Naked Science Forum
On the Lighter Side => New Theories => Topic started by: professorv on 14/01/2012 02:56:29
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Hi, i saw a new work derived from the Lorentz equation that seems to work in the special case where v=c.
Someone knows if it is right?
Its a 4 pages work so, i will put just the link.
pages 13 to 16
http://vlassius.com.br/tatc/texto2W.pdf
thanks
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I skimmed the article. Is it your work?
At some point, it defines D3 & D3T, in which I defines a universe without time. However, if you drop out time, then you have no velocity, as velocity is defined as (change of distance)/(change of time). So, distance does not equal velocity... unless your time (whatever your favorite unit is) = 1.
Likewise, if you set Time = 0... your (change in distance)/(change in time) becomes infinite.
Often limits and epsilon are used to explore values infinitely small, or close to an asymptote.
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No, it is not mine.
There is a lot of things in there, i am interesting in the Lorentz equations pages 13 to 16
thanks
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You cannot use the framework of Special Relativity to move outside SR and postulate answers from a frame moving at relative velocity c. It is an axiom of SR that any local frame of inertial motion is in relative motion less than c - if you postulate anything from or of a frame at c, then you need to start again from scratch. To start from scratch you only have axiomata of the invariable speed of light, causality, frame invariance, and the basic laws of motion - everything else needs to be proved.
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Yes, that is the point!
This work was done from the scratch using just Lorentz basis. It is not using the Lorentz Transformations or Lorentz Factor or SR, just the basis from where this thee came.
If the work uses exact the same basis and same logic, maybe it is right.
Someone can find any error? (equations ar pretty simple and seems to be OK)
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Fig 1 represents the right triangle from which the time dilation factor was formulated.
Side ct:
This is the only side for which both terms are constant. The speed of light, c, is constant. Time, t, in the rest frame is constant. Therefore, judged from the rest frame the length of side ct is constant.
Side vt:
Again t is constant as judged from the rest frame. the relative velocity of the moving frame is referenced by v. therefore at relative velocity 0 side vt does not exist. For v>0 the greater the relative velocity the longer side vt is.
Side ct’:
Here c is, of course, constant and the value of t’ is, necessarily, dependent on the only other non constant value v from side vt. Time in the moving frame is t’.
The formulation is as follows:
a*a+b*b=c*c the Pythagorean theorem
c*c*t’*t’+v*v*t*t=c*c*t*t substitute values
c*c*t’*t’=c*c*t*t-v*v*t*t the long version of the time dilation equation
t’=t*sqrt(1-v*v/c*c) solved for t’- the time dilation equation
To demystify and simplify the following calculations the constants c and t are given values then the long version of the equation is simplified. c=1 and t=1
c*c*t’*t’=c*c*t*t-v*v*t*t the long version of the time dilation equation
t’*t’=1-v*v c*c=1 t*t=1 then simplify – this is the “short version” of the equation
To use this process velocity, v, must be expressed as a decimal fraction of c. .01c, .5c, .9c etc.
If there is any doubt as to the validity of this method feel free to perform the long calculation. The result is the same.
For the question of what happens if v=c:
In that case since c=1 then v=1 and as per above t=1
c*c*t’*t’=c*c*t*t-v*v*t*t the long version of the time dilation equation
1*1*t’*t’=1*1*1*1-1*1*1*1 substitute 1 for the appropriate values
t’*t’=0 simplify
t’=0 if t’=0 then side ct’ has no length and, therefore, does not exist.
For the question of what happens if t=0:
For t=0, c=1
Per the figure:
Side ct does not exist because t is 0
Side vt does not exist because t is 0
c*c*t’*t’=c*c*t*t-v*v*t*t the long version of the time dilation equation
1*1*t’*t’=1*1*0*0-v*v*0*0 substitutions
t’*t’=0
t’=0
per calculation:
Side ct’ does not exist because t’ is 0
For the question of what happens if v=0:
t’*t’=1-v*v the short version of the equation
t’*t’=1-0
t’*t’=1
t’=1
This particular calculation will be referred to later.
More examples:
For v=.866c
t’*t’=1-v*v the short version of the equation
t’*t’=1-.866*.866
t’*t’=1-.75
t’*t’=.25
t’=.5
For v=.01c
t’*t’=1-v*v the short version of the equation
t’*t’=1-.01*.01
t’*t’=1-.0001
t’*t’=.9999
t’=.99994999
The question now is what exactly do ct, vt and ct’ represent and why did Lorentz decide to use this formulation. The answer in understandable terms, diagrams and animations can be found in the Cal Tech video “The Mechanical Universe and Beyond” number 42 “The Lorentz Transformation” starting about minute 11 or so. You can Google it or follow this link: http://www.learner.org/resources/series42.html?pop=yes&pid=611#
Briefly stated: Lorentz and Einstein visualized two mirrors with a light pulse moving at the speed of light from, in this case, the bottom mirror to the top mirror in the moving frame. As seen from within the moving frame the path of the light pulse is side ct’. The distance that the mirror assembly or light clock in the moving frame traversed during time t of the rest frame is represented by side vt. The path of the light pulse from the bottom mirror to the top mirror as seen from the rest frame is represented by ct, the hypotenuse of the right triangle.
