Is age relative?

[ramollari]

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.

[MiGUi]

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 lenght depending on the speed.

[geometer]

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.

[ramollari]

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.

[geometer]

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.

[4newton]

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.

[Twistedseer]

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 travelling 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

[geometer]

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.

[4newton]

Twistedseer:OK if your observer is at rest, in relation to the light sources one in front of him/her and one behind, but travelling 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.

[geometer]

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.

[4newton]

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.

[yogi]

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.

[yogi]

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?

[Fredrik]

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 (http://www.physicsforums.com/showthread.php?t=47487) 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:

[4newton]

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.

[yogi]

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.

[Fredrik]

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".


...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.

[yogi]

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 dont 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.

[pervect]

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 dont 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.


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 (http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html)

A reference to the entire sci.physics Twin Paradox FAQ

Twin Paradox FAQ (http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html)


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


- 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 occuring 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.

[4newton]

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.

[pervect]

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.

[russ_watters]

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."

[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).

[yogi]

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????????????

[yogi]

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?

[russ_watters]

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.

[4newton]

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.

------------

[pervect]

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.

[Fredrik]

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.

[russ_watters]

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!

[4newton]

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.

[Fredrik]

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.


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.


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).


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).

[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.

[pervect]

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.

[4newton]

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.

[yogi]

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 earths 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.

[Fredrik]

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.


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.


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).


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).


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".

[russ_watters]

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?

[russ_watters]

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 earths 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.

[4newton]

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.

[Fredrik]

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).



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.


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.


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.


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).


...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.

[4newton]

"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.

[Fredrik]

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.


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).


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?


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.

[yogi]

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.

[4newton]

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.

[pervect]

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 infinte 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.

[Garth]

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

[Fredrik]

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).


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).


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.


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).


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).


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".


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".


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?


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.


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).


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.


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.


...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?

[pervect]

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.

[yogi]

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

[Garth]

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 .
Exactly - you are describing the theory of Self Creation Cosmology. (plenty of posts on that in these Forums) A Brans Dicke type scalar field endows particles with inertial mass and interacts with the matter field.

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.
The Equivalence Principle is violated in SCC - but in Eotvos type tests only to about one part in 10^-17 about three orders of magnitude less than present experimental sensitivity. However the scalar field exerts a force on all particles, equally to within this variability (10^-17), but not on photons which "fall" ar a rate 3/2 the Newtonian acceleration of gravity, this is testable but it has not been done to date.

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.
In all previous tests SCC predicts the same outcomes as GR. However we await the results of Gravity Probe B - the first experiment able to distinguish between them.

Garth

[4newton]

Fredrik:
I am preparing a set of drawings and the total concept in one document; it will include your last request, which I interpret to be a drawing of the path of light between inertial frames in my drawing . I think having more detailed and labeled drawings will make it easier to understand. I will try to include answers to all your other comments at one time.

[Fredrik]

Excellent. I should probably tell you that I won't be able to visit this site tomorrow, so if you post it tomorrow you'll have to wait at least a day for a reply.

[4newton]

Fredrik and all:

Here is a drawing that will illustrate space-time from an absolute viewpoint. Because as shown before there is a disagreement of terms used. I will use terms that are defined by the drawing. No other meaning or connotation is intended.

The drawing is a Minkowski space-time illustration.

Line AG and line HI are the lines of spatial rest frames. Spatial rest frames have transitions only in the time dimension. All vertical lines in the drawing are spatial rest frames.

Line AF shows the slope of the speed of light.

The spatial distance separates AG and HI AH. A light pulse is sent from B in frame AG to point E in frame HI and reflected back to D. This is the normal path of light that is being reflected back to the starting point. It is seen that the path of light is of equal length in both directions.

With the requirement that the speed of light is constant AF, the path of light is drawn between frames JL and MO. Both frames JL and MO are moving with a constant velocity indicated by the slope of JL and MO, in this case equal to one-half the speed of light. The distance AH = JM.. The path of light is JKL. It is seen that the distance the light must travel is longer going from J to K then the path of light in the case of B to E.. However the distance from K to L is shorter than the light path from E to D.. The total time over the entire path is Q-D longer than B to D

The difference between BED and JKL is as stated in Special Relativity where ( v ) is the slope JL and ( c ) is the slope AF.

The two paths of light in the MM experiment are represented by paths JKL and BPQ with JKL being in the direction of travel and BPQ perpendicular to the direction of travel. Note the total time of travel is the same for both paths. Both one way times however changes with velocity.

I hope from this you can see that Minkowski space-time is absolute and that this is in total agreement with SR.

[Garth]

The drawing is a Minkowski space-time illustration.
I'm afraid not 4newton! In your diagram you have drawn a Euclidean space not a Minkowski space. The sheet of paper that you used to draw the diagram is Euclidean and there is only so much that you can do with it to illustrate Lorentz transformations, well very little actually. You have to be very careful.

Basically a moving inertail frame of reference is not on a world-line that is simply a rotation of the observer's axes; otherwise Lorentz transformations would be cyclical, go fast enough (rotation by 2pi) and you would stand still!

Instead in a true Minkowski diagram a moving particle's world line asymtotically approaches the pi/4 AF dotted line.
I hope from this you can see that Minkowski space-time is absolute and that this is in total agreement with SR.
Nice try but no! - In a true Minkowski diagram moving inertial observers are equivalent, there are no preferred frames of reference.

Garth

[4newton]

Garth:
I would be very interested in seeing your Minkowski diagram a moving particle's world line asymptotically approaches the pi/4 AF dotted line.

[Garth]

I do not have the means to send you a diagram.

However: Take your diagram, move J to A so the two systems have the same origin.

Now as J is moving relative to A his space and time axes have to be inclined at an angle to A's: J’s space axis is inclined upwards w.r.t. A’s.

On a Euclidean space diagram the space and the time axes are simply rotated, however on a Minkowski space diagram, on your diagram, J's space axis turns anti-clockwise and his time axis turns clockwise. From A's point of view J’s axes are no longer orthogonal but turned inwards.

However J's point of view is that it his own axes that are orthogonal, and it is A's axes that are 'turned inwards'.

As the axes of a 'moving' observer, as seen by a 'stationary' observer, turn inwards they asymptotically approach the light null world-line at pi/4 as the relative velocity approaches c.

The geometry of the light path reflected off your co-moving mirrors is the same in both frames of reference; they are equivalent.

I hope this helps, try drawing it again.
Garth

[4newton]

Garth:
As you rotate your axis of the moving frame what is your relationship to the speed of light line AF? Are you saying that you think the speed of light line also rotates?

[Fredrik]

You're still missing the point 4newton. Most of what you said in #54 is correct, but it has very little to do with relativity. The only events in your diagram where relativity is relevant is K and N, where light is reflected off a moving mirror without losing speed (like a tennis ball would). There is absolutely nothing in your diagram that gives any indication about what events are simultaneous to a moving observer.

Look at the drawing I attached. (It's ugly because I did it in Paint). The line marked t' is the world line of an observer who is moving to the right. (The line marked t is the world line of an observer that you would describe as stationary). The thin lines that change direction when they reach the line marked x' are light rays that the moving observer emits to the right at times -t3, -t2 and -t1. Mirrors have been placed at locations in space chosen so that the reflected light will return to the moving observer at times t1, t2 and t3. The moving observer would of course disagree with the time coordinates and say that the rays were emitted at times -t3', -t2' and -t1' but what's important is that he would agree that the times from emission to event O (the origin) is the same as the times from event O to detection (at times t1', t2' and t3').

Think about what this means. If light is emitted at time -t1' and is reflected at some unknown time and returns at time t1, then the "unknown" time of reflection must be t'=0. The reflection event has the same time coordinate as event O, and is therefore simultaneous with it.

This means that the entire line marked x' is a set of events that are simultaneous to the moving observer. Actually, any line that is parallell to x' is a simultaneity line for the moving observer.

This is not so strange as it might seem. If you have already accepted that the speed of light is the same to everyone, you shouldn't be surprised to see that the slice of spacetime that the moving observer calls "space" (the x' axis) is the one that puts the world line of a light ray exactly half-way between the x' axis and the t' axis.

Do you still think horizontal lines are events that are simultaneous to any observer?

[4newton]

I have studied you drawing and I have great difficulty understanding the concept you are trying to show. Your speed of light line I assume is the 45-degree line. Which also corresponds to your other light lines and of course the lines that are perpendicular to your light lines are also speed of light lines in the opposite directions. I can also understand your line t’ if you intend it to be a world line of a moving frame. All this is the same as my drawings. I do not understand what you line x’ is intended to be. If it is a world line it is to the right of the speed of light line and therefore anything moving on that line would be moving faster than the speed of light. I am certain this is not what you intend to say. It would help if you could relate how you drawing has anything to do with observation or reality.

In my drawing lines JL and MO are the same as AG and HI only they are rotated according to relativity. A light source moving on line JL sends out a pulse along the speed of light path JK and is reflected by a mirror at K and back to the light source that would than be at L. This is the same as the light path BED.

If you use this method to make a clock and the distance between the source and the mirror and back to the source in BDE is equal to the distance that light travels in one second 300 km. Then the light in the BED would take 1 second to return to the source.

Like wise you will notice that the distance between J and M is also equal to 300 km but this frame is moving in space, in this case one-half the speed of light. The total path of the light JKL is longer then the path BDE even though the distance between the source and the mirror is the same in both cases. The light arrives back at the source in JKL at a later time compared to BDE. The time difference varies asymptotically as the speed of the moving frame approaches the speed of light line.

This is relativity.

The line MNO is to show that the same is true no matter which direction the light travels.

I think it would help if you and Garth would go back and read Einstein’s paper.

It is essential to have time defined by means of stationary clocks in the stationary system, and the time now defined being appropriate to the stationary system we call it “the time of the stationary system.”

Translated by W. Perrett and G. B. Jeffery.

I covered simultaneity in previous post please review them and let me know what you don’t understand.

---

[Fredrik]

I have studied you drawing and I have great difficulty understanding the concept you are trying to show.

OK. I'll try to explain it.


Your speed of light line I assume is the 45-degree line. Which also corresponds to your other light lines and of course the lines that are perpendicular to your light lines are also speed of light lines in the opposite directions.

That's exactly right.


I can also understand your line t’ if you intend it to be a world line of a moving frame. All this is the same as my drawings.

Also correct. I would say that t' is the world line of an observer moving at constant velocity. (I'm not saying it's wrong to call it the world line of a moving frame, only that I prefer to call it what I called it).


I do not understand what you line x’ is intended to be. If it is a world line it is to the right of the speed of light line and therefore anything moving on that line would be moving faster than the speed of light. I am certain this is not what you intend to say. It would help if you could relate how you drawing has anything to do with observation or reality.

This is the most important part of what I'm trying to say, so you shouldn't give up until you understand it. The line marked x' is obviously not the world line of an observer. As I said in my previous post, that line is a set of events that are simultaneous to the observer whose world line is the line marked t'. (All events on the line marked x' are simultaneous with the event O).

I also explained why we can be sure that those events are simultaneous in the moving observer's frame. If there is any particular part of that explanation that you think is difficult to understand, you should ask about that specific detail.

