On the Theory of Relativity - Lorentz Contraction

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On the Theory of Relativity - Lorentz Contraction

Postby BioWizard on February 24th, 2006, 8:46 pm 

We have recently read claims from Mac that work has been done which disagrees, wholely or in parts, with widely accepted theorie(s) in mainstream physics. Mac has requested a professional review of his ideas. Dr. Don Lincoln, a particle physics researcher of some 20 years of experience, coauthor of well over 100 papers in refereed journals and author of a book on particle physics for a lay audience, has graciously agreed, upon my request, to engage Mac in a formal debate. The discussion will proceed with a post from Dr. Lincoln, in which he may delineate any additional rules of thumb for the debate, basically the standards of peer review for any publishable work, in order to keep the debate as focused and professional as possible.

Debators: Dr. Lincoln, Mr. Mac.

Gentlemen, please begin.

Edit (09:58 pm 2/25/06) : "Lorentz Contraction" has been added to the title.
Last edited by BioWizard on February 25th, 2006, 10:58 pm, edited 4 times in total.
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Welcome one and all....

Postby Lincoln on February 24th, 2006, 9:53 pm 

Dear Dr./Mr./Ms./Other (circle one) Mac....

Biowizard, chief SCF poobah, asked me to step into the relativity debates. Against my better judgment, and upsetting a long-held policy of mine, I agreed. By way of introduction (and in the interests of full disclosure), I am a research physicist and have been one for over 20 years. My views on relativity tend to be of the conservative variant, meaning I use its predictions every day. I am not a relativity researcher because, bluntly, special relativity hasn't been controversial for over 50 years. Even general relativity research is of the "let's solve even harder problems" variety, rather than anything fundamental. Basically, very smart scientists thrashed on relativity for 20 years and have understood relativity's implications in many scenarios.

There are some physicists who work on alternatives to relativity. There are also lay students of relativity who try the same thing. In my experience, the first are very smart people working on a hard problem. The difficulty stems in part from relativity's success. Many of the other class suffer from a lack of understanding what relativity really says. I have yet to meet a lay student of relativity that could actually calculate the relativistic predictions of many of the scenarios they propose.

Any scientific statements made here reflect my own expertise and do not necessarily reflect the opinion of my employer, the US government, the church of your choice or the American Physical Society. But they should. (With apologies to Bob Parks, for whom I have great respect.)

So if you'd like to discuss relativity, I will do so. Below are my rules and conditions. Your mileage may vary. Do not pour coffee in your lap, as it may be hot. Etc.

1.) You need to clearly delineate in your discussion whether you are pointing out a case where relativity theory fails (e.g. a published and refereed measurement with which the theory disagrees).

2.) If you are not pointing out where relativity fails, but rather believe you have a better and more correct theory, you may describe the theory in words. But at a minimum you need to have an equation or a series of equations that describe the theory mathematically. If I can't do a calculation from what you give me, I don't want to hear it. Further, you had better do some of the simpler calculations yourself (light flash at the center of a train, etc.) If you can't assign a number to a quantity that can be measured, you're not doing science. In addition, if you have a program that calculates for you, you need to post the source code and directions for running it.

3.) If you have a theory of your own, then you need to point out a difference between your theory and relativity. If they make identical predictions, then there's no reason to switch paradigms.

4.) This isn't a discussion of philosophy. I don't care one whit about philosophy in this context. Science is strictly about prediction and measurement. Gedanken experiments are just fine, but they need to be clearly specified and solvable, at least in principle.

5.) The discussion needs to maintain rigid focus. No degenerating into cocktail-party banter and witticisms. No conspiracy theories. No appeal to unpublished anecdotal memos. No referring to "the man" suppressing some brilliant person. If they are brilliant, then you need to post the paper that describes their theory in sufficient detail so we can all appreciate their brilliance too. Hearsay not allowed.

6.) Yes, I know that general relativity and quantum mechanics have not been merged, with the exception of the popular string theory and a couple of quantum gravity ideas. That certainly does mean that general relativity is likely to be incomplete. But it is on the larger realm that GR applies, so base your ideas there. And special relativity and quantum mechanics were successfully reconciled about 70 years ago.

7.) I would prefer to keep the discussion at the special relativity level. If you have enough mathematical skill to correctly do general relativity problems, then the discussion will immediately leave behind the vast majority of this bulletin board's readers and thus this is not the proper venue for that debate.

8.) Edit your text for grammar, spelling and clarity of thought. We all make typos, but if you can't communicate clearly, I'm not going to work hard to guess what you mean. Civility is a must.

9.) I will add to the discussion the level of review I would offer, were I sent a paper from a journal for review. This level of review is much more critical than most science buffs appreciate. This is not meant to put you off, but to get to the truth. If you want to do science, then this is the price of doing business. I expect the same from you.

10.) I will answer as time permits. This debate isn't my main priority and, if the debate is sufficiently difficult, it may take a while to do calculations necessary to respond.

11.) Only a single, highly focused, topic per thread. Wide ranging discussions are great at a party, but not for this debate.

12.) I need to know your level of formal (and informal) education in relativity and relevant science/math. Education doesn't make one right, but this knowledge lets me know what language I can use. If you’ve mastered differential manifolds, the debate will proceed differently than if your algebra is rusty.

13.) If you offer external citations, either web sites or journal, the caliber of the place from where the citation comes has some relevance. A private blog run by Mr. Crocker of “Fairly Odd Parents” fame does not have the same weight as a refereed article in Physical Review Letters. The ideas matter more than the placement, but the more obscure the placement, the less likely it is I will bleed over obscure mathematics. Paper-based references have more weight than web-only ones.

14.) A single experiment can in principle kill a theory, but it must be a well-designed experiment, with appropriate controls, a description of the techniques in sufficient detail that the experiment can be repeated by a practitioner. Then the experiment must be repeated. The cold fusion debacle should give pause to anyone who is too quick to use a particular result. Plus, given the enormous body of knowledge gathered in the last 100 years on the subject of relativity, a single contradictory experiment is no longer good enough. The best such an experiment can do is point to the need to redo the experiment.

15.) Finally and absolutely most importantly. Physics is an EXPERIMENTAL science. Any discussion of something that contradicts well-supported experimental results is a waste of everyone’s time.

The purpose of these rules is to keep the debate at a scientific level. The rules may evolve as the need for such evolution becomes apparent. Science is the process whereby new ideas are subjected to a Darwinian process. The good survive. The others don’t.

I do not wish to restrict the initial topic. Subject to the above rules, you may choose the point of discussion.

Please begin. May the best worldview win.

D
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Postby Mac on February 24th, 2006, 10:46 pm 

I would like to start by thanking Dr Lincoln for making this exception to his "Better Judgement" :D it is my hope that he will be glad he has and I feel certain members here are going to thoroughly enjoy this new subforum.

I also want to thank BioWizard (perhaps others I am unaware of) for having thought of this process, I think it is going to prove to be a vital asset the SCF regardless of the outcome of this first debate. (I prefer "Discussion" to the term debate since I do not see this as being adversarial but mutually (hopefully) educational.

Having said that I will await a PM from BioWizard pending Dr Lincoln having received and had the oportunity to comment on my responses to each of his terms for debate.

Please feel free to call me Dan rather than my forum user name.

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Postby Mac on February 25th, 2006, 7:04 pm 

Dr Lincoln,

I have received a PM from BioWizard indicating I should proceed.

Let me first make a general opening statement as to my position. I think that will clarify the jist of the debate.

I find relativity is likely a correct principle. However, I also find aspects of it which seem more acceptable if certain areas of Special Relativity are reinterpreted. It leads to ultimate conclusion which are devoid of what are otherwise generally referred to a being "Counter Intuitive" features of relativity.

