consistent with one another.
 
  • #17
yogi said:
we have no reason to suspect that simply changing from one reference system to another causes any physical event to occur that is going to result in an age difference when the twins are reunited.
This comment makes it clear that you have misunderstood SR, and in particular the concept of simultaneity and the resolution of the twin "paradox". No one has said that the change from one frame to another will cause any kind of event to occur.

In one frame, a certain set of "slices" of space time (technically 3-dimensional spacelike hyperplanes) can be thought of as "space, at different times". (Each "slice" consists of events that are simultaneous in that frame). In another frame, a completely different set of "slices" are "space, at different times". That is what you need to understand to understand the twin "paradox".

yogi said:
...but the explanations that attempt to resolve this particular aspect of the theory are not at all consistent with one another.
So? That's probably true, but if it is, it only means that some of them did something wrong. There are plenty of ways to misunderstand SR.
 
  • #18
I suggest you explain your analysis to Selleri, Resnic and some of the others who have written college text(s) on relativity .. and who have come to entirely different conclusions re the twin(s). Your comment is typical of relativists - "if you don't see it my way, you just don't understand relativity"
Only problem is, there are several different relativity churches each preaching a different gospel, and they all claim to be absolutely right




The simple fact of the matter is, if two clocks log different ages between the time they are separated and the time they are returned to the same reference frame, there must be a physical reason - you can take all the time slices you want, but what you get is observational information - from which you make a transition to real time discrepency. All explanations purporting to resolve the paradox of the twin(s), somewhere in the analysis, make this shift (sometimes the transition is subtile, but it is always there).

Einstein intuited that a returning two-way traveler would log a lesser time than a clock which remained in the same frame (1n 1905 - long before there was any evidence of actual time dilation). He guessed that the answer was somehow connected with the turn around acceleration. But we now know that acceleration (in and of itself) has no influence upon local clock rate. Any effect can only be observational vis a vis what the returning twin judges to be a change in the Earth time (if he does in fact so observe). Moreover- in the triplet version - there are no accelerations.
 
  • #19
yogi said:
I suggest you explain your analysis to Selleri, Resnic and some of the others who have written college text(s) on relativity .. and who have come to entirely different conclusions re the twin(s). Your comment is typical of relativists - "if you don't see it my way, you just don't understand relativity"
Only problem is, there are several different relativity churches each preaching a different gospel, and they all claim to be absolutely right

There are in fact many different explanations for the twin paradox. The specific objection that there are "too many" explanations is even covered in the sci.physics.faq.

faq said:
Too Many Explanations: a Meta-Objection

An old lawyer joke:

"Your Honor, I will show first, that my client never borrowed the Ming vase from the plaintiff; second, that he returned the vase in perfect condition; and third, that the crack was already present when he borrowed it."

Or to quote Shakespeare: "Methinks the lady doth protest too much."

Why so many different explanations? Are the relativists just trying to bamboozle their opponents? To prevail, a defense attorney just has to stir up doubt about the plaintiff's case; she's not required to give her own theory of what happened. But a physical theory should tell a single coherent story.

Relativity here pays the price of permissiveness. It says to us, "Pick whichever frame you like to describe your results, or use spacetime diagrams and don't choose a reference frame at all. They're all equivalent, I don't mind." No wonder that one explanation ends up looking like three or four.

Most physicists feel that the Spacetime Diagram Explanation is the most fundamental. It does amount to a sort of "Universal Interlingua", enabling one to see how superficially different explanations are really at heart the same.

Note specifically that the math is not ambiguous. One can generate a large number of different English explanations. The math, however, is very clear about which clock reads a longer time - there are no "different" versions of relativity as Yogi attempts to claim. Relativity unambiguously tells one what clocks read when they are reunited after a journey through space-time, and which one readds the longest.

The reference for the original quote:

Too Many Explanations

A reference to the entire sci.physics Twin Paradox FAQ

Twin Paradox FAQ

yogi said:
The simple fact of the matter is, if two clocks log different ages between the time they are separated and the time they are returned to the same reference frame, there must be a physical reason - you can take all the time slices you want, but what you get is observational information

so far so good

yogi said:
- from which you make a transition to real time discrepency. All explanations purporting to resolve the paradox of the twin(s), somewhere in the analysis, make this shift (sometimes the transition is subtile, but it is always there).

There isn't anything else to explain other than what clocks measure. The rest of the interpretation after my "so far so good" comment, including any notion of "real time", or any notion of "shifting", or "transition" is occurring in one's (Yogi's, in this case) own head, due to philosophical concerns.

Having seen this type of response before, it seems very likely that Yogi has a pre-conceived philosophy of how time "should" act that is at variance with how clocks actually do act. Prefering to believe his philosophy rather than the measured results, he simply discounts observational evidence, claiming that the clocks aren't actually measuring "real" time.
 
  • #20
There isn't anything else to explain other than what clocks measure. The rest of the interpretation after my "so far so good" comment, including any notion of "real time", or any notion of "shifting", or "transition" is occurring in one's (Yogi's, in this case) own head, due to philosophical concerns.

Having seen this type of response before, it seems very likely that Yogi has a pre-conceived philosophy of how time "should" act that is at variance with how clocks actually do act. Preferring to believe his philosophy rather than the measured results, he simply discounts observational evidence, claiming that the clocks aren't actually measuring "real" time.

I think you should read my posting before you criticize Yogi. His question is legitimate in light of my posting. You seem to have a pre-conceived philosophy that clocks are time.

If you take clocks on two different paths and when you bring them back together they read different elapse time then you can not by any reason, logic, of law of physics say that both kept real time. If you purpose is to keep the nature of time a mystic art that only a select few can understand then you approach works fine.

All clocks keep an indication of time through a mass energy relationship. Mass is subject to change with spatial transition, velocity. All the clocks up to this point measure mass or changes in mass.

Real time and clock time agree on any proper time line ( t,0,0,0) where time is on the Y-axis and spatial position is on the X-axis. Any frame that is not changing with respect to distance is a rest frame at any point in space.