As previously stated and shown mathematically with the moving frame at relative velocity 0 side vt does not exist and therefore, as judged from the rest frame ct=ct’. At any relative velocity >0<c side vt of the right triangle exists. If side vt of the right triangle exists then side ct is the hypotenuse. The hypotenuse is the longest side of a right triangle. Since ct is the longest side of the triangle side ct’ is shorter than ct. At relative velocity 0 the length of side ct’ which is perpendicular to the direction of motion is the same as length ct which is constant as judged from the rest frame. At any relative velocity >0<c the length of ct’ is less than the length of ct as judged from the rest frame.
The Special Relativity stipulation that length perpendicular to the direction of motion is not changed as judged from the rest frame if the constant relative velocity of the moving frame is changed is disproved. At relative velocity 0, ct’=ct at relative velocities >0<c, ct’<ct.
Butchmurray
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butchmurray
That is a very good explanation to Lorentz work but, if we want to
expand it, we cannot use the same parameters.
Rest frame:
In the original problem, two frames is moving at v1 and v2 speed. Then,
one is chose as a Reference Frame and v1 or v2 is chosen to be equal to
zero as Rest Frame.
To use v=c, we have a problem to do this, since both are at c speed. As
c is constant in all frames of reference, as expected the second frame
would be in the same position of the first (chosen as Reference).
About your answer:
"Side vt:
Again t is constant as judged from the rest frame. the relative velocity
of the moving frame is referenced by v. therefore at relative velocity 0
side vt does not exist. For v>0 the greater the relative velocity the
longer side vt is."
Side vt is also ct for this formulation as v=c thus, the same that you
talked some lines before.
"To demystify and simplify the following calculations the constants c
and t are given values then the long version of the equation is
simplified. c=1 and t=1"
Its not possible to set t=1 if we want to find something new about t.
"The Special Relativity stipulation that length perpendicular to the
direction of motion is not changed as judged from the rest frame if the
constant relative velocity of the moving frame is changed is disproved.
At relative velocity 0, ct’=ct at relative velocities >0<c, ct’<ct."
This equations is prior to SR so, we cannot use SR, the velocity will be
exact the same in any frame of reference if v=c
Using the equation that you provided (change * to . just to be easier to
read):
"c*c*t’*t’=c*c*t*t-v*v*t*t the long version of the time dilation
equation"
if v=c and t'=t (as c is invariant between frames)
c.c.t'.t'= c.c.t.t -v.v.t.t
c.c.t'.t'= c.c.t'.t' -c.c.t'.t'
c.c.t'.t'= 0
t'.t'= 0/c.c
t'.t'= 0
t'=0 (the time to get the point of event is zero)
If you set c=1, it gets the same answer
t'.t'= t'-t'
t'.t'=0
t'=0
Those are the same answer of the pdf.
I took some time to understand the work described on pdf and, I think I
understand it.
Maybe you can see now why i am interested in this, it seems to work out.
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"Side vt is also ct for this formulation as v=c thus, the same that you
talked some lines before".
I know. I didn’t want anyone to forget.:)
"Using the equation that you provided (change * to . just to be easier to
read):"
It may be misinterpreted as a decimal point, but no big deal.
“ "To demystify and simplify the following calculations the constants c
and t are given values then the long version of the equation is
simplified. c=1 and t=1"
Its not possible to set t=1 if we want to find something new about t. “
In the case that you wanted to know what the outcome would be if time was 0, t was set to 0 not to 1.
" "The Special Relativity stipulation that length perpendicular to the
direction of motion is not changed as judged from the rest frame if the
constant relative velocity of the moving frame is changed is disproved.
At relative velocity 0, ct’=ct at relative velocities >0<c, ct’<ct."
This equations is prior to SR so, we cannot use SR, the velocity will be
exact the same in any frame of reference if v=c "
You are absolutely correct. The equations are prior to SR and that is my point. With no reference to SR Lorentz in his formulation of the equation, indirectly in mathematical terms not only shows that at relative velocity 0, ct’=ct and at relative velocities >0<c, ct’<ct but also length perpendicular to the direction of motion is not the same as measured from within the moving frame as it is observed from the rest frame. Although that is proven prior to SR, at some later time SR antithetically, effectively stipulates “length perpendicular to the direction of motion is not changed as judged from the rest frame if the constant relative velocity of the moving frame is changed” and “length perpendicular to the direction of motion is the same as measured from within the moving frame as it is observed from the rest frame” in contradiction to the equations. That is a fault of and consequently a flaw in SR.