I think it will be more efficient if we take this a step at a time and see where we might agree and where we do not before posting a complex gendanken at this juncture which could have potentially many areas that could be pitfalls to coming to a mutual resolution.

My first question of you is:

"Do you agree that time and distance (dimension) are physical enities and that speed is a scaler quantity calculated from the ratio of those physical enities where s or v = d / t?"
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Postby Lincoln on February 25th, 2006, 7:16 pm 

I would agree that distances and times are physical quantities. They are not distinct quantities however. Further they are not quantities the numerical values of which are agreed upon by all observers. Finally, I would state that velocity is a differential quantity, v = dx/dt. Your value is for an average velocity or for a constant velocity. I presume that the usage of the word speed and scalar rather than velocity indicates a one-dimensional problem.

D
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Postby Mac on February 25th, 2006, 7:33 pm 

Dr. Lincoln,

We are in general agreement with an exception which will be the basis for this thread. The term speed and scaler were used in that I was not wishing to imply some vector of the motion.

The next question is to determine which group of physicist you are in. I have had conversations with many over the years and unbelievably there have been different opinons on this next issue.

"Do you believe that Special Relativity predicts not only Lorentz Contraction of material objects but also predicts "Spatial Contraction", that is that the distance between a moving observer and a distant star would also contract relavistically"?

It is my opinion that Special Relativity does predict spatial contraction. It is also my opinion that that prediction is part of my envisioned problem with Special Relativity and there is an alternative which does not require scraping relativity.

The objective of this thread from me is to explore both the acceptability of the basis for such change and the ultimate conclusion differance it makes to Special Relativity and the consequences.
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Postby Lincoln on February 26th, 2006, 1:21 am 

Without the tiniest shred of doubt Special Relativity theory implies spatial contraction, not just object length contraction. The truth is of course more complex. There is a constant of the equations, the so-called proper time. This is the same in all reference frames and supplies the fundamental underpinnings of relativity, which can only be properly understood in the so-called 4-momentum formalism, which mixes space and time, rather than treating them as separate. Failure to appreciate the 4-momentum formalism is the root-cause of most misconceptions of SR.

But within the context of SR as taught at the undergraduate level, one can say that space contracts, not just objects. In fact, a trivial example will invalidate any person's statement that SR suggests that objects contract rather than space. Take an object of length one meter. After motion, its length as observed by someone in a moving reference frame is contracted. This would also be true of a hypothetical object of length 2 meters. The existence or non-existence of matter is irrelevant to the point. Note that this argument/example strictly only applies to the mathematics of relativity (which is how I interpreted your question) and not necessarily to reality, although special relativity is essentially universally taken to represent reality.

(P.S. Dr. Lincoln is far too stuffy. Don will do.)

D
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Postby Mac on February 26th, 2006, 1:59 am 

Lincoln wrote:Without the tiniest shred of doubt Special Relativity theory implies spatial contraction, not just object length contraction.

.........................................................

(P.S. Dr. Lincoln is far too stuffy. Don will do.)

D


Don,

Thank you. I fully agree with your post.

Given gamma = 1 / (1 - v2/c2)0.5

BioWizard please note that the above expression did not post correctly.

Don it should read gamma = 1 / (1 - v^2 / c^2) ^0.5


Considering that Special Relativity predicts foreshortening of distance by d' = d/gamma is it not true that a number of counter intuitive things occur for example:

1 - Given a large initial seperation, if I accelerate away from earth at high relavistic velocity the earth actually gets closer the faster I receed.

2 - For an object measured to be 100 light years away to an observer moving at a relative velocity of 0.866c the distance becomes only 87.2 light years distance at a velocity of 0.9c. That is 12.8 light years change.

Assuming an acceleration of 1g, the change requires approximately 12 days and would consume about 3% of one light year which can be Ignored.

That means the spacecraft closure to the object was 12.8 light years in 12 days. That equates to v = dx / dt = 1.167E11m/s or 389c.!

.... = 1.167E^11m/s

3 - As an observer approaches the velocity of "c" the entire Billions of light years diameter of the universe, its entire contents being billions of galaxies and trillions of stars, etc, must all become compressed down into a volume of a few cubic feet!

The mass and energy density of such a universe is incomprehensable. I believe the counter intuitive aspects of Special Relativity mandate some reconsideration of the process.

The solution I believe is that Special Relativity commits errors in its physics structure. That is there has been no emperical data or observation confirming spatial length contraction in the 100 years of relativity. It is merely inferred mathematically based on certain assumptions.

That assumption is that velocity is invariant and the same in both frames. But velocity is a calculated result of physical parameters of time and distance. There was no basis to assume a common velocity The physical parameters that were known are distance (d) and time (t) and dilated time (t').

Based on those known factors one should consider that what really happens between frames is v' = d / t'. That is at 0.866c distance is not contracted to one half but velocity in the moving frame appears to be twice that or 1.72c.

I'm aware that these numbers are prohibited by Special Relativity but please bear with me. This view seems indicated if you consider the fact that the total trip time of the moving observer is accounted for by the known dilated condition of his clock. That means distance did not change.

To clarify for other readers let me present a comperable situation using an everyday analogy.

Take two cars, "A" and "B". "A" has a speed-o-meter and a working o-dometer, plus a perfectly working clock. "B" doesn't have a speed-o-meter or o-dometer and he isn't aware that the batteries in his clock are low and it is ticking at only one half the rate as car A's clock. They set off and drive side by side and after one hour according to "A" they stop.

According to car "A" they were driving 60 km/h and they went 60 km and arrived in just one hour and everything is just fine.

But "B" disagrees he says look we if we were going 60 km/h then we only went 30 km, not 60 km because we only drove for one half hour.

We obviously are not going to accept that "B" only went 30 km because his clock ran slow. But that is what Special Relativity does.

The correct way to view this to now have meter markers placed along the 60 km trip course. Now when "B" is driving alongside "A" going 60 km/h according to "A" then "B" sees meter markers passing by at a rate of 33.3333n meter markers per second according to his clock. So when they arrive in one half hour by his clock he concludes they went 60 km but drove 120 km/h.

Accepting this view of relativty it remains mathematically consistant but the above counter intuitive aspects vanish. The v = c limit in relativity only applies to velocity relative to the rest frame view. In the moving frame view velocity approaches infinity as he approaches v = c relative to the rest observer.

But the universe remains quiesent and undisturbed by relavistic changes made to the moving observer.

I understand this is speculation but it does not deny any observed facts or emperical data and it does eliminate many counter intuitive issues. Relativity survives

Edited for spelling and mathematical functions 26 Feb 7:55AM - MacM
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Postby Lincoln on February 26th, 2006, 1:33 pm 

I will read, absorb and answer, but first require clarification. I expect that you have used some language in a sloppy manner. Either that, or we already have deviated from special relativity.

Specifically in point 1, you state that you are accelerating at high velocity. These two terms cannot be used in this context. Further, acceleration is outside the purview of SR. Ditto in point 2.

The short response to point 3 is yes, SR says exactly that (at least sort of). But I await your clarifications before I further respond.

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Postby Mac on February 26th, 2006, 1:42 pm 

Lincoln wrote:I will read, absorb and answer, but first require clarification. I expect that you have used some language in a sloppy manner. Either that, or we already have deviated from special relativity.

Specifically in point 1, you state that you are accelerating at high velocity. These two terms cannot be used in this context. Further, acceleration is outside the purview of SR. Ditto in point 2.

The short response to point 3 is yes, SR says exactly that (at least sort of). But I await your clarifications before I further respond.

D


I fully understand and agree that accelerating frames is outside the purview of SR. However pragmatically and understanding that at any instant in time taking the limit toward zero the accelerating object can be considered to be inertial and at a specific velocity.

Understanding that acceleration is actually a GR consideration but taking a macroscopic view of the consequences it is the sequences of instantaneous results that I am applying as SR.