When you transition in the spatial dimension you still stay in sync with real time but your clock slows down because the mass of all parts of the clock increase. The reason for the increase is another thread.

I hope this post makes things clearer.
 
  • #21
4Newton said:
I think you should read my posting before you criticize Yogi. His question is legitimate in light of my posting. You seem to have a pre-conceived philosophy that clocks are time.

If you take clocks on two different paths and when you bring them back together they read different elapse time then you can not by any reason, logic, of law of physics say that both kept real time.

Why not? In fact, both clocks do measure time. You are apparently imputing some properties to "real" time that has no basis in observation or measurement. The only basis I can see for your statement is that you have some preconceived notions as to how clocks "should" work. Then, when you notice a variance of how clocks actually do work compared to how you think they should work, you decide that the clocks must be wrong.
 
  • #22
Careful, 4Newton - we've been down this road before and you know where it goes.

Clocks, by definition, measure time. "Real" time. In fact, it takes a leap of logic (or, rather, illogic) to assume that something that by definition keeps "real time" doesn't keep "real time."
 
  • #23
4Newton, I've read most of what you've written in this thread and you're making a lot of mistakes. Too many to comment them all. Why don't you just explain as carefully as you can what your main objection to relativity is, and we can discuss that. (When I say "carefully" I don't mean that I think you should use many words. Just make sure that it's always clear what you mean. In most of your posts in this thread, it isn't).
 
  • #24
pervect - no, I do not have a bais as to the issue as to what clocks should read (note my post above - if clocks don't measure real time, what the hell do they measure?). Nor do I have any reason not to agree with the transforms - they give the correct aging difference - the problem is not with the math, it is with the interpretation.- I do not take issue with the experimental evidence - but the experimental evidence is incomplete - we have no idea as to whether a high speed muon actually experiences a reciprocal time dilation when it attempts to access clock rates in the Earth frame - we do not have an experimental test that proves the second postulate (one way isotrophy in all inertial system) and we do not have a physical theory to explain time dilation within the framework of SR. There are other theories that yield the same result(s) as all of the experiments that are cited as confirmation of SR ... moreover some of these theories better explain some things. You are correct in saying that I do not believe in the observational evidence --- for example that one twin looking at the other twins clock can have a physical consequence - each twin can only truly measure his own proper time in his own frame with which he is at rest - and unless there is something intrinsically different about two rest frames in relative motion, they must both measure the same lapse of time to the turn around point, and they should both measure the same lapse of time on the inbound voyage... so the difference in the case of the non accelerating triplet scenero, should be zero - but we all seem to agree that it isn't. Maybe some inertial reference frames are more or less equivalent than others??
 
  • #25
As a matter of curosity with regard to those who are criticising 4Newton, if clocks don't measure local time, but rather the rate at which processes take place, how would we know the difference?
 
  • #26
yogi said:
As a matter of curosity with regard to those who are criticising 4Newton, if clocks don't measure local time, but rather the rate at which processes take place, how would we know the difference?
If every single piece of evidence we have says that clocks measure real time, what basis do we have to assume they don't?

Your misunderstanding, like 4Newton's, is based simply on the fact that you don't like what SR says and are looking for a way out.
 
  • #27
I can now see what the problem is. Everyone on here seems to be suffering from the problem of definitions. Below is the common thought of proper and improper time.
http://www.wordiq.com/definition/Proper_time
To be more precise, proper time is the time measured between two events which happen in the same location.

Suppose there is another frame of reference, which is moving in velocity v, so the events are occurring in different places according to it, then the relation between the time measured between the two events in the resting frame and the moving frame is

tau = (\Delta t_{proper}) = (\Delta t_{improper}) \cdot \sqrt{1-v^2/c^2}

http://aci.mta.ca/Courses/Physics/4701/EText/Proper.html
We refer to proper time as the time which is measured by an observer which is present at the same location as the events which mark the beginning and the ending of the event. Another way to say this is that the proper time is measured in a reference frame in which the events occur at the same spatial point.

Wikipedia
Proper time is time measured when the clock is at rest relative to the person looking at it. The distinction between proper time and the measured time is necessary because of the effects of time dilation, which is outlined in Einstein's theory of special relativity.

To be more precise, proper time is the time measured between two events which happen in the same location.
From the above:

Is it safe to say that we all agree that proper time is the time line in a zero rest frame?

Can we also agree that all frames that are not changing spatial location are zero rest frames?

Do we agree that all clocks tick at the same rate in all zero rest frames?

From the above they use the term improper time when referring to time in moving frames.

If we all agree on this then we can move on to the definition of clocks and time.
I will also try to attach a simple space-time drawing so we can all be on the same page.

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Attachments

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  • #28
4Newton said:
I can now see what the problem is. Everyone on here seems to be suffering from the problem of definitions. Below is the common thought of proper and improper time.
From the above:

Is it safe to say that we all agree that proper time is the time line in a zero rest frame?


Can we also agree that all frames that are not changing spatial location are zero rest frames?

The term "proper time" is standard, as per your definitions.

The term "zero rest frame" isn't standard. I thought intially that you might be thinking of an inertial frame, but this is apparently not the case, because some of your remarks would not apply to inertial frames. I get a feeling reading your text that a "zero rest frame" is probably a preferred frame. This concept doesn't have much utility, because the laws of physics are the same in all frame according to relativity and what experimental evidence we have. This means that there is no particular frame that can be singled out as being "at rest" via any physical means.

Do we agree that all clocks tick at the same rate in all zero rest frames?

Assuming that you mean to compare one clock to another, a clock that is in an inertial frame that is moving with respect to another inertial frame will not tick at the same rate. This is why I suspect that your non-standard term "zero rest frame" is not an inertial frame.
 
  • #29
The Wikipedia definition is actually not very good. The worst part of it is this sentence:

"To be more precise, proper time is the time measured between two events which happen in the same location."

This statement doesn't make much sense, since different observers don't agree on whether two events happens "in the same location" (i.e. at the same spatial coordinate), unless their relative velocity is zero.