It's really hard to tell what you understand and what you don't understand. You seem to understand that the points in a spacetime diagram represent events, i.e. a location in space and time. To find the x coordinate of an event, just draw a vertical line through the event and see where that line intersects the x axis. To find the t coordinate of an event, just draw a horizontal line through the event and see where that line intersects the t axis. However, you don't seem to understand (or even care) how to find the coordinates that another observer would use. This is not something that can be ignored.

Any event that has coordinates (t,x) in a spactime diagram will have have different coordinates (t',x') in the frame of an observer who's moving relative to the "spatial origin" (the point in space that's represented by the t axis in the diagram). It is easy to find the set of events that have x'=0. This is just the world line of the observer. This is the line I marked t' in my drawing. It is more difficult to find the set of events that have t'=0 (i.e. the x' axis), but the trick I used is sufficient to find them. Since we know that the speed of light is the same to all observers, we know that if the moving observer emits light to the right when his clock displays 4:59:48, and that the light is reflected by a mirror and returns to the observer when his clock displays 5:00:02, the reflection must have happened when the clock was at 5:00:00.

It is obvious from the diagram that the reflection must happen on the line marked x'. This means that this line is the x' axis, i.e. the line where t'=0. This line consists of all events that are simultaneous with the event at the origin of the diagram. This line is what the moving observer would call "space, at time t'=0".


In my drawing lines JL and MO are the same as AG and HI only they are rotated according to relativity.

You don't seem to realize that this rotation is exactly the same in non-relativistic theory. This part of what you're saying has nothing to do with relativity.

It seems pointless to comment your diagrams any further until you've understood what I'm saying about simultaneity.


I think it would help if you and Garth would go back and read Einstein’s paper.

You really have to stop assuming that you are right and everyone else is wrong. Garth, pervect and I understand special relativty. You don't. Not yet anyway, but you can learn if you listen.


I covered simultaneity in previous post please review them and let me know what you don’t understand.

I already have. It's often hard to tell if what you're saying is wrong or "not even wrong" because you sometimes don't make sense. The biggest problem is that you're implicitly assuming that what you're trying to prove is true, which is the worst mistake you could possibly make.

What would you say if I made a diagram that consists of one vertical line, and one horizontal line, that represent two spatial dimensions, and said that this diagram proves that the concepts of left and right are absolute? Would you accept that as proof? Of course not. Your proof is flawed in exactly the same way as this one that I just made up.

[4newton]

I think I see what your drawing is saying. You are talking about light synchronization of clocks. As shown in:
http://homepage.sunrise.ch/homepage/schatzer/space-time.html

The only problem you have is that you can have more than one light synchronized clock in the same moving frame. The many different possible clocks will not agree with each other.

If you look at my drawing GST-02 you will see that in an absolute spatial rest frame light will transition in all directions that are equal distance from the source in the same amount of time X0 to X1 or X1 back to X0 take the same amount of time. T1-T0 = T2-T1. If the light starts at X0 at 3:58 and arrives back at 4:02 then the clock is at the reflection point is 4:00.

In a moving frame X’0 the light does not transition the same path in all directions that are equal distance to the source. The time to the reflection point will be the fastest perpendicular to the direction of travel and the time to the reflection point will be the longest in the direction of travel as shown in GST-02.

The difference between a spatial rest frame X0 and a frame moving at one half the speed of light X’0 is shown in the drawing GST-02. A light path, X’0 to T’3, that is perpendicular to the direction of travel is 1.2 times longer then the path from X0 to T1. A light path that is in the direction of travel X’0 to X’1 is 1.7 times longer.

The question is; what if any is the real time.You really have to stop assuming that you are right and everyone else is wrong. Garth, pervect and I understand special relativty. You don't. Not yet anyway, but you can learn if you listen.I think you should consider that this cuts both ways. The laws of physics are not elected by popular vote.I already have. It's often hard to tell if what you're saying is wrong or "not even wrong" because you sometimes don't make sense. The biggest problem is that you're implicitly assuming that what you're trying to prove is true, which is the worst mistake you could possibly make.I don’t think you are trying to understand what I am saying. You have never questioned any particular point that you say does not make sense.

I am not trying to prove anything. I am simply trying to resolve contradictions and suppose paradoxes in theories of the universe.

You make the assumption that your understanding of the theories is absolutely correct in spite of the contradictions and paradoxes. Your solutions are that we just need to accept concepts that make no sense. How do you resolve the fact that clocks do not agree and yet you say that clocks tell real time? You assume that clock time is absolute and that all of nature must bend to match that concept.

I only look to see if there is a more global understanding of space-time that does not conflict with observation. I have posted a viewpoint based on accepted theory that resolves some of the conflicts. There is no circular logic here. The entire posting here is based on the accepted theory that the speed of light is an absolute constant and as a result the relationship of space and time is also absolute.What would you say if I made a diagram that consists of one vertical line, and one horizontal line, that represent two spatial dimensions, and said that this diagram proves that the concepts of left and right are absolute? Would you accept that as proof? Of course not. Your proof is flawed in exactly the same way as this one that I just made up.Not so, the difference is that even you accept that the speed of light is and absolute. And if you drew a line in your example above and said it is an absolute then you would be totally lacking if you could not show an absolute relation between the vertical and horizontal lines. You seem to be blind to seeing anything as absolute. Relativity does not mean that there are no absolute relationships.

[Fredrik]

The only problem you have is that you can have more than one light synchronized clock in the same moving frame. The many different possible clocks will not agree with each other.

What do you mean by "in the same moving frame"? That doesn't make any sense. Do you mean that there are events that are not in the moving frame? In that case, what do you mean by "frame"?


You make the assumption that your understanding of the theories is absolutely correct in spite of the contradictions and paradoxes.

There are no contradictions or paradoxes in SR.

Have you ever thought about what it would mean if there were? SR is just the mathematical theory of Minkowski space. If SR is logically inconsistent, then the definition of Minkowski space must be too. But Minkowski space is just \mathbb R^4 with a funny metric. The metric is just a function and couldn't possibly introduce any logical inconstencies into the theory. So if Minkowski space is inconsistent, the inconsistencies must come from the real numbers. But real numbers can be constructed from the rationals (as Dedekind cuts, or as equivalence classes of Cauchy sequences), and the rationals can be constructed from the integers. This means that if SR is inconsistent, the integers are too.


Your solutions are that we just need to accept concepts that make no sense. How do you resolve the fact that clocks do not agree and yet you say that clocks tell real time? You assume that clock time is absolute and that all of nature must bend to match that concept.

But the concepts do make sense. The theory doesn't have to be wrong just because you don't understand it.


There is no circular logic here. The entire posting here is based on the accepted theory that the speed of light is an absolute constant and as a result the relationship of space and time is also absolute.

What absolute relationship are you talking about? Would it be e.g. that the world lines of light are exactly half-way between the time axis and the space axis? Then why aren't they in your diagrams? The world line of a moving observer is his time axis. Yet you insist that space in a moving observer's frame is a horizontal line in your "absolute" diagram. If that's the case, then the world line of a light ray is closer to the time axis than to the space axis, so the speed of light in that frame can't be the same as in the "absolute" frame.


If you look at my drawing GST-02...

Let's look at your drawing... The fifth diagram is the one that interests me. I'm sure you agree that x'=0 along the upper line. On what line would you say that t'=0?

[4newton]

What do you mean by "in the same moving frame"? That doesn't make any sense. Do you mean that there are events that are not in the moving frame? In that case, what do you mean by frame"
http://plato.stanford.edu/entries/spacetime-iframes/A “frame of reference” is a standard relative to which motion and rest may be measured; any set of points or objects that are at rest relative to one another enables us, in principle, to describe the relative motions of bodies. A frame of reference is therefore a purely kinematical device, for the geometrical description of motion without regard to the masses or forces involved. A dynamical account of motion leads to the idea of an “inertial frame,” or a reference frame relative to which motions have distinguished dynamical properties. For that reason an inertial frame has to be understood as a spatial reference frame together with some means of measuring time, so that uniform motions can be distinguished from accelerated motions.The top right drawing fig. 1 (X0, X1, T0, T1, and T2) is a non-moving frame (frame with no spatial transition). I use the term moving and non-moving so it is not confused with non-inertial frames, (frames under acceleration).

The drawing fig. 4 (X’0, Z’1, T’3, and T’2) and fig. 5 (X’0, T’0, X’1, T’1, X’2 and T’2) are the lines of objects that are in the same inertial frame (moving in space at a transition equal to one half the speed of light). X’0 and T’2 are the same in both Fig. 4 and Fig. 5. Fig. 4 is the left view of Fig. 5 consistent with any engineering drawing.There are no contradictions or paradoxes in SR.

But the concepts do make sense. The theory doesn't have to be wrong just because you don't understand it. You have never heard of the Twin paradox? I have just given you an example of the speed of one way light clocks being different at the point of reflection in the same frame.

What absolute relationship are you talking about? Would it be e.g. that the world lines of light are exactly half-way between the time axis and the space axis? Then why aren't they in your diagrams? The world line of a moving observer is his time axis. Yet you insist that space in a moving observer's frame is a horizontal line in your "absolute" diagram. If that's the case, then the world line of a light ray is closer to the time axis than to the space axis, so the speed of light in that frame can't be the same as in the "absolute" frame.The speed of light is constant. The relationship of the speed of light to spatial distance is always the same. The relationship of the speed of light to time is always the same. What you do, how you move, or what you think can never change that relationship. All actions of the smallest possible function occur at the same time throughout the whole universe as demonstrated in previous posts. As also demonstrated in previous posts no actions change the Now. All perceived changes are the result of viewpoint and not any change of the above relationship.

You seem unable to overcome you preset thoughts and look at things from a different viewpoint. You keep trying to look at everything from the viewpoint of an observer in a frame. The math will work no matter your viewpoint because all things are related but you need to have a relational formula for every event.

If you can open your view to a more global one it is then possible to examine the nature of other types of time keeping instruments and much more that you have never thought of.Let's look at your drawing... The fifth diagram is the one that interests me. I'm sure you agree that x'=0 along the upper line. On what line would you say that t'=0?I am not sure what you are asking. Maybe the above reply answers you question.

[Fredrik]

The link to the page that talks about frames doesn't help. I know what a frame is. But I still don't know what you mean when you say things like "you can have more than one light synchronized clock in the same moving frame". That doesn't make sense. If a physical object like a clock is "in" one frame, than it's also in all the others.

A sentence like this one would make sense: "The object has a different shape in frame A than in frame B". But a sentence like this one makes no sense: "The object is in frame A".


The drawing fig. 4 (X’0, Z’1, T’3, and T’2) and fig. 5 (X’0, T’0, X’1, T’1, X’2 and T’2) are the lines of objects that are in the same inertial frame (moving in space at a transition equal to one half the speed of light).

Here it seems that you believe that "in the same inertial frame" means "moving with the same velocity", but that would be wrong. When people (other than you) say things like "the velocity of this object in frame A is v" they don't mean that the object is any more in frame A than in frame B. They are only specifying in what frame the velocity is what they say it is, which is absolutely necessary, since the velocity (but not the presence of the object) depends on the choice of frame.


You have never heard of the Twin paradox?

The "twin paradox" is not a paradox. When SR is used correctly the result is always that the astronaut twin is younger than his brother when he gets back. I have explained why in other posts in this forum. (You should try to understand what I'm trying to explain to you in this thread before you try to understand the twin "paradox").