I hope that clarifies my meaning and that you accept that premis. It is my intent to demonstrate the consequence of SR's prediction of spatial contraction.

To apply the strict application limit of SR and GR in this case would seem to restrict an accelerating observer from having observation or physical contact with the surrounding universe during acceleration. That would infer that when we are going 30 Mph and accelerate to 60 Mph we could not see the change in speed nor changes in distance to objects along our path.

I would find that an unacceptable restriction to everyday reality soly to support relativity.

REWRITE for Clarity: 1 - Given a large initial seperation, and moving away from earth at high relavistic velocity, then begin to accelerate and the earth actually gets closer the faster you receed.


Edited 26 Feb 19:22PM for typos and added clarification content - MacM
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Postby Lincoln on February 28th, 2006, 5:40 pm 

Hi....

First some minor details. As I may have mentioned to BioWizard, the months of March through May will require me to focus my efforts on some critical equipment refurbishment. Thus I will have fewer waking moments for this debate.

Now back to your points. To use SR in an accelerating reference frame is always a bit dangerous and frequently not done. Nontheless, as you pointed out, one can solve some carefully-designed problems using SR and acceleration. Since I had not done such a problem for a while, it took a little longer to do the calculation than a standard one might have.

Further you use the word intuitive rather liberally. Intuition is not an extraordinarily good guide. It is possible to generate a relativistic intuition and many physicists have. So you really can't use intuition as an supporting principle. Measurement and consistency of theory are the only true arbiters between different world views.

For your point 1, I assume two objects are separated by a distance d_o. Both are objects are at rest. At time t = 0, one object accelerates in an increasing radial direction as compared to the other. It accelerates for a distance d, as defined in the original rest frame. During that time, it accumulates an energy E and at the end of the acceleration region it is travelling with a lorentz gamma_F. Its gamma as a function of distance x (where x is defined to be 0 < x < d and is only valid in the original rest frame and only during the acceleration period) is:

gamma = (x / d) * (gamma_F - 1) + 1

Then the distance between the two objects in the accelerating frame is:

d' = (d_o + x)/[(x/d) * (gamma_F - 1) + 1].

Which, if I have done my algebra properly, reduces to the correct answer in the obvious cases (gamma_F = 1 or x = 0 or d_o = 0).

I leave it as an exercise for the student (those of you who were physics students certainly remember this phrase) to find the criteria whereby the accelerating reference frame leaves the distance unchanged.

In any event, for any gamma above that threshold, yes, I think the distance shortens with increasing acceleration. Below that threshold, you get increasing distances in both frames.

For point 3, I guess I concur, with the amplification that the lorentz contraction is only in the direction of motion. Thus the universe is still infinite in the transverse direction. So the volume is clearly decreased due to lorentz contraction, but not to the degree that you suggest.

Your point 2 is described with insufficient precision to solve. While your basic point is quite understandable, I await a more precisely defined problem. For instance you do not define specify the relative directions of your 0.866 c and 0.9 c. I also am uncertain as to the need for two velocities for the point you are attempting to make. Further, at least one of your numbers (accelerating at 1 g for 12 days bringing you to a distance of 3% of a light year) is, I believe, wrong. Such an acceleration over the specified time will bring the speed of the object to 3%c, while the distance covered is more like 0.05% of a light year. Given the small velocities in the problem, you can do this calculation using simple Newtonian dynamics. In any event, tighten the definition of the problem and I'll take another look at it.

Finally, your analogy to other readers is a bit weak. It presupposes no lorentz contraction effects and therefore posits non-uniform light speed. You need to describe how the wavelength and frequency of light is affected by the non-constancy of the speed of light, in order to see how they would be manifested in interferometer experiments.

What precisely is it that offends you about relativity? The time dilation is essentially trivial to establish experimentally. The constancy of the speed of light is less so. The lorentz contraction is established (even pre-Einstein) by the null result of Michelson-Morley experiment. I am attempting to translate a more modern example of lorentz contraction from recent heavy-ion data, but the calculation and comparison to experimental results will take some additional work, as I do not have access to the most modern data in the most useful format. Additional massaging will be required.

The really fundamental insight into relativty and its most interesting property is that each and every object is always travelling through spacetime (not space) at the speed of light. The more velocity it has in space, the less velocity it has in time. And that's the fundamental crux of the whole thing. This idea requires a more sophisticated mathematical structure...the so-called 4-momentum formulation. But from it one can easily see that everything that bothers non-physicists about relativity comes from the equivalence of space and time and the constancy of the speed of light in spacetime. It even explains why the maximum speed is the speed of light. Now specifically why the speed of light has the numeric value it does, well that's an unanswered question. But not an interesting one for the context of this debate.

D
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Postby Mac on March 1st, 2006, 12:11 am 

Don,

Lincoln wrote:Hi....

First some minor details. As I may have mentioned to BioWizard, the months of March through May will require me to focus my efforts on some critical equipment refurbishment. Thus I will have fewer waking moments for this debate.


Certainly understandable and appreciated.

Now back to your points. To use SR in an accelerating reference frame is always a bit dangerous and frequently not done. Nontheless, as you pointed out, one can solve some carefully-designed problems using SR and acceleration. Since I had not done such a problem for a while, it took a little longer to do the calculation than a standard one might have.


Correct. I am impressed with your candor. My historical experience has been to have the professional dig in and put forth impediments to proceeding.

Further you use the word intuitive rather liberally. Intuition is not an extraordinarily good guide. It is possible to generate a relativistic intuition and many physicists have. So you really can't use intuition as an supporting principle. Measurement and consistency of theory are the only true arbiters between different world views.


Agreed. The universe (nature) really doesn't seem to care if we find it intuitively correct. :D But consistancy may be valid in more than one format and the one selected for Special Relativity is not to the exclusion of others. It is only important that they are consistant and do not conflict with emperical data or observation.

For your point 1, ./...................................................................................................................

In any event, for any gamma above that threshold, yes, I think the distance shortens with increasing acceleration. Below that threshold, you get increasing distances in both frames.


Again we are in agreement. But it is a counter intuitive consequence of the prediction of spatial contraction in SR that under the conditions I have specified the faster one accelerates away from earth the closer the earth becomes.

For point 3, I guess I concur, with the amplification that the lorentz contraction is only in the direction of motion. Thus the universe is still infinite in the transverse direction. So the volume is clearly decreased due to lorentz contraction, but not to the degree that you suggest.


I take exception to the assumption that the universe is infinite in any direction, though I suggest that is a matter of opinion and unproveable either way. But assuming it is infinite then it could not contract to zero in the direction of motion even at v = c.

Assuming it is not infinite (and I base that on the understanding that nothing physical can become infinite) then indeed my example is exagerated but in theory the universe collapses to a virtual zero volume at v = c.

Your point 2 is described with insufficient precision to solve. While your basic point is quite understandable, I await a more precisely defined problem. For instance you do not define specify the relative directions of your 0.866 c and 0.9 c.


Valid complaint. My opology. I to frequently think others know what I mean and don't give adequate specifications.

The velocity vectors are both along the line of sight to the cosmic object.

I also am uncertain as to the need for two velocities for the point you are attempting to make.


The reason I used two velocities is to put the gendanken into a relavistic regime to start. Then make a small change which has a large affect in a shorter period of time.

Further, at least one of your numbers (accelerating at 1 g for 12 days bringing you to a distance of 3% of a light year) is, I believe, wrong.

Such an acceleration over the specified time will bring the speed of the object to 3%c, while the distance covered is more like 0.05% of a light year. Given the small velocities in the problem, you can do this calculation using simple Newtonian dynamics. In any event, tighten the definition of the problem and I'll take another look at it.


dv = at. 1g = 9.8m/s^2. 12 days = 3,600 seconds/hour * 24 hours/day * 12 days = 1,036,800 seconds.