Mathematically, "proper time" is defined as the integral of

d\tau=\sqrt{dt^2-dx^2-dy^2-dz^2}=dt\sqrt{1-v^2}

along a path through spacetime. (You can't just define proper time between two events. Proper time is always defined along a path).

If this path is the world-line of a clock, then "proper time" is the time that will be measured by the clock.
 
  • #30
pervect, fyi, 4Newton believes there is a universal rest frame, which then makes the time measured in that frame "real" while other measurements of time are not. Yes, I've tried to explain why that's wrong.

Indeed, the definition of "proper time" itself suggests that every clock measures it!
 
  • #31
Just as I thought. No one seems to agree on the terms being used.
pervect: seems to agree with the definition of proper time but he and no one else like the term zero rest frame.
The term "proper time" is standard, as per your definitions.The term "zero rest frame" isn't standard.
Fredrik: disagrees with the common definition of three sources.

russ_watters: disagrees with the definition and thinks proper time should be what clocks measure, as I read it, no matter the frame the clock is in.
Indeed, the definition of "proper time" itself suggests that every clock measures it!
To have some point of agreement. If you look at the attached drawing MST-2.pdf can we reach an agreement on what to call the vertical line A to D with all vertical lines representing transition in the time dimension as per Minkowski space-time. Also what is the name of the frame that would be on that line? As indicated by the drawing a frame on that line has no spatial transition.
 
  • #32
4Newton said:
Fredrik: disagrees with the common definition of three sources.
I'm not saying that the guys who wrote those articles don't know what proper time is. I'm just saying that they are pretty bad at explaining it. If I didn't already know and understand the correct definition (which can be found in any standard textbook on general relativity, e.g. Robert Wald's "General Relativity"), I wouldn't understand what these guys are trying to say.

4Newton said:
russ_watters: disagrees with the definition and thinks proper time should be what clocks measure, as I read it, no matter the frame the clock is in.
This is not in disagreement with the definition.

4Newton said:
To have some point of agreement. If you look at the attached drawing MST-2.pdf can we reach an agreement on what to call the vertical line A to D with all vertical lines representing transition in the time dimension as per Minkowski space-time.
I would call that vertical line "the time axis" (of this particular coordinate system).

4Newton said:
Also what is the name of the frame that would be on that line? As indicated by the drawing a frame on that line has no spatial transition.
"the frame that would be on that line"... That doesn't make much sense to me. The whole spacetime diagram represents one frame (i.e. one coordinate system).

I will try to explain a few things here. A straight (and timelike) line like BE can represent the world-line of another inertial observer. In that case, the events on that line all happen at the same point in space to him, i.e. in his rest frame. That line is his time axis.

If that guy (the observer whose world-line is BE) carries a stopwatch that he starts at B and stops at E, it will measure the proper time along the line BE. The proper time along a path is the same as the coordinate time of an observer whose world line is that path.

The time that you would measure between the events B and E (if your world-line is BD) is just (C-B) (since C is simultaneous with E in your frame).
 
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  • #33
Indeed, 4Newton, it seems the only one who wants to argue about the definition is you. The rest of us agree on it. You've passed from arguing the theory to arguing the definitions of the terms in the theory. Its an invalid line of reasoning.
 
  • #34
4Newton said:
Just as I thought. No one seems to agree on the terms being used.

I'm afraid that I must interpret this remark as a "nice dodge", a debating tactic, rather than a serious attempt at discussion.

I see a general agreement that the various definitions you quoted for "proper time" are reasonably close to the mark (at most, one poster thought that your definition was not very rigorous and could be improved).

I also see a general reluctance on your part to define the term "zero rest frame". Russ's explanation of this term is much clearer than yours at this point. I should point out that it really isn't our job to define your terms for you.

I would guess that you are having a hard time quoting defintions for this term (as you did for proper time), either because you made it up yourself, or because you got it from some less than authoritative source.
 
  • #35
russ_watters:
Indeed, 4Newton, it seems the only one who wants to argue about the definition is you. The rest of us agree on it. You've passed from arguing the theory to arguing the definitions of the terms in the theory. Its an invalid line of reasoning.
I think you totally misunderstand my question about definitions. I am not and do not argue definitions. I am asking for a definition that all agree to so that I may use that definition in explaining my thoughts.

Fredrik:
4Newton, I've read most of what you've written in this thread and you're making a lot of mistakes. Too many to comment them all. Why don't you just explain as carefully as you can what your main objection to relativity is, and we can discuss that. (When I say "carefully" I don't mean that I think you should use many words. Just make sure that it's always clear what you mean. In most of your posts in this thread, it isn't).
I have no objections to relativity. All I am or have been doing is analyzing the nature of relativity and trying to pick out facts of the relationship of space-time in view of relativity.

Fredrik:
I'm not saying that the guys who wrote those articles don't know what proper time is. I'm just saying that they are pretty bad at explaining it. If I didn't already know and understand the correct definition (which can be found in any standard textbook on general relativity, e.g. Robert Wald's "General Relativity"), I wouldn't understand what these guys are trying to say.
This is why I asked for some word or term to help describe the attached drawing.
I will try to explain a few things here. A straight (and timelike) line like BE can represent the world-line of another inertial observer. In that case, the events on that line all happen at the same point in space to him, i.e. in his rest frame. That line is his time axis.
I have no problem with line BE being a world line. Are not all lines in Minkowski space-time world lines, BD, AF, or ED.
If that guy (the observer whose world-line is BE) carries a stopwatch that he starts at B and stops at E, it will measure the proper time along the line BE. The proper time along a path is the same as the coordinate time of an observer whose world line is that path.
Are you saying that all time measured no matter what you path, is proper time?
The time that you would measure between the events B and E (if your world-line is BD) is just (C-B) (since C is simultaneous with E in your frame).
Now this is where we run into a problem. If you take a clock and go from B to E your clock will tick at a slower rate. The rate of your clock dependent on the rate of transition, velocity, from B to E as stated by SR, If however you made no spatial transition and went from B to C your clock does not change it’s rate.