X’0 and T’2 are the same in both Fig. 4 and Fig. 5. Fig. 4 is the left view of Fig. 5

"The left view"?! I can only guess what you mean, because you're not making sense here either. I'm guessing that you mean that to an observer who's moving to the left in figure 4 (not drawn), the lines in figure 4 would look like in figure 5. That's not correct. The line X'0---Z'1 should be rotated counterclockwise by the same amount that the line X'0---T'2 has been rotated clockwise. This is absolutely necessary to ensure that the speed of light is the same in both frames (i.e. to both observers).


The speed of light is constant.

Yes, it's certainly not accelerating. If you mean that it's the same to all different observers, I wonder why it isn't in your diagrams. (If it's c in figure 4, it's more than that in figure 5).


The relationship of the speed of light to spatial distance is always the same. The relationship of the speed of light to time is always the same.

This is "not even wrong". (It's not clear what it means).


As also demonstrated in previous posts no actions change the Now.

You haven't demonstrated anything.


All perceived changes are the result of viewpoint and not any change of the above relationship.

I agree with that (if I understand you correctly), but all you've done is to choose an arbitrary observer's viewpoint and refuse to consider what the world looks like to any other observer. How can you talk about different viewpoints when you refuse to even consider the viewpoints of the observers you call "moving".


You seem unable to overcome you preset thoughts and look at things from a different viewpoint.

That's not true. I'm just not going to abandon a logically consistent viewpoint, completely free from paradoxes and contradictions, for one that isn't.


I am not sure what you are asking. Maybe the above reply answers you question.

No, it didn't. The reason I'm asking is that this is the most important concept in all of relativity (the one you need to understand to understand all the "paradoxes") and you don't seem to understand it.

I will ask the question again, in a different way. This time I have interpreted your figure 5 as representing the viewpoint of an observer who's moving to the left with speed v in figure 4, as the events in figure 4 occur.

Let's call the observer whose world line is the left vertical line in figure 4 "A" and the observer who's moving to the left in figure 4 (world line not drawn) "B". Suppose that observer A chooses to use the event at the lower left corner of figure 4 (where the vertical and the horizontal lines meet) as the origin of both space and time coordinates. Also suppose that B uses coordinates such that he is at x=0 all the time, and has t=0 when he passes the vertical line (in figure 4) that is the origin of spatial coordinates to A.

I would like to know which of these statements about figure 5 that you agree with, and which you disagree with.

1. The world line of observer B is a vertical line touching (T'0,X'0).
2. The world line of observer A is the line from (T'0,X'0) to (T'2,X'2).
3. Observer B's time axis (events with spatial coordinate 0 in frame B) is a vertical line touching (T'0,X'0).
4. Observer A's time axis (events with spatial coordinate 0 in frame A) is the line from (T'0,X'0) to (T'2,X'2), i.e. a line through (T'0,X'0) with slope 1/v.
5. Observer B's spatial axis (events with time coordinate 0 in frame B) is the horizontal line drawn in the figure.
6. Observer A's spatial axis (events with time coordinate 0 in frame A) is a line through (T'0,X'0) with slope v.

[Frigga]

The twin paradox...
Here is a real life and local example.
If you were to send your twin to Mercury for 1 Earth year, once the twin returns there would be a difference of roughly 1-3 minutes in difference in age. This may seem very small in electronic time but when you're talking larger distances it adds up rapidly and exponentially. This happens due to the speed of Mercury's orbit around the Sun and the gravitational interaction.

Age is relative...could you imagine living on Mercury(if it were possible), your life would be very very much shorter.

[4newton]

Fredrik:
You seem to have a lot of problems understanding some very simple ideas. I did not know that you did not know how to read engineering drawings or what front left and right views were. I now present to you a 3D view maybe this will help. See drawing GST-06.

Fig. 1 is a simple stationary spatial ring. Around the ring is a reflecting surface. A light source at A sends a pulse of light out in all directions. The light pulse strikes the ring at time t1 and is reflected back to the source. All the reflections B, C, D… arrive back at the source E.

You will note that it takes the same the same amount of time for the light to travel from the source A , t0 to the ring, at t1 as it does for the light to travel from the ring at t1 back to the source at E, t2 and that the time of travel is the same in all directions.

You can also see that the reflection is midpoint from the start of the pulse at A to the return when the source is at E.

In Fig. 2 you see the same ring as above moving in a spatial direction to the right, right is the direction of tilt. You can now see that the light pulse sent out from the source when the source is at G is not reflected until J at time t4 in the direction of travel. However the light pulse in the direction perpendicular to the direction of travel is reflected at H at time t3. The time for the light to reach the reflection of the ring varies with the longest time in the direction of travel and the shortest opposite the direction of travel. The total round trip path of the light will always be the same in all directions.

The round trip time for the light pulse will vary dependent on the velocity of the ring and approach infinity as the slope of the line, representing velocity of the ring approaches the slope of the line that is the speed of light.

The round trip time for the light pulse will be minimum when the velocity of the ring is zero. As in Fig. 1.

All physical laws remain the same in a moving frame. Or what ever you want to call it, because transition causes corresponding physical changes that compensate. A mechanical clock will slow down because all mechanical clocks are dependent on mass of their elements to keep time. It is well established that mass increases with velocity. This increase in mass and the resulting slow down of the clock is in agreement with the round trip time of light in the same frame.

All other functions behave in the same manner.

[4newton]

Frigga:
Fredrik seems to agree that this takes place but he does not think it is a paradox. Everyone else realizes that if SR say that all physical laws are the same in all inertial frames and that your clock is based on physical laws. Then clocks after some time in one inertial frame disagree with clocks in another inertial frame contradict the first statement. To be nice we call that a paradox. SR is right in most cases just as Newton’s laws were right. It is these small “paradoxes” that should lead us to find a more true understanding of the universe. This is just as Einstein did with Newton.

All theories are open to expansion.

[Garth]

In the absence of gravitational fields, i.e. curvature, SR is the appropriate theory. (So Mercury was not a good example).

The paradoxes of time, such as the Twin Paradox, are resolved by the understanding that simultaneity is also relative.

There is no paradox in the understanding that a clock in one inertial frame is observed to 'tick' at a different rate to a clock in another mutually moving inertial frame.

Things get interesting when curvature is introduced.

Garth

[Fredrik]

You keep ignoring the things that prove you wrong. I will make one last attempt to explain this to you 4Newton, but if you keep ignoring what's important I will not waste any more time on you.

Look at this (http://w1.873.comhem.se/~u87325397/4Newton.jpg). It's just the drawing you did, with a few comments. Is there anything in it that you disagree with?

(In the drawing, I'm using primes to distiguish between the coordinates used by observer A and observer B. A is using the unprimed coordinates. B is using the primed coordinates).

Do you understand that different observers will have different opinions about what the time axis is, and that this implies that they also must have different opinions about what "slice" of spacetime they should call space?

If you put the line where t'=0 and y'=0 at any other place than where I have drawn it, A and B wouldn't agree about what the speed of light is.

[4newton]

Fredrik:
Now we are on the same page. I have no problem with you drawing.

The point is that the one way time to reflection is different in different directions. This is a difference within the same frame. You will need to contort space a great deal to make the times come out equal.

You have two choices. You can keep the idea that clocks are absolute and modify the rest of nature to maintain consistencies or you can accept the fact that there is a more basic nature of time and that other functions of nature do not change except with applied action.

The concept I have given you simplifies the idea of space and time and has no paradoxes. It also allows you to proceed with understanding the larger universe, force, energy…

If you maintain the first choice you will have a hard time understanding anything more, as is the current problem in physics today.

[Fredrik]

Now we are on the same page. I have no problem with you drawing.

Are you absolutely sure that you agree with this drawing? I'm very surprised by your answer, because this is just what I've been saying all along, and you've had objections every time. (All of them were either wrong or irrelevant, and usually made no sense).

For example, you have previously said that what I'm saying is wrong because you can have more than one light synchronized clock in the same moving frame and they wouldn't agree with each other. (I can't tell if this one is wrong or irrelevant, because it doesn't make sense to me).

Why have you changed your mind? Are you sure you understand what I'm saying? One of the things I'm saying is that "space" is not the same set of events to different observers.

Haven't you been saying the exact opposite the whole time?

[russ_watters]

Frigga:
Fredrik seems to agree that this takes place but he does not think it is a paradox. Everyone else realizes that if SR say that all physical laws are the same in all inertial frames and that your clock is based on physical laws. Then clocks after some time in one inertial frame disagree with clocks in another inertial frame contradict the first statement. To be nice we call that a paradox. SR is right in most cases just as Newton’s laws were right. It is these small “paradoxes” that should lead us to find a more true understanding of the universe. This is just as Einstein did with Newton. As others have said and you refuse to accept, the paradoxes are not paradoxes in SR, they are paradoxes in Newtonian physics. SR is what allows us to resolve the paradox. It should be perfectly obvious that if there is a paradox in a theory, the theory doesn't work and needs to be fixed.

And the part that you are calling the paradox is, in fact, the resolution to the paradox. The paradox is in the ages of the twins, not the way the theory reads.

[4newton]

Fredrik:
Either I or you or both of us have not been able to understand each other. I have another drawing to bring our current understanding together. I did not understand that you where talking about a y space line. You had that line labeled as x’.

I have now included your y-space line at the angle you show. All distances are in comparison to Fig. 1.
Line GJ is the time-distance for light to reach the ring in the forward x direction with the frame moving in the x direction. Line GH is the time-distance for the light to reach the ring in the y direction within the same frame.

The time it take the light to reach H is (t3)=(t5)/2 and in this frame moving at one half the speed of light. It is 1.2 times longer than the time in Fig. 1 AB or t1. The time it takes the light to reach J is 1.7 times longer than t1.

Clocks synchronized at G and moved to the ring before the frame is in transition may test this. All clocks being in the same frame will agree on the time. After the light reaches the ring and the clocks are stopped then the clocks can be brought together and the above times will be verified.

How does SR resolve this difference?

[4newton]

russ_watters:
I don’t have a disagreement with SR. I agree that SR can define time as clock time for all observers. It still is true that if you go through the two clocks experiment they will not agree. The question is, are the drawings I have presented representing reality including SR. If you think they do not please let me know where they differ.

If we can agree on the representation of reality then we can proceed to the next step.

[Fredrik]

I have another drawing to bring our current understanding together.

Let's not bring any more drawings into this. We should focus on the details of the one we've been discussing recently. (There's also no need to draw the y direction).


I did not understand that you where talking about a y space line. You had that line labeled as x’.

What are you talking about?! I stated very clearly that the lower green line (which is the same line that I labeled x' in another drawing) is in the t-x plane, which is perpendicular to the y axis.

The horizontal black line is the x axis. That's where the t and y coordinates are zero. (Remember that the unprimed coordinates are used by observer A). It is also the direction that observer A (if he's facing the y direction) would call "right".

The lower green line is the x' axis. That's where the t' and y' coordinates are zero. (Remember that the primed coordinates are used by observer B). It is also the direction that observer B (if he's facing the y direction) would call "right".

Note that the x and x' axes do not coincide. At event G (the origin), both observers are at the same point in space, facing the same direction (we assume, as part of the definition of the observers A and B), but an event (like a phone ringing) that's on B's right in his "now", is in observer A's future. It hasn't happened yet to A. It will happen (on his right hand side) some time in the future.