9.8m/s^2 * 1,036,800 s = 10,160,640m/s delta. 10,160,640m/s delta / 299,790,000m/s = 0.03389c

s =Vo*t + a*t^2 / 2 = (259,618,140m/s * 1,036,800 s) + (9.8m/s^2 * (1,036,800 s)^2 / 2) = 2.692E14m + 5.267E12m = 2.745E14m.

1 lyr = 2.9979E8m/s * 3.6E2Sec/Hr * 24 Hr/day * 365 days/yr = 9.454E15m.

2.745E14m / 9.454E15m = 0.029 = 3%.

What am I missing?

Finally, your analogy to other readers is a bit weak. It presupposes no lorentz contraction effects and therefore posits non-uniform light speed. You need to describe how the wavelength and frequency of light is affected by the non-constancy of the speed of light, in order to see how they would be manifested in interferometer experiments.


Your response seems to imply that light would become variant in the framework I have proposed. I don't follow that conclusion.

It presupposes that the invariance is based on SR relativity's spatial contraction. While there are alternative explanations for such invariance.

What precisely is it that offends you about relativity?


I am not offended. I am less than impressed by the unwillingness of most to consider alternative explanations. Notice I am not saying give up the invariance of light or give up time dilation. Nothing that has been demonstrated emprically must be given up to think alternative explanations.

The alternatives seem to provide a more rational explanation for our observations. It simply does not seem appropriate that one should use a calculated value and impose that result on another frame. That the frame should use physical enities and make its own calculations.

While testing of alternatives has been far less prevelant and generally scorned in the mainstream, I am more inclined to believe the alternative where there is an alternative explanation for invariance of light and physics does not impose a calculated value on the frame and then force a change in physical reality.

The time dilation is essentially trivial to establish experimentally.


Agreed.

The constancy of the speed of light is less so.


Agreed.

The lorentz contraction is established (even pre-Einstein) by the null result of Michelson-Morley experiment.


M&M only supports a concept of material contraction, not spatial contraction. I in fact find it borderline bizzar that we can talk about contractimg, curving, etc something which has permittivity, permability and is packed with unimaginable energy but relativity denies any physical existance.

I am attempting to translate a more modern example of lorentz contraction from recent heavy-ion data, but the calculation and comparison to experimental results will take some additional work, as I do not have access to the most modern data in the most useful format. Additional massaging will be required.


I would look forward to any substantiating emperical findings that supports spatial contraction.

The really fundamental insight into relativty and its most interesting property is that each and every object is always travelling through spacetime (not space) at the speed of light. The more velocity it has in space, the less velocity it has in time. And that's the fundamental crux of the whole thing. This idea requires a more sophisticated mathematical structure...the so-called 4-momentum formulation. But from it one can easily see that everything that bothers non-physicists about relativity comes from the equivalence of space and time and the constancy of the speed of light in spacetime. It even explains why the maximum speed is the speed of light. Now specifically why the speed of light has the numeric value it does, well that's an unanswered question. But not an interesting one for the context of this debate.

D


I am aware of the merging of space-time via the 4-momentum. I am familiar with Lorentz Transforms but these are mathematical concepts and frankly have little to do with a physical universe. That is they may well be useful at predicting things but they do not describe the underlying physical structure.

Unless I have missed some point of your reply, you have agreed to my conclusions in #1 and #3. I anticipate you will also agree with #2. You are also hedging a bit by playing down the signifigance of such consequences as "getting closer the faster you fly away from something".

I contend that elimination of issues like 1 - 3 above, by considering a different relativity is fundamentally indicated. I do not advocate throwing out the baby with the bath water but I do think relativists should be more open about the unacceptability of some consequences of SR as structured and advocated and admit that it likely is not a true description of the physical reality.


Edited for typo's 28 Feb 06, 21:12PM - MacM
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Postby Lincoln on March 1st, 2006, 9:58 am 

Professionals don't dig in their heels capriciously. They simply have better things to do than argue about a theory which has agreed with all measurements. And, if you can't get a yardstick and measure the distance between this star and the next, all the while travelling at various high speeds, that isn't so critical. The measurements that CAN be made agree IDENTICALLY with the predictions of relativity.

You focus, for some reason, on spatial contraction. The whole time dilation thing is freakily bizarre from a pre-Einstein point of view. Yet this is utterly, unambiguously and nearly trivially shown. (Well as trivial as particle lifetime experiments ever are.) The constancy of the speed of light is a bit harder. But assuming the constancy of the speed of light is completely consistent with the doppler effect observed by stars receding at substantial fractions of the speed of light.

Focusing on the energy side of things, which is where the measurements are the best, we know that a particle has a rest mass and further this rest mass can be converted to energy. The annihilation of electrons and protons always results into two photons, each carrying 0.511 MeV of energy. Further, pumping energy into a particle increases its velocity. You can measure the velocity of the particle and the energy of the particle and it agrees identically with Einstein's E = gamma * m * c^2. Further, no matter how much energy we pump into an accelerated particle, it has never been measured to exceed the speed of light. Period.

So the whole 4-momentum (energy, momentum and mass) thing has been established to agree with data to incredible precision. Time dilation is observed. Light has never been measured to have a velocity other than 3E8. Object contraction contraction is not something that I think has been directly observed. (Note this may reflect ignorance of an experimental result, rather than a failure to prove.) But everything else has been observed. So, if you believe that spatial time contraction is not observed, but time is, along with the constancy of the speed of light, as well as conservation of energy and the relationship between the energy of light and its wavelength, I think you've put yourself in a box.

Regarding more piecemeal responses to your post. (I'm not a big fan of the insert-and-reply approach.)

The universe may or may not be infinite. Its radial dimension exceeds 13.7 billion light years. Because of the flatness of space observed by the angular separation of the non-uniformities of the 3K background radiation, we think it likely that the universe experienced a period of rapid (super-luminal!) growth early on. (Note that this does not negate relativity, as relativity describes the motion of things through space, not the expansion of space itself.) If this theory is true, and it is a new enough idea (25 years) that the debate continues, although it is winding down, then the universe is enormously bigger than the piece we see.

But in any event, space is very, very big. The contraction as v approaches c will cause the longitudinal distance to contract. However, since relativity does not allow a massive object to reach c, this is now a calculus limit problem. Zero times infinity can be zero, infinity or a real number, depending on the relative sizes of the infinity and the zero.

Your example 2 still requires clarification, as you have not specified radial or antiradial motion for the cosmic object. In fact, the point in which I claimed an error in calculation stems from the confusion of how the example was specified. I was calculating

s = 0.5 * g * t^2

which gives 0.05% of a lightyear. You had it going with an initial velocity, which was not clear to me. Your calculation is not relativistic, as a constant force will not provide a constant acceleration in this instance. At low velocity, you can use Newtonian formulae, but as you get upwards towards 0.1 c, you need to account for the relativistic effects. The easiest way to do this is to use the work-energy theorem, whereby you calculate the amount of energy increase and from that calculate the velocity increase. But even in your calculation, the effect due to the acceleration term is negligible (about 2%) as compared to the initial velocity term. I would say that the acceleration term is actually even smaller, but since it is not a dominant one, it can be neglected (for this specific example only).

Perhaps I didn't understand your car analogy. It seemed to me that because you were keeping space the same and slowing down a clock, someone was claiming that the speed was higher. I presume that this would be true for light as well. Please clarify.

If you are distinguishing so religiously the idea of "object" vs. "spatial" contraction, I am not sure what I had in mind will satisfy you. Because I was thinking about something that you would call object contraction. So what are you requiring to demonstrate or falsify spatial contraction? It would appear to me that again you are putting yourself into a box. How would you do the measurement? Take a string and run it from one star to another, then measure the length of the string? Then accelerate the string and measure its length? How can you measure in a way that does not require a physical object, or instead uses a known velocity and a time measurement to infer distance?