If you stop at E your clock will now tick at the same rate as the clock at C location. However the clock at E will not agree with the clock at C in accumulated time.

As can be seen there are differences as the result of the path taken. This has nothing to do with definitions. If the terms, real time, proper time, world line, clock time, rest frame, zero rest frame, can not be used to indicate the difference then it would be useful if the different paths and time over the different paths could be referred to by some words that indicated the differences. If you have any words that describe these differences I would be very happy if anyone would tell me the correct terms to use.
 
  • #36
Perhaps 4Newton has in mind a frame where the CBR is isotropic.

When the issue of the universal applicability of SR arises, it is almost always defended by resort to its postulated tenants. But these postulates are the root of the contention. By way of example, we can question whether all inertial frames are equal in the sense that every experiment will yield the same result - measurement of the dipole CBR anisotrophy is clearly not the same at different times of the year - (the Earth's orbital tangent velocity very nearly approximates an inertial frame ) so the most fundamental belief upon which Einstein founded his theory (that it is not possible to detect velocity wrt space), is questionable.
 
  • #37
4Newton said:
I have no objections to relativity. All I am or have been doing is analyzing the nature of relativity and trying to pick out facts of the relationship of space-time in view of relativity.
This is surprising, because some of the things you've said seem to contradict relativity.

4Newton said:
Are not all lines in Minkowski space-time world lines, BD, AF, or ED.
Every curve can be called a world line, but only a straight line can be the world line of an inertial observer. The line also has to be "timelike". A line like BF (not drawn in the diagram) can't be the world line of an actual physical observer because that guy would have to move faster than the speed of light.

4Newton said:
Are you saying that all time measured no matter what you path, is proper time?
I suppose that you could put it that way, but what I'm really saying is that a clock measures the proper time along the clock's world line (almost no matter what that world line looks like; it has to be timelike, but it doesn't have to be straight).

4Newton said:
Now this is where we run into a problem. If you take a clock and go from B to E your clock will tick at a slower rate.
It will tick at a slower rate to you (assuming that your world line is AD), but it will always tick at the same rate to me (assuming that I'm moving with the clock).

4Newton said:
If the terms, real time, proper time, world line, clock time, rest frame, zero rest frame, can not be used to indicate the difference then it would be useful if the different paths and time over the different paths could be referred to by some words that indicated the differences. If you have any words that describe these differences I would be very happy if anyone would tell me the correct terms to use.
I don't know that "real time" would mean, unless it's a synonym for "proper time". I think I've made it clear enough what "proper time" and "world line" means. (Let me know if you disagree). "clock time"... Isn't that just another synonym for "proper time"? The spacetime diagram represents the "rest frame" of an inertial observer. His world line in this diagram is AD. I don't know what a "zero rest frame" is, unless it just means "rest frame".
 
  • #38
Where does it end, 4Newton? You've had this same discussion here before and it didn't take you where you wanted it to. I'd imagine you've had the same discussion in other places before you came here and had the same unsatisfactory result. Is there ever a point where you've repeated the same discussion enough times to re-evaluate your position in it?
 
  • #39
yogi said:
Perhaps 4Newton has in mind a frame where the CBR is isotropic.

When the issue of the universal applicability of SR arises, it is almost always defended by resort to its postulated tenants. But these postulates are the root of the contention. By way of example, we can question whether all inertial frames are equal in the sense that every experiment will yield the same result - measurement of the dipole CBR anisotrophy is clearly not the same at different times of the year - (the Earth's orbital tangent velocity very nearly approximates an inertial frame ) so the most fundamental belief upon which Einstein founded his theory (that it is not possible to detect velocity wrt space), is questionable.
You are wrong, yogi, in that the CMB does not provide a frame in which the laws of the universe are different from everywhere else.

You are correct that the Earth has a measurable velocity through the CMB, and due to our various orbiting motions, that velocity changes - but that fact does not affect our local laws of physics. For exampe an MM experiment performed on earth: If the CMB were really the classical aether, the MM experiment would show it.
 
  • #40
This is surprising, because some of the things you've said seem to contradict relativity.
Your term “seem” to contradict relativity is the major problem I am having on this topic. No one appears to be knowledgeable enough on the subject of SR to point out where there is any contradiction with relativity. Every one just states that it is wrong and then throws out some terms that are suppose to prove it. When I ask what they mean by the terms you see what happens.

Every curve can be called a world line, but only a straight line can be the world line of an inertial observer. The line also has to be "timelike". A line like BF (not drawn in the diagram) can't be the world line of an actual physical observer because that guy would have to move faster than the speed of light.
If every curve or straight line is a world line then that term has little meaning when trying to describe the difference between a clock that moves between BD and one that moves between BE. By that definition both clocks move on world lines.
I do agree that line BF can not be the world line of an actual observer.
I suppose that you could put it that way, but what I'm really saying is that a clock measures the proper time along the clock's world line (almost no matter what that world line looks like; it has to be timelike, but it doesn't have to be straight).
This again is all well and good and I have no problem agreeing with that but it still does not help with the difference between clocks.
It will tick at a slower rate to you (assuming that your world line is AD), but it will always tick at the same rate to me (assuming that I'm moving with the clock).
I agree with this also, but the question still remains. A clock that goes from B to D by way of C shows more accumulated time than a clock that goes from B to D by way of E.. The clock that goes from B to C to D will always have the most accumulated time and will have ticked at the fastest possible rate. This is the basis for the twin paradox.
I don't know that "real time" would mean, unless it's a synonym for "proper time". I think I've made it clear enough what "proper time" and "world line" means. (Let me know if you disagree). "clock time"... Isn't that just another synonym for "proper time"? The space-time diagram represents the "rest frame" of an inertial observer. His world line in this diagram is AD. I don't know what a "zero rest frame" is, unless it just means "rest frame".
Now I think I see the difference between us. You seem to think that the drawing is that of a moving, inertial, frame. This can not be so. In this drawing according to Minkowski space-time line AD is where delta is (ct) and dx=0, dy=0, and dz=0 also your transition of light line AF would not be at a 45 degree angle if this was an inertial frame. The angle would be dependent on your spatial transition as seen by the angle between AF and BE.