If you are at all serious about learning relativity, there's something you should know: There is no way that you will ever understand relativity without understanding this. This fact (that the x and x' axes do not coincide) is the most important fact in all of SR.

I don't know how you could misunderstand my drawing like that. I hope you will understand it now. Perhaps you had problems because you've forgotten one basic fact from geometry: If two lines intersect, there's exactly one plane that contains them both.

Do you understand this now? Do you agree that the x' axis must be where I've drawn it, or would you put it somewhere else?

[Fredrik]

We were talking about paradoxes earlier. A lot of people seem to have misunderstood what a paradox is, so I will try to explain it.

A paradox in a physical theory is a prediction about the outcome of an experiment that disagrees with another prediction made by the same theory. A theory that contains a paradox is logically inconsistent, and would be thrown out with the garbage. There are no paradoxes in SR. (If there were, we would probably have to throw out all of mathematics).

The "twin paradox" might seem to be a paradox of SR, but it isn't. A correct application of the theory will always yield the result that the astronaut twin is younger when he gets back. People who don't understand the theory very well might come to a different conclusion, but that's only because they are making mistakes.

[4newton]

Fredrik,
If you insist on only looking at the observer clock being absolute then you must change the shape of space as you have done. This of course is not correct except in the view of the moving observer. Space for all other observers has not changed. If you look at
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/
You can see my space-time drawing in motion. As you can see this is not only just my idea of space-time. This is not basically anything new in presenting space-time and is well supported.

I think we have wasted enough time on points of view. If you can not find anything wrong, except the point of view, in my drawing representing observation then I will go on to space-time and the Big Bang.

You have not commented on the one-way speed of light being reflected at different times by the ring. I assume you have no disagreement. You have not disagreed with the fact that you can have a spatial rest frame where there is no spatial transition. This is a point that russ_watters and I had a disagreement on. Russ do we now agree that there is a spatial rest frame?

I think the idea of simultaneous events will be much clear when considered with the Big Bang.

[Alkatran]

http://casa.colorado.edu/~ajsh/sr/paradox.html

Read the entire site. Then click "forward to Centre of the lightcone", continue reading and moving forward, or back if necessary, until you understand why we're right (according to experiment).

[Garth]

http://casa.colorado.edu/~ajsh/sr/paradox.html

Read the entire site. Then click "forward to Centre of the lightcone", continue reading and moving forward, or back if necessary, until you understand why we're right (according to experiment).
Great link, thanks.

Garth

[russ_watters]

You have not disagreed with the fact that you can have a spatial rest frame where there is no spatial transition. This is a point that russ_watters and I had a disagreement on. Russ do we now agree that there is a spatial rest frame? If by "spatial rest frame" you mean an absolute/universal reference frame from-which to measure all velocities, distances, and times, of course not!

[4newton]

These illustrations of course point up the fact that you have space with different dimensions in two different reference frames located at the same center point in space-time. In order to accept this you must discard the fact that static objects always have the same spatial difference between them regardless of your reference frame. The distance between the earth and the sun does not change just because you are in motion.

You must abandon the idea that clocks directly tell real time. You must think of a clock as just another variable in space-time. If time is another dimension as everyone seems to claim then you must follow the rules for dimensions.

[Garth]

These illustrations of course point up the fact that you have space with different dimensions in two different reference frames located at the same center point in space-time. In order to accept this you must discard the fact that static objects always have the same spatial difference between them regardless of your reference frame. The distance between the earth and the sun does not change just because you are in motion.

You must abandon the idea that clocks directly tell real time. You must think of a clock as just another variable in space-time. If time is another dimension as everyone seems to claim then you must follow the rules for dimensions.
"the same spatial distance" is in fact in SR the space-time interval, in time units this is the proper time, or the "real time" told by an inertial clock that is moving along the geodesic that joins the two events. This is invariant between "different frames". The space distance and the time interval between two events as measured in a particular frame do change "just because you are in motion", they do change when measured in different inertial frames in relative motion with each other.
You obviously haven't read the entire site Alkatran posted for us - it is standard SR, "read, mark, learn and inwardly digest".
Garth

[Fredrik]

If you insist on only looking at the observer clock being absolute then you must change the shape of space as you have done.

As usual it's not easy to understand how you misunderstood me this time. Are you saying that I'm treating the time on B's clock as more fundamental then A's clock? I would never do that.

I haven't changed the shape of space. Space is always a plane in 2+1 dimensional relativity. I'm just saying that different observers disagree about what plane that is. (Note that this is not a paradox).

I haven't changed space. I'm not saying that the x'-y plane is space in any objective way. The x-y plane is still "space" to A (but not to B).


You have not commented on the one-way speed of light being reflected at different times by the ring. I assume you have no disagreement.

You're just saying that if the mirror is far away it will take some time before the light reaches it. That's trivial and irrelevant.

I understand that you've been trying to say something else too, but I'm not sure what that is.


You have not disagreed with the fact that you can have a spatial rest frame where there is no spatial transition.

That sentence doesn't even make sense, but I'm guessing that you are trying to say that some objects can be stationary in some objective sense. That's not the case, so if that's what you mean, I disagree.


The distance between the earth and the sun does not change just because you are in motion.

If you change your velocity, that will obviously not change any objective facts about the earth and the sun, but spatial distance is not even something that can be defined in an objective way. If you measure the distance between the earth and the sun before and after you change your velocity you will get different results. This is because you're not measuring the same thing. You're measuring two different things and calling them both "distance".


You must abandon the idea that clocks directly tell real time. You must think of a clock as just another variable in space-time.

I have probably misunderstood this, because I actually agree with it. The problem is that you think there is a "real" time. (If there's a preferred rest frame, then a clock that is stationary in that frame defines a preferred time).

Edit: At first glance, it may seem that I disagree with Garth about "real" time, but I don't. He is of course right about proper time. Proper time is invariant so it makes sense to call it "real".

It would make sense to explain the relationship between proper time, coordinate time and clock time here, but I don't have the time (no pun intended) to do it now. Perhaps tomorrow.

[4newton]

russ_watters
If by "spatial rest frame" you mean an absolute/universal reference frame from-which to measure all velocities, distances, and times, of course not!

That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

However, don’t you consider the Big Bang as the reference point for our universe?

I have been reading some of your post and it is interesting that we think alike on many points. I feel that we are coming together on more and more ideas I hope we can reach more agreements. I place great value on your viewpoints.

[Alkatran]

russ_watters


That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

However, don’t you consider the Big Bang as the reference point for our universe?

I have been reading some of your post and it is interesting that we think alike on many points. I feel that we are coming together on more and more ideas I hope we can reach more agreements. I place great value on your viewpoints.

The big bang expanded a point to the current universe. The center isn't fixed... it's everywhere (this is what I've been told).

Or think about it this way: if two people are moving at different speeds, will they measure the center to be in the same place? :rolleyes: Chances are it doesn't matter what speed you're moving at the center stays fixed (just a guess!)

[russ_watters]

russ_watters

That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

However, don’t you consider the Big Bang as the reference point for our universe? Yet another misunderstanding you have of what a theory in physics says: the Big Bang theory says nothing of the sort. In fact, it says exactly the opposite. Wait, this isn't all an elaborate cover for Geocentrism, is it?

[Fredrik]

If by "spatial rest frame" you mean an absolute/universal reference frame from-which to measure all velocities, distances, and times, of course not!


That is not what I had in mind in my question. I was only thinking about transition in time without any spatial transition.

If there is such a thing as "transition in time without any spatial transition" in any absolute sense, it would imply the existence of the absolute frame that Russ is talking about.

[4newton]

041117-04
If there is such a thing as "transition in time without any spatial transition" in any absolute sense, it would imply the existence of the absolute frame that Russ is talking about.

The discovery of the Big Bang requires a change or at least extensions of relationships. It is true at this time that the Big Bang is the primary reference point. We know that it happen at some location in the unknown all. We also know that it took place about 15 billion years ago. If you had a clock at the time of the BB and looked at it today it would indicate 15 billion. This number is of course just for discussion.

This is where thing get interesting. Do all clocks that move out from the BB in all directions accumulate the same time, tick at the same rate? The answer must be yes. If this were not so, accumulated time and the rate of clocks would be different through out the universe. You could have places in the universe that transitions could take place in zero time. The whole universe would be chaos.

Observation of red shift tells us that the universe is uniform and consistent and that clocks that are not in spatial transition tick at the same rates everywhere in the universe. The same atoms produce the same spectral line everywhere.

From the BB all that is the universe is expanding outward in all directions. After the formation of mass objects the expansion of all objects continued in a line normal to the expanding surface.

Space is measured and spatial transitions take place between objects in the universe. From the standpoint that you are able to measure if you are moving to or away form objects then you may maintain a point with out spatial transition in our universe.

If the whole universe is in spatial transition then the only way you could tell is by measuring the one-way speed of light.

From the above you can see that it is impossible to tell the absolute position of the universe in “whatever” but you are able to reference all positions from the Big Bang and you are also able to tell change of spatial position between objects in the universe.

The BB theory is even less egocentric than SR or any other theory. It makes us realize that nature has done a lot to make us feel important in the past and now maybe we are ready to know we are very small but are still considered important for a grand purpose.

[Alkatran]

This is where thing get interesting. Do all clocks that move out from the BB in all directions accumulate the same time, tick at the same rate? The answer must be yes. If this were not so, accumulated time and the rate of clocks would be different through out the universe. You could have places in the universe that transitions could take place in zero time. The whole universe would be chaos.


15 billion years according to proper earth time I think.

It is NOT THE SAME AMOUNT everywhere!

Things move relative to each other, meaning they move faster/slower through time relative to each other, meaning they haven't measured to same time from the 'beginning'. (The moon is always moving relative to us, so it is moving slower through time according to us)

[russ_watters]

Two things:

-4newton, since the BB happened everywhere, you cannot use it as a reference point.

-Alkatran, its slightly more complicated than that: The expansion of space is not motion, so it doesn't cause time dilation. But there are, of course, other motions going on that do.

[Alkatran]

Two things:

-4newton, since the BB happened everywhere, you cannot use it as a reference point.

-Alkatran, its slightly more complicated than that: The expansion of space is not motion, so it doesn't cause time dilation. But there are, of course, other motions going on that do.

That's what I meant. I probably gave the wrong idea by saying "everywhere"

I figured the moon example would make it clear that I meant according to different observers.

[Fredrik]

The discovery of the Big Bang requires a change or at least extensions of relationships. It is true at this time that the Big Bang is the primary reference point.

A lot of things are different in a spacetime that has non-zero curvature and a big bang singularity. That's why I think it's a mistake to start talking about GR now. You don't even understand the basics of SR yet. You will not be able to understand stuff like simultaneity in GR unless until you have understood it in SR.


We know that it happen at some location in the unknown all.

No it didn't. The big bang theory says that the distance between any two points on any spacelike hypersurface goes to zero as the "time after the big bang" goes to zero. It doesn't say that there was a "bang" at some point in space.

[4newton]

Fredrik:
A lot of things are different in a space-time that has non-zero curvature and a big bang singularity. That's why I think it's a mistake to start talking about GR now. You don't even understand the basics of SR yet. You will not be able to understand stuff like simultaneity in GR unless until you have understood it in SR.Let me try to explain to you your position on SR.
If back in the Middle Ages I walked on to your farm and asked you about your world. You would tell me that the world is flat and that the sun goes around the earth. I would than try to explain to you that the earth is round like a ball and is spinning. I would also tell you that the earth is really going around the sun.