Finally, relativity most emphatically does not just predict object contraction, as we have both agreed. To posit an object contraction in the absence of spatial contraction requires a theory which somehow distinguishes between a space point which includes matter vs. one in which there is nothing. This is notably absent from relativity of course. It only deals with positions and time.

And further, if you posit object contraction in the absence of spatial contraction, what precisely do you see as contracting within an object? Atoms are, after all, separated by space. An object of this form (mostly space with small, localized bits of matter spread uniformly throughout), experiencing contraction, is showing spatial contraction. In fact, I think this is the thing you need to focus upon. If you would accept measuring galaxies being closer to one another as evidence of spatial contraction, why is it not just as correct for atoms getting closer to one another? And if objects spatially contract, then trivially so does space. This is, unless you are somehow imagining the interatomic forces increasing in strength in one direction, but not in the two transverse ones. And for you to assert that, I would need you to posit a well-described theoretical framework.

D
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Postby Mac on March 1st, 2006, 11:40 am 

Don,

Perhaps I should have been more explicit about professionals digging in their heels. :D I was more generally referring to those I have communicated with via the internet forums wherein they clearly have some time.

I am not actually focused on length contraction but the rules limit the discussion to only one topic and it has been the first chosen. You can be assured there are others. Ha.

Objects not exceeding the speed of light is actually a frame dependant point of view. An observer that points flashlights in opposite directions sees the beams seperate at 2c but each beam is certainly limited to "c".

With respect to particles not exceeding "c" regardless of energy input. You must ask yourself the velocity limit of your accelerating force. It is EM is it not? I don't want to deviate from the rules and get into other topics but this issue appears to be more about energy transfer efficiency than relativity directly.

I would certainly agree it would seem to be a box if I were to also accept that the invariance of light had no other explanations. But it does. Even if it didn't I would have to contend that the conditions I have pointed out as a resuslt of spatial contraction mandates that we go find alternative explanations.

With respect to the diameter of the universe I have seen a recent study which calculated that it is 156 Billion Lyr not 15 Billion lyr but the fact that it is big certainly goes unchallenged.

We are in agreement that my #2 used Newtonian acceleration calculations but as you have pointed out the differance in result doesn't alter the conclusion.

Acceleration of an observer that has a relavisitc velocity to an object should see distance change at multiples of "c" if spatial contraction were physically real. In spite of the fact that we see objects receeding at almost v = c near the edge of the universe and inspite of the fact that we have an accelerating and decelerating velocity relative to such objects due to our orbit around the sun, we do not see such an affect.

My point being that if spatial contraction were true then we should infact see distance change rates in such objects which exceed v = c by many multiples.

With respect to the car analogy and light velocity. Your fixation on the invariance issue is because you accept that observation as being soly due to spatial contraction. I see no reason to assume that light in the case where only the clock dilates (no spatial contraction) and the observers computed higher velocity relative to material things would result in light being recorded as anything other than "c".

Relativity comes into existance because you envision a photon having some magical power to exist to every observer at the same velocity regardless of the velocity of the observer to the source. Suppose for example that photons are frame dependant. That is they only exist at some quantum energy level, then moving observers are not observing the same photons.

I would have to say it is not "I" that is in a box but physics and SRT. Because the "inability" to prove or falsify spatial contraction means Special Relativity is not even a valid theory. To be considered validtheory it must be falsifiable.

As to what is contracting if not space, that is a tough one but it seems recent studies have shown anisotropy in the CMB and that we have an absolute velocity to the CMB. In fact another recent study computed the velocity by a study of cosmic muons that reached the earth. The numbers varied in good agreement with the absolute motion of the earth to the CMB.

Link added: http://redshift.vif.com/JournalFiles/Pr ... 3N2MON.PDF

In other words I suggest that the CMB is indicative of a spacial medium and that relativity is a function of absolute motion (however immeasureable) and not mere relative velocity. Relative velocity simply provides no physics input. Cases can be cited where only one observer accelerates (F=ma) and that is the observer which undergoes time dilation, not the resting observer. That is what emperical data actually supports. It does not support the concept of reciprocity of relative motion.


Edited to add link and correct typo's, 1 March 09:45AM - MacM
Last edited by Mac on March 1st, 2006, 12:56 pm, edited 1 time in total.
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Postby Lincoln on March 1st, 2006, 12:48 pm 

Well, the professionals digging in their heels is a protective measure. This is because we have all had dealings with relativity and/or quantum mechanics haters/skeptics/whatever you want to call them. The discussions are rarely scientific, frequently religious and never, ever, ever result in the skeptic conceding anything. This is why I only reluctantly acceded to Bio's request. Most physicists have more sense than me.

Now regarding the points at hand, I think the first discussion is resolved.

Michelson-Morley clearly supports Lorentz-Fitzgerald contraction. One can claim this is object contraction or spatial contraction. However, since the separation between atoms is only space, the contraction of an object requires either the atoms come closer together or that the space between them is contracted. Clearly relativity resolves the conundrum through spatial contraction, but of course the decreased distance within a non-contracted space is not excluded from this single chain of thought. But you then need to posit a mechanism that explains this, or the spatial contraction of relativity holds. And I won't pursue this chain of thought further without a plausible mechanism for this advanced (or an explanation not tendered thus far).

I concede that a person shooting two objects oriented 180 degrees from one another and at 0.9 c would claim that their recession velocity to be 1.8 c. There's nothing within relativity that negates this. But you knew this and it's not even a very interesting point. However, if you asked either object to determine the other object's velocity, it would be sub-lightspeed.

I've heard the argument about electromagnetism accelerating particles being the explanation why we can't exceed the speed of light. In fact the last person who contacted me out of the blue was a proponent of this idea. He even held conferences on the subject. Very sad. However the argument is, as frequently stated, totally fallacious. The usual argument is that a rocket, continuously venting exhaust out the back, can exceed the speed of light due to the law of conservation of momentum. This argument is made within a Newtonian framework. Doesn't work. Here's why.

If an electron is accelerated in a Newtonian fashion, using particles of light speed, it will accelerate until its energy is 0.5 * m(electron) * c^2. And this just isn't the case. Thus you need something to explain the energy build up in the absence of additional velocity.

The size of the universe is unknown. The edge of the visible universe is currently taken to be 13.7 billion light years, where the precision of the measurement is small enough that the ".7" part of the number is significant. However, the universe is likely larger than that. This is beyond the trivial point that the universe has expanded since the CMB light was emitted. There are many calculations, none restricted very much by the data, as to the size of the universe. I don't know wherer you got the 156 GLY number, but it is no more supported than many other thoughts. Personally, I suspect the universe is not a mere factor of 10 larger than the visble horizon. I suspect it is much, much larger than that. Ten just isn't a "natural" number. But I digress.

We are not in agreement regarding your point 2. We merely clarified a number you stated. Since your calculation does not include time dilation, (I think?) I've not calculated anything. I can obviously make up the problem I think you're posing, but I don't want to waste time on a problem that you may later claim inadequately illustrates your point.

You claim that relativity comes into existence because of the invariance of the speed of light. This is absolutely correct. This bothered me inordinately when I first heard of the idea. This is why I come back to the proper 4-momentum formulation of relativity, in which you can transform between reference frames by using 4-Dimensional rotation matrices and the Minkowski metric. The essential point, stripping the whole thing from the matrix formulation is the following. The most important way to look at relativity is to consider the so-called "Lorentz invariants". Two of these are the proper time and the rest mass. These can be straightforwardly written as:

m^2 c^4 = E^2 - (p c)^2
and
(c t)^2 = (c tau)^2 - (x)^2

where x is the 3D position vector, tau is the relativistic time, t is the proper time, p is momentum, E is energy, m is the rest mass and c is the speed of light.