Where does it end, 4Newton? You've had this same discussion here before and it didn't take you where you wanted it to. I'd imagine you've had the same discussion in other places before you came here and had the same unsatisfactory result. Is there ever a point where you've repeated the same discussion enough times to re-evaluate your position in it?
I think you can see that I have re-evaluated my understanding from our first discussion. I have gone back and re-studied SR I have analyzed Minkowski space-time and I have had some very satisfactory results in other postings. Why should it end? I am learning a lot. This is not the extent of the ideas I would like to present. I do however know that I must learn to present them in an acceptable manner. From the acceptance on other postings I can see that I am starting to learn. I can also see that from this thread I still seem to have some lack of ability to communicate.
 
  • #41
4Newton said:
Your term “seem” to contradict relativity is the major problem I am having on this topic. No one appears to be knowledgeable enough on the subject of SR to point out where there is any contradiction with relativity. Every one just states that it is wrong and then throws out some terms that are suppose to prove it. When I ask what they mean by the terms you see what happens.
The reason I said "seem" is that half the time I don't even understand what you're trying to say. Let's look at a few examples:

"If the speed of light is constant, then all points equal distant from the observer are simultaneous."

Huh?!? What does this mean? Distance in space? Distance in spacetime? If it's distance in spacetime, are you using the Euclidean metric or the Minkowski metric? Actually it doesn't matter much, because if you mean anything but distance in space, the statement is very wrong (unless you're just trying to say that from a light ray's perspective every event in spacetime happens at the same time), and if you mean distance in space...all points at any distance are of course simultaneous.

"Twin 1 must exceed the speed of light in space-time to arrive back on earth. If he did not exceed the speed of light in space-time he would never be able to return to Earth at the location that he left."

Are you talking about his four-velocity? The four-velocity is defined in a way that makes sure that it's magnitude is always 1 (actually c, but I'm using units in which c=1).


4Newton said:
By that definition both clocks move on world lines.
Everything moves on world lines. The world line of an object is just the path it takes through spacetime.

4Newton said:
This again is all well and good and I have no problem agreeing with that but it still does not help with the difference between clocks.
...
I agree with this also, but the question still remains. A clock that goes from B to D by way of C shows more accumulated time than a clock that goes from B to D by way of E.. The clock that goes from B to C to D will always have the most accumulated time and will have ticked at the fastest possible rate. This is the basis for the twin paradox.
I still don't understand what the problem is, and what question still remains.

4Newton said:
Now I think I see the difference between us. You seem to think that the drawing is that of a moving, inertial, frame.
Spacetime diagrams are supposed to represent the coordinates of an inertial observer. No inertial observer is any more or any less "moving" than any other.

4Newton said:
This can not be so. In this drawing according to Minkowski space-time line AD is where delta is (ct) and dx=0, dy=0, and dz=0
In this inertial frame (which represents the coordinates of the observer whose world line is AD), the events A and D have the same spatial coordinates, but different time coordinates. But to the observer whose world line is AE, A and D would not have the same spatial coordinates. To him the x coordinate of event A is 0 and the x coordinate of B is negative. (What is "stationary" in your frame is "moving to the left" in his frame).

4Newton said:
...also your transition of light line AF would not be at a 45 degree angle if this was an inertial frame. The angle would be dependent on your spatial transition as seen by the angle between AF and BE.
This is just wrong. The angle of the world line of a light ray is always 45 degrees, in every inertial frame.
 
  • #42
"If the speed of light is constant, then all points equal distant from the observer are simultaneous."

Huh?!? What does this mean? Distance in space? Distance in spacetime? If it's distance in spacetime, are you using the Euclidean metric or the Minkowski metric? Actually it doesn't matter much, because if you mean anything but distance in space, the statement is very wrong (unless you're just trying to say that from a light ray's perspective every event in spacetime happens at the same time), and if you mean distance in space...all points at any distance are of course simultaneous.

From post #6
Einstein used simultaneity to prove relativity.
In his experiment he used two simultaneous light flashes equal distant from an observer at rest with respect to the sources of the light. If the speed of light is constant, then all points equal distant from the observer are simultaneous. The simultaneous condition of the source may be established by synchronizing the two sources at the observer then moving them away each in the same manner to points that are equal distance.

Post #6 and others are given to show proof that all actions in our universe are simultaneous. The proof is from Einstein’s relativity. The basic reason for our disagreement is that I believe and I am showing proof of absolutes in our universe. When you start from a closed mindset that everything is relative and there are no absolutes you close your mind to understanding anything I am saying.

Your statement that, “all points at any distance in (space) are of course simultaneous”, is in agreement with me and the proof I gave. I think you will find some others about to disagree with you.

"Twin 1 must exceed the speed of light in space-time to arrive back on earth. If he did not exceed the speed of light in space-time he would never be able to return to Earth at the location that he left."

Are you talking about his four-velocity? The four-velocity is defined in a way that makes sure that it's magnitude is always 1 (actually c, but I'm using units in which c=1).

Because of possible disagreements over definitions I would prefer not to use any terms at this point. All that I am pointing out is that the length of line BD is shorter than the length of lines BED and transition along the vertical axis is at the same rate as transition on the horizontal axis as shown by the line AF speed of light.. Transition BD is at a rate equal to the speed of light. In order to remain in sync with BD any transition in the spatial dimension must exceed the speed of light in that space-time vector BE as indicated by the length of the lines.

I still don't understand what the problem is, and what question still remains.
The question is. Why do clocks indicate different accumulated time when brought back together after moving over different paths in space-time and how can anyone say that clocks measure real time when they disagree. Again looking for absolutes. It is obvious and I think agreed by all that all clocks keep time at the same rate and tick the fastest on all vertical lines that have no spatial transitions. Except of course AF if you could take that path your clock would always read zero.

Spacetime diagrams are supposed to represent the coordinates of an inertial observer. No inertial observer is any more or any less "moving" than any other.
Who made that rule? Minkowski space-time is not an inertial frame.