You of course would insist that I don’t know what I am talking about and that until I accepted the idea that the earth is flat and the sun goes around the earth I could not possibly understand the way the world works.

From your point of view on the farm you have every proof that you are right. If you can not change the mind set that there are other points of view that may be more valid then yours then you will never leave the farm.

The question is, if the view of space-time I have presented is wrong where does it disagree with observation or experiment? You have never addressed this main point. If SR and the space-time I have drawn both account for experiment and observation, which view point, should be accepted? Should we accept a view that requires conflict with logic or one that is logical on all counts?No it didn't. The big bang theory says that the distance between any two points on any spacelike hypersurface goes to zero as the "time after the big bang" goes to zero. It doesn't say that there was a "bang" at some point in space.Could you please describe or draw this concept. If you have trouble drawing you may find Open Office of help
http://www.openoffice.org/
The program is free and it does have a drawing function and a conversion to PFD files.

R. G.

[4newton]

Russ:
-4newton, since the BB happened everywhere, you cannot use it as a reference point.That is an interesting viewpoint. Of course the logical extension of that is that the universe is still everywhere so nothing has changed. I think it is quite logical to understand that a balloon that is not inflated occupies a different space than when inflated. You will need to explain why the universe before expansion can not be compared with the universe today.

Is space real? Is time real? Does the universe exist? If the answer to any of these questions is no then there is no reason for physics.

R.G.

[4newton]

Alkatran:
15 billion years according to proper earth time I think.

It is NOT THE SAME AMOUNT everywhere!

Things move relative to each other, meaning they move faster/slower through time relative to each other, meaning they haven't measured to same time from the 'beginning'. (The moon is always moving relative to us, so it is moving slower through time according to us).If the time is not the same everywhere what time is it right now on an object 10 billion light years away. Remember that what is taking place there right now will take 10 billion years to reach us.
R.G.

[Alkatran]

Alkatran:
If the time is not the same everywhere what time is it right now on an object 10 billion light years away. Remember that what is taking place there right now will take 10 billion years to reach us.
R.G.

I just told you that different observers will measure different times as having passed. How would I know the entire history of some random object 10 billion light years away? Chances are it hasn't observed the same passage of time as the stuff that made the sun.

[Alkatran]

Russ:
That is an interesting viewpoint. Of course the logical extension of that is that the universe is still everywhere so nothing has changed. I think it is quite logical to understand that a balloon that is not inflated occupies a different space than when inflated. You will need to explain why the universe before expansion can not be compared with the universe today.

Is space real? Is time real? Does the universe exist? If the answer to any of these questions is no then there is no reason for physics.

R.G.

Take a perfectly round sphere and show me the center of it's surface area.

That's why you can't necessarily pinpoint the center of our universe.

[Alkatran]

Fredrik:
Let me try to explain to you your position on SR.
If back in the Middle Ages I walked on to your farm and asked you about your world. You would tell me that the world is flat and that the sun goes around the earth. I would than try to explain to you that the earth is round like a ball and is spinning. I would also tell you that the earth is really going around the sun.

You of course would insist that I don’t know what I am talking about and that until I accepted the idea that the earth is flat and the sun goes around the earth I could not possibly understand the way the world works.

From your point of view on the farm you have every proof that you are right. If you can not change the mind set that there are other points of view that may be more valid then yours then you will never leave the farm.

The question is, if the view of space-time I have presented is wrong where does it disagree with observation or experiment? You have never addressed this main point. If SR and the space-time I have drawn both account for experiment and observation, which view point, should be accepted? Should we accept a view that requires conflict with logic or one that is logical on all counts?Could you please describe or draw this concept. If you have trouble drawing you may find Open Office of help
http://www.openoffice.org/
The program is free and it does have a drawing function and a conversion to PFD files.

R. G.

Relativity is tested everyday. If the farmer had done a scientific test, such as measuring how far the horizon was, he would realize the earth could not be flat.

What is the space time you have drawn?

[russ_watters]

If you like the flat-earth analogy and want to keep us on the flat-earth side, here's the comparison: We've led you by the hand to the edge of the world and you've looked over the edge at the nothingness below and still refuse to accept that the world is flat.

SR has, for the past 80 years, passe ever test thrown at it. It has never once been found to describe the universe on the macroscopic scale inaccurately. The problem here is that you quite simply either don't understand it or understand it but refuse to accept it. Either way, the resolution to all this is entirely up to you.

[4newton]

Russ:
If you like the flat-earth analogy and want to keep us on the flat-earth side, here's the comparison: We've led you by the hand to the edge of the world and you've looked over the edge at the nothingness below and still refuse to accept that the world is flat.I like your addition to my flat-earth analogy. You have told the same story that everyone was saying back in the Middle Ages. Just as it turned out then the earth was not flat and today the theory of SR is not the end of the story. All the observations that prove SR also apply to my GST-07 drawing. I have asked before, where is the GST space-time wrong with respect to observation or experiment.

Just as the laws of Newton still apply so also does SR. SR is just a part of the whole picture. It is the view of the egocentric observer just like the farmer of the Middle Ages. The farmer at that time could prove to you by thousands of measurements that the sun went around the earth.

R.G.

[4newton]

Alkatran:
I just told you that different observers will measure different times as having passed. How would I know the entire history of some random object 10 billion light years away? Chances are it hasn't observed the same passage of time as the stuff that made the sun. In order to consider any concept you must focus on the ideal and not be distracted by irrelevant input.
The objects both start out at the time of the BB and continue without any spatial transitions or influence each will follow a path in a straight line away from the event of the BB. See the attached drawing GST-08.

You will note that the time line, proper time or normal time, with respect to the speed of light must be on the same path as the objects direction out from the BB. The light cone for each object is 45 degrees to the path of the objects.

Object A takes the path C-A’-A and object B has the path of C-B’-B. At any time a light pulse may be sent from either object to the other. This is shown by light lines A’ to B and B’ to A. The length of each light path must be equal. Therefore from the point of any simultaneous events on either objects the light must arrive at the same time on the other object. The start of the simultaneous event may be all the way back to the BB. The point of the BB must be simultaneous for all events in the universe. By this method it is shown that at all times all events in the universe are simultaneous and that all objects in the universe have the same normal, or proper time.Take a perfectly round sphere and show me the center of it's surface area.
That's why you can't necessarily pinpoint the center of our universe.The center of a surface has nothing to do with the center of a sphere or hyper-sphere.
Relativity is tested everyday. If the farmer had done a scientific test, such as measuring how far the horizon was, he would realize the earth could not be flat.
What is the space time you have drawn?
As I pointed out before, show me where the test of relativity fails in GST-07. I will again attach GST-07.

If the farmer were not so convinced that he was right he would think to run the test. As we know that did happen later as will all truths. Has scientific thought changed very much in all this time? I am not asking that any idea be accepted out of hand. But it is just as bad to fall back to the position that everyone knows for a fact. If these viewpoints are wrong point it out in some detail. Saying that it is against some other theory is starting with a closed mind. With that approach all you can produce, like the farmer, is corn. (or something)

R.G.

[Fredrik]

If back in the Middle Ages I walked on to your farm and asked you about your world...

I wouldn't be surprised if you actually believe that your analogy is correct, but for your sake I really hope you don't.

There's at least one important difference between you and a person trying to convince a farmer in the middle ages that the world is round: That person would be able to convince the farmer that he understands the meaning of the sentence "the world is flat". You however, have not convinced anyone that you understand special relativity. You have shown us over and over again that you don't understand SR.

If you're going to try to convince people that a theory is wrong, you should first learn what the theory actually says.

By the way, the farmer would have to be very ignorant or stupid, because it's been well known for more than 2000 years that the earth is round. The ancient Greeks knew it, and were even able to estimate the size of the earth.


The question is, if the view of space-time I have presented is wrong where does it disagree with observation or experiment? You have never addressed this main point.

As far as I can tell, your "view of spacetime" is that space and time is exactly what people thought it was before special relativity was discovered. As Pervect explained very well in a post earlier in this thread, this view doesn't disagree with experiment, but requires that you think of a Lorentz contraction as an actual physical deformation of a moving object. But the really disturbing fact about this view is that you can easily combine "real" space and "real" time to form "spacetime", and then choose another hyperplane that we can think of as "space". Let's call this hyperplane "fake space" and the direction that's perpendicular to it "fake time". The problem with your view is that if someone were to assume that "fake space" and "fake time" is actually the real space and time, there's no way you would be able to prove him wrong.

The question of whose space and time is "real" arises in your view of SR, not ours. We have accepted that it's a bad idea to think of space and time as two different things. No separation of spacetime into space and time is any more real than any other.


Could you please describe or draw this concept.

Most of the solutions of Einsteins equation are not as easy to visualize as Minkowski space. Fortunately, there is one solution with a "big bang" that is easy to draw. Remember that in a spacetime diagram that represents Minkowski space, horizontal lines represent space at different times, and their vertical position indicates what time that is. Later times are drawn above earlier times. In a spacetime diagram that represents a homogenous and isotropic universe with positive constant curvature, "space at different times" are drawn as circles with different radii. (If you would like to visualize two spatial dimensions, replace the circles with spheres). In this spacetime diagram, increasing time is not "up". It's "outward".

The visualization of this particular solution is where the analogy with a balloon being inflated comes from. The universe is not the interior of the balloon, it's the surface of the balloon. The big bang is not a point on the surface of the ballon, or an outward line from the center of the drawing, or any such thing. The big bang is the point at the center.

This is why it makes no sense to say that the big bang happened at some point in space. The big bang "event" is not even a point in spacetime, since the metric can't be defined at that point.

[Alkatran]

Well of course if you pick two objects which have the same speed they're going to agree about the amount of time passed!

Consider this:
Let's say, hypothetically, that the moon and earth agree on how much time since the big bang. The moon is moving relative to the earth, and accelerating around us, so it's proper time != earth proper time. That means a moment later, they WILL NOT AGREE on how much time since the big bang!

Ok, let's say the center of the 3d sphere is the center. How does that mean ANYTHING to the 2d people restricted to the surface area of the balloon? There's no point in their 2d space which is the center of the sphere, so THERE IS NO CENTER IN THEIR SPACE. Just as THERE IS NO CENTER IN OUR SPACE (according to the big bang theory).

[Fredrik]

Just as it turned out then the earth was not flat and today the theory of SR is not the end of the story.

Of course it isn't, but you're not replacing SR with a better theory. You don't have a theory at all. You're not a scientific pioneer. You're just a guy who doesn't understand relativity.


The farmer at that time could prove to you by thousands of measurements that the sun went around the earth.

What are you talking about? Of course he couldn't.


All the observations that prove SR also apply to my GST-07 drawing. I have asked before, where is the GST space-time wrong with respect to observation or experiment.

I'm not going to comment every little detail in every one of of your drawings. It's a waste of time, because every time I show you something that you have done wrong or something that just doesn't make sense, you ignore most of what I'm saying and just make another drawing.

I will say a few words about this one, but I will not comment any more of your drawings until you've made some progress in the discussions about your previous ones.

"Line GJ is the time-distance for light to reach the ring..."

The word "time-distance" is something that you just made up. How can I comment stuff like this? Do you mean time? Do you mean distance? Do you mean something else? The time is t(J)-t(G). The distance is x(J)-x(G). The line GJH is just the world line of a photon that is reflected off the ring.