Butch
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No Butch, it's not wrong. You can define Earth as having all kinds of speeds, relative any other 'frame of reference'. Those speeds, all as perfectly valid, won't change the way your ruler and clock measure distance and time (locally on Earth). As for “length perpendicular to the direction of motion is the same as measured from within the moving frame as it is observed from the rest frame” then that must be correct as it otherwise would introduce different reality's for different observers, as described here. (http://www.askamathematician.com/2011/01/q-why-does-lorentz-contraction-only-act-in-the-direction-of-motion) /
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The point being that SpaceTime is expected to make sense for all observers. If one observer found the event to describe a different reality, then SpaceTime also would have to be assumed to 'split', similar to the idea of 'many worlds scenarios'. The difference being that this would introduce one different SpaceTime per observer, at a worst case scenario, relative many worlds in where the 'splits' is postulated to be 'invisible' for the observers, as all of them have its own 'exact copy' of a SpaceTime. It would introduce improbabilities and impossibilities for us as the 'moving' observer then, in your scenario of the perpendicular length changing, still would exist in both 'splits', which can't be as that introduces a infinite loop of 'splits'.
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No Yur_on, you misunderstood. I fully realize that no length within a frame is changed due to the relative velocity of that frame to any other frame. What I indicated was that with the mathematics of the Lorentz equations under discussion, the length of a measuring rod that is perpendicular to the direction of motion in a moving frame as judged from a different frame is dependent on the relative velocities of the frames. That’s what is contrary to the SR dictum which requires the length of that measuring rod to be the same as judged from any frame.
Butch
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"the length of a measuring rod that is perpendicular to the direction of motion in a moving frame as judged from a different frame is dependent on the relative velocities of the frames" Butch?
That's the point I was talking about above. That the perpendicular length of a rod indeed is the same for all observers watching it, assuming that they all see it from a same position, no matter their velocity relative that rod, as long as it is perpendicular relative their (relative) motion. And the link I gave explained the consequences of assuming otherwise. Althought the perpendicular rod will be time dilated it will not contract.
So, to prove your idea there you must design a experiment proving it without doubt.
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Yor_on here is proof without a doubt.
The mathematical foundation of SR is the set of equations that were formulated by Lorentz. As such these equations must conform to SR in every way. SR stipulates that length perpendicular to the direction of motion in a moving frame is the same for all observers independent of relative velocity.
For convenience the formulation and explanation of the formulation are presented again. An in depth explanation in understandable terms, diagrams and animations can be found in the Cal Tech video “The Mechanical Universe and Beyond” number 42 “The Lorentz Transformation” starting about minute 11 or so. You can Google it or follow this link: http://www.learner.org/resources/series42.html?pop=yes&pid=611#
Refer to the figure. Click it to enlarge.
Side ct:
ct is the path of the light pulse as seen from the rest frame. This is the only side for which both terms are constant. The speed of light, c, is constant. Time, t, in the rest frame is constant. Therefore, judged from the rest frame the length of side ct is constant.
Side vt:
vt is the velocity of the moving frame relative to the rest frame. Again t is constant as judged from the rest frame. The relative velocity of the moving frame is referenced by v.
Side ct’:
ct’ is the height of the light clock, length perpendicular to the direction of motion as judged from the rest frame. Here c is, of course, constant. Time in the moving frame is t’.
The formulation is as follows:
a*a+b*b=c*c the Pythagorean theorem
c*c*t’*t’+v*v*t*t=c*c*t*t substitute values
c*c*t’*t’=c*c*t*t-v*v*t*t the long version of the time dilation equation
t’=t*sqrt(1-v*v/c*c) solved for t’
Various values for v and the corresponding lengths of ct’.
For v=0 ct’=1
For v=.01c ct’=.99994999
For v=.866c ct’=.5
For v=.98c ct’=.1989974
As previously stated ct’ is length perpendicular to the direction of motion as judged from the rest frame.
The formulation of Lorentz produces a result in which length perpendicular to the direction of motion in the moving frame as judged from the rest frame is dependent on the relative velocity of the moving frame.
SR stipulates that length perpendicular to the direction of motion in a moving frame is the same for all observers independent of relative velocity.
The mathematical result and the stipulation are obviously mutually exclusive. One or both is in error. Both are internal to SR. This is proof without a doubt that there is an error internal to SR.
Thank you,
Butch
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Yor_on?
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:)
Eh, Butch, that's not a experimental fact. It's your conjecture.
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Yor_on,
You are absolutely correct. That is not experimental proof. However, all of the following are facts:
1. Per the Lorentz equations under discussion; as judged from the rest frame length perpendicular to the direction of motion is dependent on the relative velocity of the moving frame.
2. Per Special Relativity a length perpendicular to the direction of motion as judged from within the moving frame remains the same independent of the relative velocity and a length perpendicular to the direction of motion is the same as judged from either frame independent of relative velocity.
3. Fact 1 and fact 2 are mutually exclusive.
4. Fact 1 or fact 2 or both facts are in error.
5. Fact 1 and fact 2 are internal to Special Relativity
6. There is an error internal to Special Relativity.
Thank you,
Butch
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I know what you think Butch, but to prove your idea you still need to verify it relative a experiment. It has to do with the geometry of SpaceTime relative what ruler and clock you use to measure and how the frames of reference change under the arrow relative mass and (relative) motion, that as a semi educated guess :) Also your idea brings with it logical fallacies, as linked to before in this thread.
Could you prove your idea experimentally though, it would be very interesting.