The abolute beauty of this formulation is the fact that you realize that you can change perceived time and perceived space and they always must be related in a way that is invariant. And the obvious interpretation of this formulation is that ALL objects travel at ONE speed (c) through spacetime. You can change the fraction travelling through space or the fraction travelling through perceived time. As you go faster in space, you go slower in perceived time. And since c is the spacetime speed of everything, it is unsurprising that when you finally go at c in space, you cannot exceed it. You have just stolen all of the "time speed" and put it into "space speed".

Let's not get off into CMB until this is resolved. But I don't see how the cosmic muons can have any relevance to this concept. Muons are created in the upper atmosphere and reach the Earth is a quasi-isotropic manner. That is to say, the low energy protons from the sun are guided by the Earth's magnetic field, but high energy protons are cosmic in origin and of sufficient energy to be essentially undeflected by the Earth's magnetic field. I fail to see how the Earth's motion through the CMB is of relevance. And since we have mentioned CMB, the simple fact is that the CMB was emitted from a reference sphere about 14 GY ago. The light emitted was uniform and isotropic. We are in motion with respect to this sphere and so we view a doppler shift of the light. This doesn't provide any absolute reference frame. After all, the CMB emission sphere could be comoving with the Earth. But let's not get off into that yet.

So explain how the observed object contraction of Michelson Morley is either (a) not the explanation for the null ether experiment or (b) this object contraction does not require spatial contraction due to some physical mechanism that increases the electromagnetic force in one direction, but not in the two transverse ones.
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Postby Mac on March 1st, 2006, 10:31 pm 

Don,

We are all glad you lack the good sense to turn BioWizard down. :D

I believe one could view contraction of material objects as perhaps a bit of both space internal and external to the atoms having contracted. I don't however, believe that either predicts or supports the conclusion of spatial contraction of a relavistcally moving body to other objects.

That is one can envision contraction of the moving body without contraction of the space between it and someother object.

The reason of course would be that such contraction was a function of absolute motion to the universal background and not relative velocity to other objects.

We are in agreement as to the prediction of SRT that v = c is a limit. I think we disagree as to the limits of applicability. In the view I have presented v = c would be a limit from the resting observers frame view but in the moving frame view one could reach many multiples of c. In that frame one would not see the universe collapse in front of you but would see yourself traveling extraordinarily fast through the universal divide.

The concept of energy transfer efficiency can explain excess particle energy nicely without spatial contraction.

Deleted paragraph inadverently left from Dr Lincoln's post.

Ref. my #2: I take exception to your conclusion that starting with a large seperation between observer and target object that accelerating from an initially high relavistic velocity, doesn't produce a dx / dt >> c due to predicted spatial contraction. I would like to see that claim supported.

Given a rocket and a star with an initial seperation of 100 lyr at a relative velocity of 0.866c to each other and you then accelerate the rocket at 1g until you are at 0.9c; what do you claim is the closure rate between the rocket and star from the rockets frame of referance? Noting that the rate is changing please give only the peak rate of change.

In fact the issue of not including time dilation in the calculation means that including time dilation would cause distance change to appear to be even greater per given time. i.e same distance change in shorter time by the dilated clock.

I really don't have a lot of problem with the mathematics (4 momentum, transformations, etc.) as long as the users acknowledge that they are unrestricted mathematics. That is there is likely physical constraints which are not being applied that limit their applicability.

I note with some pleasure your use of the term "percieved" with respect to time-space. I have far less problem with "perception" than I do with claims of physical realities in regard to many relavistic affects.

I would find raising excess energy of an accelerated particle (which is being used to imply a correctness of the relative velocity view) but then objecting to raising the issue of cosmic muon anisotropy linked to absolute motion of the solar system to the CMB and not relative motion between the earth and the muon, to be somewhat biased.

However, I do think both issues are straying a bit from the issue of this debate, even though I believe the muon issue is more directly linked to it. That is because muon time dilation has been a major "proof" expoused by relativists and it is reciprocity in the form of spatial contraction in the muon frame which is now drawn into question in that it is not a function of reciprocity of relative velocity to earth but as a function of absolute motion to the CMB.

You seem to believe, erroneously, that an absolute motion concept must identify the absolute value of motion. I disagree with that. In the muon case we can see that relavistic affects are not merely due to relative velocity to the earth. We really do not need to know or understand the CMB relationsip to perhaps some other frame that is not observed or measureable.

1 - M&M was not actually a null result. Many simular experiments have been run since and they too were not null results. Each infact produced cyclical dinural results.

The results however, were only a fraction of what the old static ether concept predicted. This became the basis for the "Entrained" ether concepts. That is ether that is dragged along with a massive body.

I am not advocating any of them but merely trying to keep this as factual as possible.

2 - No "One Way" light velocity tests have been completed to detect the affects of relative motion. Round trip light motion which might include (c + v ) and (c - v ) components produce a net null result.

I have been advised that we are approaching the allowed post (time limit) for this debate so I want to use this opportunity to begin a closing position.

As I said at the outset I find relativity to be an indicated fact. More specifically that emperical data supports time dilation due to "Actual" motion but not "Relative" motion.

By "Actual" velocity I mean a body only has velocity if it has undergone an F = ma period. Relative velocity is a perception, an illusion but not true motion.

Every test done over the past 100 years has not showed a reciprocity of time dilation.

i.e. - Did the pilots of the H&K atomic clock tests return home to find the earth bound clocks had lost time in relation to their clocks? Of course not.

Does a GPS orbiting clock find the earth based clock running slower than itself? Of course not.

The orbiting clock is prelaunch calibrated to offset both GR affects and "Absolute" velocity to the ECI (Earth Centered Inertial) referance frame, not a relative velocity to the surface or its clocks.

In fact a calculation of relative velocity time dilation between an orbting clock and a clock at the equator produces an incorrect time dilation.

Yes I know the arguement about orbit not being inertial, that it is an accelerating frame. I have also seen it argued that it is inertial because it is equivelent to freefall.

Your input on this issue might be appreciated by other members as well.


It is important to note that lack of time dilation reciprocity also prohibits reciprocity by length contraction. That is SR has time altered in one frame and distance altered in the other as recipocal responses to relative velocity.

As I have tried to point out using a calculated value of one frame and imposing it on another frame causing a physical change in the other frame simply is not acceptable science.

I am not saying it is not useful mathematically. I am saying it is worthless in terms of a physical theory.

The consequences of such a theory, which I have pointed out some, cannot be accepted unless we simply turn a blind eye to common sense and physical possibilities.

I chose to look at those consequences as a driving force to find a correct solution physically.

Unfortunately current physics really no longer care much for physical reality they are only concerned with the ability to predict mathematically.

I am sure neither of us have made a convert of the other but I respect your willingness to come here and give this forum some first class insight to conventional physics and for therein allowing me the opportunity to have a soap box to call for change. :D

Thanks.

Edited to make typo corrections and remove paragraph from another post - 1 March, 8:22PM - MacM
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Postby Lincoln on March 2nd, 2006, 9:45 am 

Huh...

Just a relatively short note. More later.

First, if you view length contraction as space internal and external to the atoms being contracted, then you have conceded the spatial distortion hypothesis. It appears that you want to distinguish between spatial contraction within a body and without a body. This implies that the matter/energy embodied in the object is the root cause of the spatial contraction, or that it is a fundamental property of the universe. If you pick number one, then you need to posit a mechanism. Until I hear of such a mechanism, that option can be excluded for the purposes of this debate. If it is the second, then relativity holds.

Now, if I understand your reasoning, you refute this last sentence, by suggesting that it is absolute motion to some preferred reference frame, usually called the god frame. In your case, this is the CMB (which gives a nod to George Smoot's "Faces of God" comment of 1992 that comes back periodically to haunt him.)