"Line GH is the time-distance for the light to reach the ring..."

There's no such word, but let's ignore that for the moment. Have you noticed that the light is actually reflected in the wrong direction? Since the ring has moved, the photon will hit a part of the ring that's not perpendicular to the y axis, and will therefore be reflected a little to the right, and miss the green line GK. At time t5, the photon will be to the right of the green line, and on this side of the x axis (with a negative y coordinate).

"The time it take the light to reach H is (t3)=(t5)/2 and in this frame moving at one half the speed of light."

If we pretend that you didn't make the mistake I just described, and that there is a ray of light that actually takes the path GHK (where all three points have x coordinates that are consistent with x=vt) then we must have t3=(t5-t0)/2. (Apparently you have chosen t0=0). This is definitely less than t4.

So at least you got that right, but what's your point? This wouldn't prove anything you've said.

You've made a few more mistakes, like not considering the Lorentz contraction of the ring. You're assuming that it's moving in the x direction in this frame. That means that it must be shorter in the x direction than in the y direction.

[russ_watters]

Russ:
I like your addition to my flat-earth analogy. You have told the same story that everyone was saying back in the Middle Ages. I knew when I posted it that you wouldn't understand it, but I posted it anyway to illustrate a point. The piece you are missing is the evidence. In my hypothetical example there really was evidence that the world is flat. In the real world, there isn't - but there is evidence for SR. That is why your analogy (and your analysis) fails. You don't see or refuse to accept this.

[jcsd]

Russ:
I like your addition to my flat-earth analogy. You have told the same story that everyone was saying back in the Middle Ages. Just as it turned out then the earth was not flat and today the theory of SR is not the end of the story. All the observations that prove SR also apply to my GST-07 drawing. I have asked before, where is the GST space-time wrong with respect to observation or experiment.

Just as the laws of Newton still apply so also does SR. SR is just a part of the whole picture. It is the view of the egocentric observer just like the farmer of the Middle Ages. The farmer at that time could prove to you by thousands of measurements that the sun went around the earth.

R.G.

Out of interest the idea that people in the middle ages thought the Earth was flat (some may of, but an eductaed person would not of thought this) is a 19th century myth.

[robphy]

Sorry for jumping in late. But I don't understand GST-07. Although it claims a resemblance to http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/ , GST-07 has some errors (as Fredrik points out)... the most serious is the absence of length contraction along the x-direction. Without length contraction, event K is not the intersection of the reflected rays from J and from H (assuming the constancy of the speed of light). In addition, GH should be congruent to HK... which means that the center of the second cyan ellipse should be halfway between G and K.

Additionally, it's not clear to me what 4newton's position is and how GST-07 tries to support it.

[Fredrik]

Most of the solutions of Einsteins equation are not as easy to visualize as Minkowski space. Fortunately, there is one solution with a "big bang" that is easy to draw. Remember that in a spacetime diagram that represents Minkowski space, horizontal lines represent space at different times, and their vertical position indicates what time that is. Later times are drawn above earlier times. In a spacetime diagram that represents a homogenous and isotropic universe with positive constant curvature, "space at different times" are drawn as circles with different radii. (If you would like to visualize two spatial dimensions, replace the circles with spheres). In this spacetime diagram, increasing time is not "up". It's "outward".

4Newton, I had not yet looked at your drawing GST-8 when I wrote this. The drawing is exactly what I'm talking about, except that the light cones are drawn wrong. The world lines of light rays should not be drawn as straight lines here. They should be drawn as curves that make a 45 degree with every straight line through the big bang (lines like CA and CB) that it crosses. In other words, the light cones should be somewhat V-shaped, but the top of the V should be bent outward.

If you understand that the blue circle represents space at a certain time, and that A and B are the same two points in space as A' and B', then you should already know that the big bang didn't happen at some point in space. What point would that be? What point on the blue circle would represent the position where the big bang happened?

[Fredrik]

Object A takes the path C-A’-A and object B has the path of C-B’-B. At any time a light pulse may be sent from either object to the other. This is shown by light lines A’ to B and B’ to A. The length of each light path must be equal. Therefore from the point of any simultaneous events on either objects the light must arrive at the same time on the other object. The start of the simultaneous event may be all the way back to the BB. The point of the BB must be simultaneous for all events in the universe. By this method it is shown that at all times all events in the universe are simultaneous and that all objects in the universe have the same normal, or proper time.

This is an interesting argument, but is it correct? Let's find out.

"Object A takes the path C-A’-A and object B has the path of C-B’-B"

You should have explained what this drawing represents before you started talking about the path of objects. I will do it for you. We started out by attempting to find solutions of Einstein's equation that describe spacetimes that can be "sliced" into one-parameter families of spacelike hypersurfaces that are homogeneous and isotropic. The drawing is a spacetime diagram that represents one such solution. In this particular solution, the spacelike hypersurfaces are 3-spheres.

The easiest way to construct a coordinate system on a spacetime that is a one-parameter family of 3-spheres is to take the parameter that labels the 3-spheres to be the 0th coordinate (i.e. the "time" coordinate) and use a coordinate system that's appropriate for a 3-sphere to define the other three coordinates. (This is not the only way however).

With this choice of coordinates, any two points on the same 3-sphere (from this one-parameter set of 3-spheres) are simultaneous in the sense that they have the same time coordinate.

We can think of these 3-spheres as "space" at a different times, but it's important to realize that this "time" is just a parameter that labels the different 3-spheres. We can't just assume that e.g. A and B are simultaneous in any kind of "absolute" way. We can however be certain that any two clocks that are stationary in this frame will tick at the same rate. This is obvious because of the symmetries we have imposed on these solutions (homogeneity and isotropy). Because of this, it is natural to choose the value of the time parameter to be the time displayed by a clock (any clock) that's stationary in this frame.

"At any time a light pulse may be sent from either object to the other. This is shown by light lines A’ to B and B’ to A."

There are two things you could mean by "at any time":

1. At any value of the parameter that labels the 3-spheres (i.e. "on any one of the 3-spheres")
2. At any "real" time, where you have assumed that the parameter represents some kind of "real" time

The second alternative is pretty much what you're trying to prove, so you wouldn't want that to be one of your assumptions, would you? You probably meant 2, but I'm going to try to find a way to make sense of your proof, so I'll pretend that I believe that you meant 1.

The light lines are drawn incorrectly. See my earlier post about this.

"The length of each light path must be equal."

OK. (You should have explained why, but since I already know why, it doesn't really matter to me).

"Therefore from the point of any simultaneous events on either objects the light must arrive at the same time on the other object."

Do you think anyone understands what you're trying to say here? I have no idea what "from the point of any simultaneous events on either objects" is supposed to mean. You're not making sense.

"The start of the simultaneous event may be all the way back to the BB. The point of the BB must be simultaneous for all events in the universe."

You're still not really making sense. When you say stuff like "simultaneous for all events ..." it really sounds like you have absolutely no idea what you're talking about.

"By this method it is shown that at all times all events in the universe are simultaneous and that all objects in the universe have the same normal, or proper time."

This is a bizarre claim. "By this method it is shown..." No, it isn't.

It's hard to tell what you're thinking, but I can make a guess, based on what I've read here, and in your previous posts. This is what I believe you're trying to say:

"If the big bang happened N seconds ago to the observer at A whose world line is GA'A, it must also have happened N seconds ago to the observer at B whose world line is GB'B. Since A and B are just two arbitrary points in space, this means that every stationary observer at a point on the same 3-sphere (i.e. on the blue circle) will agree that the big bang happened N seconds ago. This proves that all points in space are simultaneous, in an absolute sense, and that anyone who says that it makes just as much sense to think of two events that are not on the same 3-sphere as simultaneous is just wrong".

The last sentence is OK until the first comma, but not after that. I would agree that it makes sense to think of two points on the same 3-sphere as simultaneous, but this is not a very profound statement. It's kind of like saying that "bald guys have no hair".

There is nothing in your analysis that justifies the conclusion that simultaneity is absolute.

[4newton]

Fredrik and all:
My little story is only to illustrate that we are all affected by preconditioned ideas as we come together here. Russ I am sorry. I could not help myself when I turned your thought around a little. It’s a weakness I have.

I have never said that SR is wrong just as you cannot say that Newton’s laws are wrong. Both are right in within their context. They are not, however the total stories. Einstein did not have any knowledge of the BB and could see no relationship beyond the observer. His total theory is the relationship of observer to observer. His one great exception was the speed of light. He recognized the speed of light as a constant and invariant, or absolute, for all observers.

We seem to have a problem with the idea of dimensions. I thought it is recognized by all that there is a time dimension and a spatial dimension. It may be necessary to go into more detail on the nature of dimensions.

The idea of time distance is simply the conversion of time into the same units as the spatial dimension by multiplying time (in seconds) by the speed of light (meters per second) with the result of time distance in meters. ( ct ) I thought you were familiar with this concept.

You are starting to see my point. How do we know what real space-time is? At this time Minkowski space-time looks like a better starting point than SR, in light of the BB and a dynamic universe. It is important not to take a dogmatic approach in favor of any theory but to examine the theories point by point in view of observation and experiment. Just as with Einstein and SR the pieces are all there it how you put them together that makes the difference.

I will skip your thoughts on GST-07 at this time in light of your comments on GST-08.

You are correct on the drawing not representing the true light path. I did not want to complicate the drawing and be misunderstood. It was not important to understanding the concept I am trying to convey. It is also difficult to draw. If you understand that concept you must also understand that all objects including light in transition must transition outward from the BB together independent from any spatial transition. As the curve you describe indicates. You now need to ask the question. What is the difference between the outward transition from the BB and our transition in the time dimension? If every hypersurface is a segment of time then the transition outward from the BB must be the time dimension.

The BB is not just a point in space. You have two choices. The universes started at some point in an absolute frame of all dimensions or all the dimensions of the universe are the result of the BB. There is no way to tell the difference at this time. In either case all actions, of the smallest and shortest possible, occur at the same time at the point of the BB. All objects, including radiation… transition outward in the expansion direction. From you thoughts before you seem to think that is the time dimension and I agree with you. As you agreed before all actions that are simultaneous on any hypershpere will remain simultaneous on all hypershere’s.

[4newton]

Alkatran:

Well of course if you pick two objects which have the same speed they're going to agree about the amount of time passed!

Consider this:
Let's say, hypothetically, that the moon and earth agree on how much time since the big bang. The moon is moving relative to the earth, and accelerating around us, so it's proper time != earth proper time. That means a moment later, they WILL NOT AGREE on how much time since the big bang!

Ok, let's say the center of the 3d sphere is the center. How does that mean ANYTHING to the 2d people restricted to the surface area of the balloon? There's no point in their 2d space which is the center of the sphere, so THERE IS NO CENTER IN THEIR SPACE. Just as THERE IS NO CENTER IN OUR SPACE (according to the big bang theory).

The point is that all objects in the universe are in transition outward from the BB. That is the basic idea of the expansion of the universe, this is verified by observation, red shift…

The transition outward from the BB is not a spatial dimension. Also verified by the same above observation. It is also agreed by most that all clocks that transition without any spatial motion will tick at the same rate and will accumulate the same total time. All clocks on every hypersphere as illustrated by the blue line in GST-08 will tell the same time from the BB. This expansion transition is also a convenient candidate for what we recognize as the time dimension. The same behavior of clocks is observed when no spatial transitions are taking place and only time is passing even when the clocks are separated in space.
Clocks only change rate and accumulation of time when they are in transition in the spatial dimension.