If you state that there is no condition that can have zero spatial transition show me some proof or reason of logic. Btw by definition is not proof.

The rest of you statements revolve around this same point. Minkowski space-time is real, absolute, it is not a relative viewpoint. Even if you assume that it is a relative viewpoint there is nothing that prohibits a viewpoint that has absolute zero spatial transition.

If you are able to go one direction at the speed of light limit and the opposite direction up to the same limit then by all rules of logic, experience, math... there must be a center point where the spatial transition is zero.
 
  • #43
4Newton said:
From post #6
Einstein used simultaneity to prove relativity.
In his experiment he used two simultaneous light flashes equal distant from an observer at rest with respect to the sources of the light. If the speed of light is constant, then all points equal distant from the observer are simultaneous. The simultaneous condition of the source may be established by synchronizing the two sources at the observer then moving them away each in the same manner to points that are equal distance.
This still doesn't make much sense to me. What do you mean by "all points equal distant from the observer"? Suppose that you add a y-axis to your spacetime diagram. x and y represents two spatial dimensions, and t the time dimension. Suppose also that the light signals are emitted at (0,-a,0) and (0,a,0), where the first coordinate is the time coordinate. Does "all points equal distant from the observer" mean the circle t=0, x²+y²=a², or does it mean the cylinder x²+y²=a²? Maybe it means something completely different. You really have to start specifying these things.

If you're talking about the circle, you have already restricted your attention to simultaneous events. It's always a bad idea to assume what you're trying to prove.

4Newton said:
Post #6 and others are given to show proof that all actions in our universe are simultaneous.
I don't even know what you're trying to say. To me it looks like all you have "proved" is that all events on any horizontal line in the spacetime diagram are simultanous (to the observer whose world line is AD), and this is obvious anyway since all points on such a line have the same time coordinate. (This is what we mean by "simultaneous". Two events are simultaneous in a frame if they have the same time coordinate in that frame).

4Newton said:
The proof is from Einstein’s relativity. The basic reason for our disagreement is that I believe and I am showing proof of absolutes in our universe. When you start from a closed mindset that everything is relative and there are no absolutes you close your mind to understanding anything I am saying.
You haven't proved anything yet. I don't even know what you're trying to do. I've tried to understand what you're trying to say, but I can't really make sense of it. My best guess is that this is what you have done:

You start with one observer's point of view and restrict your attention to a set of events that are simultaneous to him. Then you "prove" that those events are simultaneous to him (which is something you had already assumed, without mentioning it explicitly). Then you extend this result, without motivation, to other observers, and claim that all observers agree about what events are simultaneous. This would mean that there's an "absolute" rest frame, and that's your conclusion.

Am I wrong about this?

4Newton said:
Your statement that, “all points at any distance in (space) are of course simultaneous”, is in agreement with me and the proof I gave. I think you will find some others about to disagree with you.
Perhaps I didn't express myself clearly enough. First of all you have to remember that in SR, "the universe", "space", or whatever you want to call it, is just a horizontal line in the spacetime diagram. Different horizontal lines represent space at different times. But you also have to remember that you can't just assume that another observer will think of the same set of lines, as "lines of simultaneity", i.e. as lines that represent space at different times. If you open any good book about special relativity (I recommend the chapters about SR in "A first course in general relativity" by Bernard Schutz) you can find a proof of the fact that the postulate about the speed of light implies that the lines in your spacetime diagram that are simultaneity lines ("space at different times") to another observer, are not horizontal (unless his world line is exactly vertical).

To the observer whose world line is AD, distance "in space" means distance along a horizontal line. To an observer moving with velocity v, it means distance along a line with slope v.

There's more that I would like to comment but I have to go to bed. Maybe tomorrow.
 
  • #44
Russ - as I said above - when issues re SR arise - relativists always pontificate SR as an indisputable principle. - but you get exactly the same results when you apply the transforms to a fixed ether frame as did Lorentz. Or if you use Selleri transforms. Moreover, these alternatives intrinsically abrogate the twin or triplet paradox because the aging is not reciprocal. Einstein happened to be biased on the issue of whether velocity wrt space has any meaning. We now know that velocity wrt to the CBR does have meaning - Note that I didn't say that Galilean type frames where mechanical experiments are agreed to yield equal results would be affected by motion relative to the CBR - but experiemts attempting to measure one way isotrophy in free space might be a different story. .. This is the crux of SR, it is the one thing that distinguishes SR from the other theories that predict the same results for the experiments that have been made - and until that test has been made, SR continues to rest upon a leap of faith.
 
  • #45
In Minkowski space-time you are only able to show space as a single dimension. It is not possible to have all three spatial dimensions with 45-degree light lines. The speed of light limit is the vector sum of the three spatial dimensions. This is also true because you can only move in one direction at a time, in the spatial dimension, so although you have an unlimited degree of freedom to move in any direction any selected direction is perpendicular to the time dimension.

Time dimension is (ct) and the spatial dimension is (s) where (s) is any x,y,z, but ds is the vector sum of x,y,z.

I don't even know what you're trying to say. To me it looks like all you have "proved" is that all events on any horizontal line in the spacetime diagram are simultanous (to the observer whose world line is AD), and this is obvious anyway since all points on such a line have the same time coordinate. (This is what we mean by "simultaneous". Two events are simultaneous in a frame if they have the same time coordinate in that frame).

You still insist on referring to the drawing as a moving frame. It is not. This is an absolute coordinate system. All moving frames would lie on BE like lines. All vertical lines are at spatial positions without motion.

The exercise of simultaneous actions is to show proof as you have stated to validate the absolute Minkowski space-time drawing. In the simultaneous exercise equal distance is just that. Equal distance in all directions to form a sphere from a center point.

You start with one observer's point of view and restrict your attention to a set of events that are simultaneous to him. Then you "prove" that those events are simultaneous to him (which is something you had already assumed, without mentioning it explicitly). Then you extend this result, without motivation, to other observers, and claim that all observers agree about what events are simultaneous. This would mean that there's an "absolute" rest frame, and that's your conclusion.