I find the concept of an abolute coordinate system fairly hard to fathom. The CMB that we see comes from a sphere of radius 13.7 GLy, centered on the Earth. Because of the constancy of the speed of light, we see a doppler shift of the wavelength of light....the cause of the dipole microwave anisotropy. I don't know what worldview you hold as to the creation of the universe (Big Bang, Steady State, hand of god or what...all without relativity), but depending on which one, you get different predictions. However, the appeal to some absolute reference frame then obviates the need to explain the standard Gedanken experiment of two particles moving in a universe devoid of any other features, including CMB. You should think about how you would handle that situation.

I have not said I disagree with your #2, simply that I have not looked carefully at it. Actually I intend to do so, but still find the definition lacking. Here is what I will do. I will define a problem and you can give it the thumbs up or down. I use a particle accelerator as my example, as I know how to calculate it easily, and the accelerations are such that I can get to near light speed in a couple of meters. (Plus a rocket has the whole varying mass problem to add to the situation.) A particle accelerator is placed a 100 lyr from Earth. Said accelerator has no motion in the radial direction. An electron, initially at rest in the accelerator, is then accelerated with a constant force until it is moving at 0.8 c, moving radially outwards. The acceleration distance is (say) on the order of meters, in the accelerator's rest frame. Discuss the velocity of the Earth, as viewed by the electron. Since the electron sees the universe contracted, you are concerned that the Earth will appear to leap towards the electron at superluminal speeds. I chose the scenario and numbers so as to be able to easily calculate. Do you accept this (well-defined) problem as illustrating your point?

Your comment "Unfortunately current physics really no longer care much for physical reality they are only concerned with the ability to predict mathematically." flirts dangerously with, but does not quite cross, the snarky line. Physicists only care about the degree to which the results of their mathematical calcuations agree with measurements. The theory is of course interpreted, but only to the point whereby it predicts additional physical phenomena. Beyond that, we leave world view debates to philosophers.

P.S. You frequently go back and edit old posts. I've often answered one, only to find that after I posted it that the web site changed. Either you need to sit on your posts until you are sure of them, or I need to wait a day or two to make sure that they have settled down. I don't care which. But the case where a reply is to an earlier version of a post simply isn't working.

I will handle the remainder of the piecemeal aspects of the post later, perhaps as early as today.

D
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Postby Mac on March 2nd, 2006, 10:26 am 

Don,

My view is indeed that relativity is in regard to object energy to a universal background. I object to the suggestion this is a God frame.

Off topic but God solutions are unthinkable to me.

My view is simular to Big Bang but without a "Singularity". It is more of a "Big Rip" view.

"N"othingness becomes "S"omethingness by Bifurcation. N ---------> (+S) + (-S) or 1 + (-1) ---------> 0 for Black Holes.

No creation because collectively everything adds to zero.

If you are computing the closure rate of the electron to the earth, including the spatial contraction claimed for the electron frame, then yes I would think your example would work.

I note that #2 is actually a subset feature of #3 which you have already agreed on. So I think the problem here is in the communication as to what I have meant.

My position is not that I can replace relativity. That would be the terra firma of physicist such as yourself (if they would only try to find such processes) but that the features I am pointing out which are casually considered to be merely "Counter Intuitive" are impossible physical nonsense and mandate a different physical theory.
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Postby Lincoln on March 2nd, 2006, 11:42 am 

Religious overtones aside, it's still called the god frame.

I was in the shower today, somewhere between lather, rinse (repeat), when I realized that I made an error in my calculation. The shower part of this story is relevant because if I were a lawyer, you'd be just buried in billable minutes. I believe the conceptual error also suffuses your intuition.

The usual Lorentz contraction equation is calculated at a single time. However you are measuring a distance at two separate times. Thus in order to do this properly, you need to go back to the general space/time transformation equations and start over. This is easy to do in the context of an inertial reference frame. However, you are positing comparing a space and time in one inertial frame, to another reference frame that may be inertial after the non-inertial period or to an accelerating reference frame, in which the particle/rocket/whatever is non-inertial.

The space/time relativity equations have embedded within them four variables. x position, time, velocity and the speed of light. Generally two of those are made constant....v and c. In my previous calculation, I made time and c constant. Of course, time is not constant.

Bad physicist! Bad! No donuts for you!

I shall redo. It may be that you have defined the problem in such a way that the numerical answer does not change. Were this a standard relativity problem, it could be solved in a few minutes. The non-inertial aspects of this problem require thought and calculus. This will take a while to get to. My priorities are elsewhere, but I will see if I can get to it.

But it may very well be that your intuition is guided by the fact that you are mis-using the Lorentz contraction equation.

More on the piecemeal reply later.

D
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Postby Mac on March 2nd, 2006, 3:32 pm 

Lincoln wrote:Bad physicist! Bad! No donuts for you!
:shock: :D


I actually feel you are over complicating the issue by attempting to produce a specific mathemtical result. If one looks at #3 and applies that ultimate condition from a rest postion in #2, that is accelerating at 1g for (as I recall) about 90 days to approach v = c, you clearly have 15 Billion lyr dimensions being traversed in much less than 90 days due to the dilated clock of the accelerating frame.

Specific calculations aside it seems unargueable that the pilot of such a craft sees his change in speed and the change in distance to remote objects even during acceleration. So while I admit the mathematics are complex I think pragmatically it is quite simple dx / dt >>>> c as viewed from the accelerating frame under these conditions.

Since we do not observe any such relationships to relavistically moving remote objects in the outer fringes of the universe it suggests further that spatial contraction is an invalid concept.
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Postby Lincoln on March 2nd, 2006, 4:14 pm 

I disagree with you strongly. The essence of a physics theory is to calculate something. If one tries to "reason" without the relevant mathematics, it is quite possible to misuse equations and come to erroneous conclusions, as I believe is currently the case.

Now taking off my mathematician's hat and putting on my physicist's one, I believe I can explain the conundrum that lead me to realize I made an error. While the superluminal issue you raise offended me, I have rarely used acceleration in a special relativity context and thus my intuition is less developed in that situation than it might be. However, one thing I do know is the following. After the acceleration phase is complete, relativity mandates that the Earth be receding at 0.9 c in the rest frame of the electron. According to the problem we have set up (and probably incorrectly), the moment the electron goes ballistic, the velocity of the Earth in the rest frame of the electron goes instantaneously from superluminally closing to receding at 0.9 c. And singularities of this nature are physically impossible. There is no way that relativity would predict such a stupid thing.

So we have one of two options. The first is to toss Relativity. The second is to figure out where the principles of SR have been misused. And since (a) SR works pretty well and (b) it's been a while since I needed to do acceleration in the SR context, I figured I made a mistake. In retrospect, it is obvious that I did. I will correct the problem and probably retract my earlier concession. More when I know.

And, if you will forgive me, people who can't do this calculation are exceedingly likely to misuse relativity's principles. They simply don't have relativistic intuition. [This isn't an insult....I made the same mistake. The difference is that I realized that the answer must be in error and the root-cause was a misapplication of SR's rules.] This is, I believe, what this discussion is all about. Thus one must do a calculation for a clearly-specified problem to understand what is going on.

My apologies for adding noise to the discussion. I will correct my mistake.

In the interest of focus, I will defer responding to your various other points. After all, this question was your starting point and, until it is resolved properly, we are no longer discussing the central issue.

Mathematics mach frei....

D
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Postby Mac on March 2nd, 2006, 8:52 pm 

How can you strongly disagree then state what I said your position would be? I don't mean this in any derogatory manner but current physics is about calculation not physical reality. That is my point in the examples as to the consequences of a pure mathematical model without physical restraints.

However, one thing I do know is the following. ....................................................
................................................................................................

There is no way that relativity would predict such a stupid thing.