[4newton]

Robphy:
Sorry for jumping in late. But I don't understand GST-07. Although it claims a resemblance to http://physics.syr.edu/courses/modu...ONE/LightClock/ , GST-07 has some errors (as Fredrik points out)... the most serious is the absence of length contraction along the x-direction. Without length contraction, event K is not the intersection of the reflected rays from J and from H (assuming the constancy of the speed of light). In addition, GH should be congruent to HK... which means that the center of the second cyan ellipse should be halfway between G and K.

Additionally, it's not clear to me what 4newton's position is and how GST-07 tries to support it.

The whole thread is about simultaneous events in space-time. The discussion revolves around the idea of simultaneity being relative to the observer or referenced to a universal event.

My drawing is not correct. Just my poor 3d drawing technique. The web site is correct.
The drawing is to show that the one way time to reflection is different dependent on direction of transition.

If you add contraction in the x direction only then the light pulse will not arrive back at the same point that the light does from the path in the y direction. See the MM experiment. If you contract the entire ring then you will not have a clock difference when you bring the moving clock back to the static clock. (The twin paradox)

Please feel free to give your opinion on the concept of simultaneity.

R.G.

[Fredrik]

I have never said that SR is wrong

Yes you have. You claim that there are paradoxes in SR, which would be a much more serious problem than a mere disagreement with experiment. You also claim that only one of the infinitely many ways to split spacetime into space and time is correct, but it's obvious from the mathematics of SR (and GR) that it isn't so.


Einstein did not have any knowledge of the BB

Wrong. Of course he did. The big bang theory is based on solutions of Einstein's equation that were found a long time ago, in the 1920's I think.


At this time Minkowski space-time looks like a better starting point than SR, in light of the BB and a dynamic universe.

SR is the theory of Minkowski space, and nothing more, so you're really saying that SR looks like a better starting point than SR, which is a pretty strange thing to say.

There is no big bang in Minkowski space.


I will skip your thoughts on GST-07 at this time in light of your comments on GST-08.

In other words, you will ignore the fact that your GST-07 is incorrect and (more importantly) pointless, and proceed as if it wasn't.


If every hypersurface is a segment of time then the transition outward from the BB must be the time dimension.

Yes, but these spheres are not the only spacelike hypersurfaces that can be called "a segment of time". Any spacelike hypersurface will do. This means that there are many ways to split spacetime into space and time, just as in SR.

I really think that you should focus on SR (i.e. Minkowski space) instead of GR. You will not understand stuff like simultaneity in GR until you understand it in SR.

[4newton]

Yes you have. You claim that there are paradoxes in SR, which would be a much more serious problem than a mere disagreement with experiment. You also claim that only one of the infinitely many ways to split spacetime into space and time is correct, but it's obvious from the mathematics of SR (and GR) that it isn't so.You seem to be unable to grasp the concept that a theory may be valid within defined limits and totally wrong outside of those limits. If SR or GR were correct in all cases Einstein would not have failed to find unification. SR is a fine little theory and describes very well what an observer will see in most cases. It has the same problem that all egocentric views have, they are always wrong on the large scale. The bad result of theories like SR is they become accepted in dogmatic way and close off the thought process to the larger view. You have accepted SR as a religion and are willing to distort the real world in favor of your belief.

It should be obvious even to you that if SR and GR are able to produce an infinite number of space-times that are different when only one is required to explain all things there must be something wrong with the theories of SR and GR on the large scale.Wrong. Of course he did. The big bang theory is based on solutions of Einstein's equation that were found a long time ago, in the 1920's I think.To what equation are you referring? Do you remember something about a static universe and a correction factor?SR is the theory of Minkowski space, and nothing more, so you're really saying that SR looks like a better starting point than SR, which is a pretty strange thing to say.
There is no big bang in Minkowski space.I think you should learn about Minkowski space-time. Minkowski space-time is time distance (ct) and space (s) that does not change with the observer. Time is absolute and space is absolute, as is the speed of light in Minkowski space-time. Minkowski treats space and time as two independent dimensions. All objects including light move at the same rate in the time dimension and the rate is not affected by transition in the spatial dimension.

If you look at the similarities of the spatial dimension and the time dimension you may start to realize the nature of dimensions. You may transition in the spatial dimension an infinite number of possible directions but you can only move in one spatial direction at a time and you can not exceed the speed of light. The same is true in the time dimension. You can transition outward from the Big Bang in an infinite number of directions but you can only move on one time line at a time and the rate of the transition is always equal to the speed of light. Any time you transition in the spatial dimension your vector sum of the transition in space-time always exceeds the speed of light since your transition in the time dimension is always equal to the speed of light.

Of course there was no BB in Minkowski space-time, but there is now. All normal time lines are known now not to be parallel and space is not a horizontal line. Space is a curve with a radius equal to the distance out from the BB. Our entire present universe is on this curved hypershpere.

If you think this is the same as SR and GR great.

If you don’t think this is Minkowski space-time then you may give me credit for it and call it Green space-time. In other words, you will ignore the fact that your GST-07 is incorrect and (more importantly) pointless, and proceed as if it wasn't.I have no intentions of ignoring GST-07 , you should realize this of me by now. I just think that if we move on to more observations the concept of GST-07 will start to resolve themselves much easier.Yes, but these spheres are not the only spacelike hypersurfaces that can be called "a segment of time". Any spacelike hypersurface will do. This means that there are many ways to split spacetime into space and time, just as in SR.There is only one hypersurface that is our universe. It is the hypersurface that is 15 billion years from the Big Bang.
There may be an unlimited number of hypersurfaces, each one a universe but they would be at a different time then our universe. We have no knowledge of these other hypersurfaces if they exist. If you have not noticed we are unable to move froward or backward outside of our current position on any time line.I really think that you should focus on SR (i.e. Minkowski space) instead of GR. You will not understand stuff like simultaneity in GR until you understand it in SR.It seems to me from your comments that you are the one that is lacking in understanding. If you must resort to insults to enhance your position you only broadcast you inability to deal with the subject. If your position is correct simply state it clearly. You have been all over the map, half-agreeing half-insulting and always obtuse in understanding. You have not shown where SR is right, with proof, compared to the statements made here. You just hold up your understanding of SR and GR as gospel and make dogmatic statements that ideas presented here don’t agree with SR or GR and therefore must be wrong. Then you state that if I , or I would guess anyone, understand SR and GR as you do we would agree with you. These are methods of control to avoid results that may prove you wrong.

[russ_watters]

You seem to be unable to grasp the concept that a theory may be valid within defined limits and totally wrong outside of those limits. "The Twins Paradox," which (1) you erroneously believe is a paradox in SR (as has been said, its a paradox resolved by SR), (2) goes right to the heart of of the domain of applicability of SR. Since both 1 and 2 are mutually exclusive, you can't be right about both points - however, you can and are wrong about both points. This should be a clear red-flag to you that you are missing something pretty basic about SR. It seems to me from your comments that you are the one that is lacking in understanding. How many times, by how many people, in how many different places, all saying the same thing does it take for you to accept that it is you who has the misunderstanding? Is there any point at which you will reconsider? You just hold up your understanding of SR and GR as gospel and make dogmatic statements that ideas presented here don’t agree with SR or GR and therefore must be wrong. Then you state that if I , or I would guess anyone, understand SR and GR as you do we would agree with you. These are methods of control to avoid results that may prove you wrong. Try saying that to your mirror and see what response you get.

[Gamish]

Under bounds of relativity, paradoxes don't exist. Now, if one were to bend the "classic" veiws of SR and Gr, one cound create many paradoxes. But, I believe that age is not relavent, only time. :surprised

"Im the master at time!"

I finally found a group I like :biggrin:

[Alkatran]

Under bounds of relativity, paradoxes don't exist. Now, if one were to bend the "classic" veiws of SR and Gr, one cound create many paradoxes. But, I believe that age is not relavent, only time. :surprised

"Im the master at time!"

I finally found a group I like :biggrin:

Age reflects time so it is relevant. What do you mean by 'classic' views of SR and GR? The ones incorrect ones?

[Fredrik]

We seem to have a problem with the idea of dimensions. I thought it is recognized by all that there is a time dimension and a spatial dimension.

What is recognized by physicists is that spacetime is a 4-dimensional manifold with a metric of -+++ signature (or +--- if you prefer that convention). What it doesn't mean is that there's only one way to "slice" spacetime into a one-parameter family of spacelike hypersurfaces, or that there are several such slicings but one of them is more real than the others. That's just an assumption that you have made, without any good reason.


It may be necessary to go into more detail on the nature of dimensions.

Books about differential geometry do that. I suggest you get one of them and read the parts where they define concepts like "manifold", "coordinate system", "tangent space", "tensor field", "metric", "geodesic" and "isometry". It's impossible to really understand GR without some knowledge about these things. You will not even understand the concept of "frames" (i.e. coordinate systems) fully until you've read at the least the first chapter of a book on differential geometry. (This stuff is also explained pretty well in some books on GR, like "General Relativity" by Wald).



How do we know what real space-time is?

The only way to find out if a particular solution of Einstein's equation is an accurate model of our universe is to do experiments and make astronomical observations.

However, I suspect that you actually meant to ask "How do we know which spacelike hypersurface really is space?". The answer to that question is that there is no reason to believe that one of them is "space" and the others aren't.

You seem to be unable to grasp the concept that a theory may be valid within defined limits and totally wrong outside of those limits.

You're still missing the point. You claim that there are paradoxes in SR, which would mean that it's not valid within it's own limits.


If SR or GR were correct in all cases Einstein would not have failed to find unification.

That's probably true. But we already know what the problem is with GR. It's not a quantum theory.


SR is a fine little theory and describes very well what an observer will see in most cases. It has the same problem that all egocentric views have, they are always wrong on the large scale. The bad result of theories like SR is they become accepted in dogmatic way and close off the thought process to the larger view. You have accepted SR as a religion and are willing to distort the real world in favor of your belief.

That's ridicilous. SR is a perfect model of a fictitious universe where there is no gravity and no quantum phenomena whatsoever. It's nothing more than that, and nothing less. Because of that, it will only agree with experiments in situations where gravity and quantum effects can be ignored.


It should be obvious even to you that if SR and GR are able to produce an infinite number of space-times that are different when only one is required to explain all things there must be something wrong with the theories of SR and GR on the large scale.

There's only one spacetime in SR. It's called Minkowski space. GR however describes many possible spacetimes (different solutions of Einstein's equation). As I said before, only experiments and observations can determine if anyone of them has the same large-scale properties as our own universe.


To what equation are you referring?

There's only one equation in GR. It's called Einstein's equation.


I think you should learn about Minkowski space-time.

Thanks for making me laugh.


Of course there was no BB in Minkowski space-time, but there is now.

What are you talking about? Minkowski space is flat. The big bang is a singularity, a point of infinite curvature.


If you don’t think this is Minkowski space-time then you may give me credit for it and call it Green space-time.

GST-07 looks like a spacetime diagram that represents Minkowski space. GST-08 looks like a spacetime diagram that represents a closed FLRW (http://en.wikipedia.org/wiki/Friedmann-Lema%EEtre-Robertson-Walker) spacetime. I don't know what Green spacetime would be. Would you like to define it?