I start with an undisputed simultaneous action, two flashing lights at the same point in space, I then move them apart with the observer at the center still having verification the two lights are simultaneous. I then state the obvious, that the change of the observers position changes his view of the lights flashing simultaneously but obviously his change of position does not change the action of the flashing lights.

I have thus separated the reality of observation from the reality of action. This is something SR failed to do.

It is also obvious that the flashing lights may be moved in any direction of any equal distance, line, circle or spherical, with the same results. This may then be done a second time. You now have an infinite number of simultaneous spheres intersecting another set of infinite number of simultaneous spheres resulting in the conclusion that all action is simultaneous through out all points of the universe.

I then go to the Minkowski space-time drawing, again this is absolute space-time with inertial frames moving on BE or ED like lines. As you have stated all horizontal lines are simultaneous time lines. Likewise all lines that the horizontal lines pass through must also be simultaneous time lines, but in action and observation moving frames fall out of sync. SR gives us the relationship of this function.

SR theory does not address functions outside of moving frames but interpretation has tried to extend and limit the concept of the universe to moving frames. This has had a negative result of hampering understanding of forces and dimensions.
 
  • #46
I've got a general comment:

It is (just barely) possible to correctly work problems in special relativity with a notion of "absolute time".

What one does is to pick some particular frame, and think of it as "special". One can then view the Lorentz contractions as actual contractions - the very atoms of matter are distorted, the time dilation as actual slowing of clocks, the synchronization differences between different observers as an "ether wind" due to motion relative to the special frame. This actually has one well-respected proponent, Bell (I don't recall his last name, he's the Bell who derived the Bell inequality).

However, usually people who attempt to work relativity with this mindset get sucked into a false claim that whatever frame they are picking as mentally special is actually special in some physical manner. This is not the case, for the "ether" here is just a mental construct. If one does the math, it turns out to be not physically detectible. The speed of light is constant for all observers in this version of relativity (just as it is for all others), and the laws of physics are constant as well. There is no measurement that will single out which frame is special. So one winds up with an infinite number of different notions of "absolute time", rather than one. There is no practical difference between the notion of an infinite number of "absolute times" and the notion that time is not absolute.

Exactly where some of the posters here fit into this spectrum is unclear. When I see people claiming at one point to be agreeing with relativity, and at another point railing against "relativisits", I conclude that either they are either really really, really confused, or not arguing in an honest manner, or both.
 
  • #47
pervect said:
It is (just barely) possible to correctly work problems in special relativity with a notion of "absolute time".

What one does is to pick some particular frame, and think of it as "special". One can then view the Lorentz contractions as actual contractions - the very atoms of matter are distorted, the time dilation as actual slowing of clocks, the synchronization differences between different observers as an "ether wind" due to motion relative to the special frame. This actually has one well-respected proponent, Bell (I don't recall his last name, he's the Bell who derived the Bell inequality).
John S. Bell argued that quantum theory and GR could be integrated into QG if a Lorentzian view of relativity was taken. i.e. 3+1D rather than 4D space-time. This required some form of preferred frame, 'absolute' might be too absolute a term for it! (Speakable and unspeakable in quantum mechanics)
Isham and Butterfield reasoned the same, or similar, argument, calling for a ‘preferred foliation of space-time. (2001, Physics meets Philosophy at the Planck Scale, ed. by C. Callender and N. Huggett. Cambridge University Press.)

I would argue too that if Mach’s Principle is brought into play then such a preferred foliation of space-time may be identified as selected by the distribution of mass and momentum in the universe, it is the one in which the CMB is globally isotropic.

A further conundrum: The Twin Paradox in a closed universe. If cosmic expansion slows down and reverses it would become hypothetically possible to circumnavigate the universe. So one twin stays put and the other goes off at 9.999…%c and eventually meets up with his/her brother/sister again. Has he/she has aged say 50 (say) years and his/her bother/sister has aged 10 billion years (say)? Or is it the other way round? How do you tell?

Just a thought - Garth
 
  • #48
4Newton said:
In order to remain in sync with BD any transition in the spatial dimension must exceed the speed of light in that space-time vector BE as indicated by the length of the lines.
I think I see what you mean now. I thought you were wrong about the definition of four-velocity, but you were talking about ordinary velocity. What you are wrong about is what the world line would look like. (It starts out almost vertical, but a little to the right, and then changes to almost vertical, but a little to the left. It can be almost vertical through the whole trip).

4Newton said:
Minkowski space-time is not an inertial frame.
That is correct. It's not a frame at all. It's a manifold. (If you really want to understand relativity you should study differential geometry).

4Newton said:
Even if you assume that it is a relative viewpoint there is nothing that prohibits a viewpoint that has absolute zero spatial transition.
Yes, there is. The idea of "absolute zero spatial transition" contradicts the speed of light postulate, time dilation, and any other relativistic effect you've ever heard of. We can talk more about this when you've done the excercise I suggest that you do at the end of this post.

4Newton said:
In Minkowski space-time you are only able to show space as a single dimension.
This is of course wrong. We can all visualize three dimensions, so you can draw two spatial dimensions ("the x-y plane") and the t axis. (I don't understand how you can say that we can't).

4Newton said:
It is not possible to have all three spatial dimensions with 45-degree light lines.
I hope that what you really mean is that we can't visualize all four dimensions in our minds (because there are three spatial dimensions in Minkowski space, and the world line of any light ray through the origin makes a 45° angle with all the spatial axes).

4Newton said:
The speed of light limit is the vector sum of the three spatial dimensions.
Wrong. Have you never heard of the "light cone"? Imagine a spacetime diagram with two spatial dimensions (because you won't be able to visualize one with three). The set {(t,x,y)|-t²+x²+y²=0} is the union of all lightlike worldlines through the origin. This is a cone, not a line. Hence the name "light cone".

4Newton said:
This is also true because you can only move in one direction at a time, in the spatial dimension, so although you have an unlimited degree of freedom to move in any direction any selected direction is perpendicular to the time dimension.
I can't tell if this is just wrong or "not even wrong".