HeHe. Glad you are enjoying this exercise.
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Postby Lincoln on March 3rd, 2006, 4:04 pm 

I was actually strongly disagreeing with the need to calculate a specific example. This is especially true in light of my suspicion that you (and I) misused the tenets of relativity. In the past when I've done relativity calculations, the most common error I have made has been using a Gallilean intuition with respect to time is handled. In the context of this debate, this error is inexcusable, but as Caesar might have said "Mea culpa".

However, I would in addition disagree with with your most recent post. This is a little off topic, but I don't expect the debate to divert because of it.

Physics is not at all about calculation. This is just simply not true. If a theory of any kind makes a prediction that is shown to disagree with measurements, the theory is discarded or rewritten to include phenomena not included in the original theory. If, as I expect to turn out to be incorrect, your superluminal example is demonstrated to be a consequence of properly-used relativity theory and further a measurement is made that proves the superluminal prediction deviates from reality, the theory will suffer one of the two fates listed above.

However, a theory CAN make a prediction that is not tested. As long as the theory is not in conflict with any verified and reproducible measurement, it is considered viable.

In modern sciences, the sole purpose of calculation is to provide a predictive number that can be compared to the same number as determined from a measurement.

Meaning is a question for philosophers, priests, rabbis and bartenders. Prediction of measurement is the bailiwick of scientists.

The calculation is progressing. I have several papers in the late stages of preparation of journal submission and a bit of recalcitrant electronics to debug and they come first. And one error is embarassing. Two, well.... So I am taking all due care.

D
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Postby Mac on March 3rd, 2006, 6:25 pm 

Don,

No rush. By all means take your time. Work does come first. But in the interim I have done some calculating of an actual case in the universe.

An object near the edge of the observable universe (13+ GLyr) has a recession velocity of 0.98c+ (z =10.)

Given the orbit velocity of the earth around the sun that means our relative velocity to such objects varies that value from 0.979 to 0.981 over a general 182.5 day period in that it would be 0.98 when the earth was moving orthogonal to the line of sight motion of the remote object and it would be 0.981 when the earth's motion was aligned to increase the recession.

It goes + or - 0.001c in 91.25 days.

The distance to the object shifts is 130,000,000 Glyr from 0.979c to 0.981c due to predicted spatial contraction.

The change from 0.98c to 0.981c occuring in 92 days is a dx / dt = 263,000,000c!!!
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Postby Lincoln on March 3rd, 2006, 6:36 pm 

Two comments:

First I am sure that SR does not apply to the edge of the universe. When you get to cosmological distances, you must consider that space itself is expanding. And SR does not restrict the speed at which space may expand, merely the speed at which objects may travel in their local space. So this calculation is a misuse of SR. The red shift is being misinterpreted here.

No fair. Perhaps we must withhold donuts from you too.....

Secondly, unless I made a mistake, the orbital velocity of the Earth is about 30 km/s. The speed of light is 3E8 m/s. So the orbital velocity change is not 0.001, but rather 0.0001.

But the first point is fatal.

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Postby Lincoln on March 3rd, 2006, 7:08 pm 

Third comment (sorry).

You are also adding velocities incorrectly. In SR, even if it applied, you can't simply add velocities v = v1 + v2. After all, if we were orbiting the sun at 0.5c, we wouldn't go from 1.5 to 0.5 c (in your example).

The velocity adding equations are...um....unpretty. But they certainly aren't linear.

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Postby Mac on March 3rd, 2006, 7:14 pm 

Lincoln wrote:First I am sure that SR does not apply to the edge of the universe.

No fair. Perhaps we must withhold donuts from you too.....


:D I am aware that universal expansion is involved in these velocities; however, I do not see how that alters the facts in terms of distance change due to relative velocity. Are you saying spatial contraction does not occur there? That would be a surprise indeed.

Secondly, unless I made a mistake, the orbital velocity of the Earth is about 30 km/s. The speed of light is 3E8 m/s. So the orbital velocity change is not 0.001, but rather 0.0001.

D


Opps. You are correct. No doughnuts for sure. :D The affect would only be 10% of what I indicated. That is a change in distance of 13,000,000 lyr or 6,500,000 ly/ 91.25 days or 0.8359 light years per second.

That is only 26,360,942c. That is a lot of latitude to not have superluminal affects predicted by Special Relativity. :D

So if I use Velocity Addittion: v' = (v + u) / (1 + vu/c^2) the result is 98% the same.

Edited to correct Velocity Adittion value - 3 Mar, 16:40PM - MacM
Last edited by Mac on March 3rd, 2006, 7:51 pm, edited 3 times in total.
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Postby Lincoln on March 3rd, 2006, 7:29 pm 

No, what I am saying is the following:

If you have two galaxies (say) 10 GLY apart. Within the two of them, the maximum speed is the speed of light. However the two of bits of space can actually be moving apart at high velocity. I will make up a number...say 0.9 c. (I have no idea if that's even close to the real number and I don't care for the point I am making here.) Since it is space itself that is stretching, not light or matter moving within space, there is no restriction on how fast they can recede. In fact, it is possible, allowed, even expected that at large enough distances, the two galaxies will recede at superluminal velocities. Everything is just a OK. This is a general relativity thing and quite outside the scope of anything we're discussing here.

Basically, while I do think your original example you posed was pedagogically interesting (even though I believe that we both initially misinterpreted SR's predictions), in this case you really have pushed SR beyond its scope of applicability. I can blather a lot about the non-uniform metric of space time and such, but those arguments are hard for me to interpret into words, so I'm not going to try.

The bottom line is that SR is designed to work in a flat and Euclidean space. If you apply it outside that condition, you will make an ever-increasing predictive error.

The good thing is your initial question is valid and SR applies just fine to it.

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Postby Mac on March 3rd, 2006, 7:47 pm 

Don,

OK. I don't want to belabor the point. But it seems to me that the issue of spatial contraction applies to distance created, even by expansion. The area where I would feel your comments have some merit would be in the claim of recession velocity. Those values do include expansion affects.

Having said that I note that you have no problem with superluminal expansion (and some does exist supposedly), so why would superluminal contraction pose a problem for you?


Edited to remove original post quoted, 3 Mar, 16:47PM - MacM
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Postby Lincoln on March 3rd, 2006, 8:14 pm 

There are two issues here. Your original question, which was posed in Euclidean space. In this space, the speed of light is constant and matter may not exceed the speed of light. It's a good question, I like it.

The second question is what happens when space itself changes shape. There is no law of relativity that requires space to move at the speed of light or slower. Space can expand at superluminal velocities. Any person who argues with you about this simply doesn't understand GR and SR. After all, even relatively mainstream physics postulates the inflation period of the early universe, during which the universe expanded by a factor of 10^50 in 10^-32 seconds or something. (The models vary considerably.) Note that since the distance to the edge of the visible universe is something like (3E8 m/s)*(3.14E7 s/yr) * (13.7E9 yr) = 1E26 meters, then the universe expanded from a subatomic size to something larger than the visible universe in 10^-32 seconds. Superluminal indeed. And, rather obviously, two particles that are stationary relative to their local space time will appear to be moving apart very fast indeed if their local space separates quickly. In fact, if you look at the universe as a whole, galaxies are moving (fairly) slowly as far as their local space is concerned. But since space is expanding (on a cosmic scale), the galaxies appear to be moving away from one another in the traditional sense.

But this has NOTHING to do with your original query. SR deals with an understanding of the laws of physics in Euclidean space, in which the speed of light is what we call locally the maximum speed.

If you want to claim that relativity is negated because of the possible superluminal velocity of space itself, you may get some poor benighted souls to agree with you, but you have departed from what SR claims. And I will be very sad if it goes that way, as until then, the debate has been an interesting one and you have clearly mulled over what appears at face value to be an inconsistency of SR.

So back to your original query. It's cute, I like it. I may well use it to torture cocky graduate students. But let's focus there, rather than misinterpreting a perceived flaw that isn't really there.

Cheers....
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