I have no intentions of ignoring GST-07 , you should realize this of me by now. I just think that if we move on to more observations the concept of GST-07 will start to resolve themselves much easier.

Actually it has made it easier to understand what it is that you have misunderstood, and why you have misunderstood it. In the closed FLRW model (i.e. in GST-08), one choice of spacelike hypersurfaces does stand out from the rest. A 3-sphere is the only shape that has a constant curvature. Perhaps this is why you believe that only they can be called "space".


There is only one hypersurface that is our universe. It is the hypersurface that is 15 billion years from the Big Bang.

You have not given us any good reason to believe that it would make less sense to call e.g. a spacelike 3-ellipsoid "space".


If your position is correct simply state it clearly.

That's what I have done, and that's what you should do.


You have not shown where SR is right, with proof, compared to the statements made here.

What you don't seem to understand is that SR is a theory of mathematics as well as a theory of physics. The mathematics of the theory can't be wrong unless pretty much all of mathematics is wrong. Suppose e.g. I define a theory that consists of the set of real numbers and the function f, defined by f(x)=2x. Is there any way this theory can be wrong? SR is not very different from this. Minkowski space is just a set, with a bunch of functions and stuff defined on it. This can't possibly be wrong. And if it were, the burden of proof would definitely be on you.

The physics of SR is just the simple statement that physical space and time can be accurately represented by Minkowski space. That statement can't be proved. It can only be disproved, and the only way to do that is by experiment.

[ramollari]

The discussion has got out of hand for me. I don't understand very well spacetime coordinates, Minkowski spaces, etc. I just know that two inertial frames of reference move at constant speed relative to each other and that speed of light c is the same for both observers. With these two conditions it is enough to show that both observers reach contradictory conclusions that throw doubt upon the validity of physical laws. I also think that age is a relevant indicator of time, because it is directly observable and cannot be relative.

[Fredrik]

I just know that two inertial frames of reference move at constant speed relative to each other and that speed of light c is the same for both observers.

This is correct.


With these two conditions it is enough to show that both observers reach contradictory conclusions...

This is wrong.

[ramollari]

This is wrong.
Ok let me clarify something. If each of the observers correctly concludes that the other's clock runs slower does this necessarily mean that there's a contradiction/paradox? This conclusion results from the fact that the frames move relative to each other at constant speed and c is the same for both observers.
Will be any of the observers ever be able to deduce the other's age without the need to return to Earth?

[Fredrik]

Ok let me clarify something. If each of the observers correctly concludes that the other's clock runs slower does this necessarily mean that there's a contradiction/paradox?

This is not a paradox. The reason is that these guys actually make the same prediction about spacetime, and SR is a theory of spacetime, not of space and time separately.


Will be any of the observers ever be able to deduce the other's age without the need to return to Earth?

They will be able to calculate the other observer's age at any point in spacetime.

[Fredrik]

They will be able to calculate the other observer's age at any point in spacetime.

This answer isn't very good, so I'll provide a better one. All observers will agree about a person's age at any point on his world line, but not at other points in spacetime. They can calculate the person's age at any point in spacetime, but in general they will not get the same result. The reason is that they may disagree about which point on the world line is simultaneous with the point they're considering (the point at which they're supposed to calculate this person's age).

This comment also answers the question that started this thread. Age is relative at most points in spacetime, but not on the world line (which is the set of events that this person is experiencing).

[4newton]

Ramollari:
You have the right idea in the first place. Don’t be put off by convoluted answers.
As proved by experiment. It is a fact that two clocks do not agree on accumulated time when one transitions away and returns to the first clock. The difference has nothing to do with acceleration or observation. The difference between clocks is only dependent on the rate and length of time of the transition. The answer given has no mechanism of the change.

This answer isn't very good, so I'll provide a better one. All observers will agree about a person's age at any point on his world line, but not at other points in spacetime. They can calculate the person's age at any point in spacetime, but in general they will not get the same result. The reason is that they may disagree about which point on the world line is simultaneous with the point they're considering (the point at which they're supposed to calculate this person's age).

This comment also answers the question that started this thread. Age is relative at most points in spacetime, but not on the world line (which is the set of events that this person is experiencing).The answer does not address the reason the clock ticks slower. The change of the tick of the clock is not a result of observation. The change is real, as proven when the clocks come back together.

The age of all observers may always be calculated at any point by any observer. Any observer may calculate the reading on any other clock. This is the basic idea of SR. If you deny this ability then SR has no use at all.

[4newton]

Fredrik:
Now that we are in TD we can work from observation and develop a theory works in all cases including QM.

A good place to start is the Big Bang. Again I ask you did the BB create all that there is including space, time, spacetime, or is there a basic frame of dimensions that exceeds the universe.

[SamCJ]

I found this exhaustive thread in archives because the question interests me. I grew tired of the differences of opinion that confused me. I would like to pose the question a little differently.

Two twins are called Earthbound and Spacestation, each is wearing perfectly accurate radioactivity decay watches and each has a pulsar pulse counter. When Spacestation gets into orbit he believes he is standing still and that Earthbound is spinning at a high rate of speed. Earthbound believes that he is standing still and Spacestation is orbiting at great speed. These respective observations go on for 20 years, after which Earthbound joins Spacestation on the space station in orbit and he takes his perfectly accurate watch and his perfectly accurate pulse counter with him.

Question: When the two compare watches and pulse counters, what will the see? Could Einstein prove your answer is correct using mathematics?
Hasn't this experiment already been done and where can I find the results?

[pervect]

The experiment has actually been done as a side-effect of the implementation of the GPS system.

The result is that the satellite clocks run faster than the ground clocks. The type of clock - quartz, atomic, pulse counter, radioactive decay, etc. is totally irrelevant in determining this result, except that the accuracy one can expect from the clock varies significantly among clock types, and some clocks may not be accurate enough to reliably measure the results because of uncontrolled varaitions in how well they keep time. (Pulse counting in particular is subject to large enviromental variation).

The satellite clocks run faster, and not slower, because of a factor that you did not realize was significant but was nonetheless very important - the altitude of the clock. To clarify this a bit, what turns out to be important is the gravitational potential energy of the clock - for more details, see some of the threads on gravitational time dilation.

For more on the GPS clocks, see

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html


Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see Lecture 32). A straightforward calculation using Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate.

Further, the satellites are in high orbits, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see Lecture 20 on Black Holes). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these relativitic effects means that if not accounted for the clocks on-board each satellite would tick faster than clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy,


Note that the GPS satellite system isn't necessarily one of the most precise tests of relativity that has been done - the GPS system was not specifically designed to test relativity. Rather, it simply illustrates that relativity is not just for textbooks anymore.

In evaluating the archive responses, you might want to note that the posts by users who eventually wound up being banned (and having their names crossed out) are generally not representative of current scientific thought.

Many times a few users can create a false sense of controversy or uncertanity about results that are really not controversial (mainly in the minds of those who are not aware of the facts, and hence falsely weight every opinion with equal value).

[SamCJ]

Thanks. I had not thought of the lesser amount of gravity at the higher altitude. Unfortunately, that oversight made you miss the point I was trying to understand. I have usually read the the ground-based twin will be the older one when they rejoin, but a time or two I read that each twin will think the other is younger. However, I have never read an explanation of how the spaceship twin can be younger when both twins believe that it is the other that is moving faster, and, as I understand relativity, they are correct in thinking that from their own perspective. By adding the watches, I was trying to remove subjective misperception by either twin as a factor. By adding the pulse counter, I was trying to create a time machine that was common to both twins. By having Earthbound join Spacestation in the space station, I was trying to remove acceleration as a factor. (I do not think Einstein mentioned subjective misperception or acceleration as a factor in determining their ages at the end of the trip, and I have not understood any of the discussion of simultanaety and frames of reference.)
I anticipate that you might respond the the space twin may be deceived about which one is moving, but we know it is he and not the earthbound twin because he went through acceleration for a relativity brief time at the beginning of the trip and he must decelerate at the end of the trip. But, if so, I say, Isn't acceleration the same as deceleration except in a different direction? If space twin's spaceship heads in the direction that the earth came from, he would appear to all earthbound people to be accelerating, but in actuality, he would be decelerating. In that event, earthbound twin really would be moving faster until the space twin tried to turn around and come back, at which time he would really have to hurry.
In any case, my question is essentially the same one that was originally asked in this thread. If there was a good answer to it, I missed it in all the confusion. (Thanks also for the tip about the lines through the names.)

[jtbell]

When the two compare watches and pulse counters, what will the see? Could Einstein prove your answer is correct using mathematics?
Hasn't this experiment already been done and where can I find the results?

Time dilation for the "travelling twin" has been incidentally observed in studies of precise timekeeping for military applications (targeting bombs etc.). The required precision is such that relativistic effects are observable even on clocks in airplanes flying around in circles.

TIMEKEEPING AND TIME DISSEMINATION IN A DISTRIBUTED SPACE-BASED CLOCK ENSEMBLE (tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf) (PDF file)

This isn't quite the same sort of situation you were asking about, but it's close enough that you might be interested in seeing these results.

[pervect]

Thanks. I had not thought of the lesser amount of gravity at the higher altitude. Unfortunately, that oversight made you miss the point I was trying to understand. I have usually read the the ground-based twin will be the older one when they rejoin, but a time or two I read that each twin will think the other is younger. However, I have never read an explanation of how the spaceship twin can be younger when both twins believe that it is the other that is moving faster, and, as I understand relativity, they are correct in thinking that from their own perspective.


I'd recommend doing the problem in flat space-time first, this means imagining that both spaceships are far from any planet and there is no gravity.

In that case, there is a very easy explanation. Each twin is correct in thinking that the other twin is moving faster, and each twin thinks that the other's clock is running slow.

However, in order for the twins to re-unite, one twin must accelerate.

The twin that accelerates is the twin that will experience the shortest amount of time. If you haven't read anything about it, there are only about a zillion articles on the twin paradox. I'd recommend the sci.physics.faq on the twin paradox as a good start

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

To do the problem with gravity involved requires considering the metric of space-time. This is a lot harder job. For starters, even describing the metric of space-time from the perspective of the orbiting satellite would be quite a challenge. The "easy" coordiante system to use to describe the metric of space-time is a coordinate system anchored to the center of mass of the most significant massive body (in this case the Earth). If you have two massive bodies, the problem becomes almost insanely difficult (unless you use pertubative methods, in which case it becomes only extremely difficult). The difficulty/reward ratio is low for the problem with two massive bodies.

If you have only one massive body, though, the metric of space-time to use is the Schwarzschild metric, which you can also read about in the wikipedia

http://en.wikipedia.org/wiki/Schwarzschild_metric#The_Schwarzschild_metric

The process of computing the elapsed time on an observer consists of integrating dtau over the path followed by the body in Schwarzschild coordinates, where dtau^2 is given

dtau^2 =
(1-r/rs)*dt^2 - dr^2/c^2*(r-rs)-r^2/c^2*(dtheta^2+sin^2(theta) dphi^2

(Note dtau is just the metric, ds^2, from the Wikipedia, multiplied by a scaling factor of -1/c^2).

This is actually not that hard to do if you are familiar with basic calculus. If you work out this intergal for the orbiting satellite and for the ground based observer, you'll get the results I described.