4Newton said:
You still insist on referring to the drawing as a moving frame. It is not. This is an absolute coordinate system. All moving frames would lie on BE like lines. All vertical lines are at spatial positions without motion.
In that case, your spacetime diagram doesn't represent Minkowski space and has nothing to do with relativity, or the universe as we know it.

Do you understand that you can draw another spacetime diagram that represents the coordinates used by the observer whose world line is BE, and that in that diagram the line AD has a negative slope. In that frame AD is moving!

I also think you should make up your mind. There are no "absolute" coordinate systems in SR. In a previous post you said that you have no objections to relativity. Then why are you contradicting it?

4Newton said:
The exercise of simultaneous actions is to show proof as you have stated to validate the absolute Minkowski space-time drawing. In the simultaneous exercise equal distance is just that. Equal distance in all directions to form a sphere from a center point.
There are a few things you should realize:

1. In your spacetime diagram (with one spatial dimension), the "sphere" is just the two points (0,-a) and (0,a).
2. The events on this "sphere" are simultaneous by definition (in this frame), so it makes no sense at all to try to prove that they are simultaneous.
3. You're doing all of this from one observer's point of view, and that means that if you're able to prove a statement such as "these events are simultaneous" you have only proved that it's true in that observer's frame.

4Newton said:
I start with an undisputed simultaneous action, two flashing lights at the same point in space, I then move them apart with the observer at the center still having verification the two lights are simultaneous. I then state the obvious, that the change of the observers position changes his view of the lights flashing simultaneously but obviously his change of position does not change the action of the flashing lights.
This is correct (but pointless).

4Newton said:
I have thus separated the reality of observation from the reality of action. This is something SR failed to do.
You haven't separated anything that wasn't separated already.

That second sentence is so wrong I don't even know where to begin.

4Newton said:
It is also obvious that the flashing lights may be moved in any direction of any equal distance, line, circle or spherical, with the same results. This may then be done a second time. You now have an infinite number of simultaneous spheres intersecting another set of infinite number of simultaneous spheres resulting in the conclusion that all action is simultaneous through out all points of the universe.
So? You're just saying that (0,-a) and (0,a) are simultaneous regardless of what a is. This is nothing new.

If you're going to prove something, you can't begin with the assumption that what you're trying to prove is true, and than use that in your proof. No logical fallacy can be worse than that.

4Newton said:
...again this is absolute space-time with inertial frames moving on BE or ED like lines.
It seems pointless to continue this discussion unless you first do this excercise:

The observer whose world line is AE (extended to infinity in both directions) shoots a laser beam in the positive x direction at time -t (according to his own clock). It is reflected off a mirror that is perpendicular to the laser beam. At time t (according to the same clock) the reflected laser beam has returned, and hits the laser. Your task is to draw the path of the laser beam in your spacetime diagram. At what point in the spacetime diagram is the beam reflected? Can you figure out what time the AE observer's clock is displaying when the reflection event happens?
 
  • #49
Garth said:
John S. Bell argued that quantum theory and GR could be integrated into QG if a Lorentzian view of relativity was taken. i.e. 3+1D rather than 4D space-time. This required some form of preferred frame, 'absolute' might be too absolute a term for it! (Speakable and unspeakable in quantum mechanics)
Isham and Butterfield reasoned the same, or similar, argument, calling for a ‘preferred foliation of space-time. (2001, Physics meets Philosophy at the Planck Scale, ed. by C. Callender and N. Huggett. Cambridge University Press.)

Unfortunately, I just don't see any evidence for a preferred foiliation of space-time.

Most of the serious attempts I see to justify this preferred foiiliation involve long-range scalar fields of one form or other.

This seems to be more or less a requirement - electromagnetism has been very well studied and it's just not a good candidate for a preferred frame. In fact, Maxwell's equations are what led directly to relativity, once they were taken seriously enough. I.e. after the Michelson Morley experiments was performed it was realized that the conflict between Maxwell's equations and Newton's mechanics should be resolved in favor of Maxwell's equations. Later evidence has shown this to be undoubtedly the correct choice.

The weak force has already been unified mathematically with electromagnetism. (I suppose one might be able to break the theoretical unification with expirimental evidence, but no such evidence has come up.) The strong force might be a very distant possibility for creating some preferred frame, but I've never, ever seen any serious proposal that points to the strong force as the source of a "preferred frame".

This winds up with the need for a new, previously undiscovered force to create the preferred frame. But there are some fairly strict limits on the existence of the direct formes of such fields, ones that interact directly with matter.

Theories in which the new undiscovered field interacts only indirectly with matter are trickier. These theories usually can be described by their PPN predictions about gravity. To date, relativity has always been correct - only time will tell as we continue to test it further whether or not its predictions continue to be correct.
 
  • #50
Garth - good post. Pervect. I don't see the difficulty in conceptualizing - or for that matter, actualizing, preferred frames. Every frame where light exhibits one-way isotrophy can be considered an "at rest frame" -INDEPENDENT OF EINSTEIN'S SECOND POSTULATE). All such frames would also be CBR isotrophic. The test for SR or any questions with regard thereto, would be the measurement of one-way light paths in a frame that moves relative thereo (again we pretend that we have never heard of the second commandment (or excuse me "postulate") and proceed to conduct tests in this second frame which is in uniform motion wrt the first. We don't do this when we run tests in the Earth laboratory - we measure dilation wrt to Earth clocks in GPS and with high speed decaying particles, and with clocks flown in airplanes, but we do not test to see if the situation is truly reciprocal, and we have not made accurate enough tests in free space to determine whether the one way velocity of light is truly isotropic.

Note again, that while MLET (Modified Lorentz Ether Theory) gets the same answers as SR and by its nature resolves the Twin Paradox, it creates other issues that cannot be easily answered. But there are other transforms that rely upon the isotrophy of round trip light paths, rather than Einsteins second postulate, to arrive at the same results - and these theories are not encumbered by the physical affects that must occur to explain MLET
 
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