Test of relativistic flattening

[UncleAl]

We assume that relativistic foreshortening is merely an illusion of spacetime perspective. Here is a Gedankenexperiment to discovert if it is real.

 

Special Relativity contains the beta factor that goes toward zero as velocity approaches lightspeed,

 

beta = sqrt[1-(v^2)/(c^2)] = sqrt[1-(v/c)^2]

 

where "v" is the velocity of the observed frame relative to the observer and "c" is lightspeed. As observed by a stationary observer, a moving body alters its mass, length parallel to its direction of movement, and rate of time flow,

 

M = m/(beta)

L = l(beta)

T = t(beta)

 

Where uppercase is the observed value and lowercase is the rest value. The relativistic projection of time ratchets by empirical demonstration. Relativistic clocks run slow compared to local clocks. A relativistic beam of a radioisotope or an unstable particle launched, propagated, and recovered is seen to have decayed proportionately less than a stationary sample. There is no paradox in the Twin Paradox, and acceleration fore and aft has nothing to do with the observed results (added small perturbation in the same sense vs. overall flight given linear acceleration, the Equivalence Principle, and GR).

 

The projection of space is held to be a figment of observation. Nobody has done an experiment where the "flattening" of space parallel to the direction of relativistic propagation has ratcheted consequences.

 

A tetrahedral carbon chiral center "flattened" by a factor of 70 at 0.9999c doesn't have much pucker at all. One might expect a degree of racemization (reopening in either direction) upon unflattening. Acceleration and deceleration of a suitable chiral ion (as low a mass as possible) does not imply heating or additional chemistry. Supersonic molecular beams from expansion into vacuum are deeply cryogenic in their own frame.

 

http://www.mazepath.com/uncleal/racem.png

http://www.mazepath.com/uncleal/racem.htm

 

This image contains three stereograms of N,N,2,5-tetramethylpyrrolidinium with two chiral centers. Carbon is pale blue, hydrogen is white, nitrogen is dark blue and has a positive charge. The chiral left-left or (S,S) isomer is first. The chiral right-right or (R,R) isomer is in the middle. The achiral left-right (R,S) isomer is third. Since the mirror image of left is right, that last molecule has a mirror plane of symmetry normal to and bisecting the plane of the ring through the nitrogen. The slight ring pucker is reversible top to bottom and races around the ring by thermal vibration, averaging to a flat ring. The methyls are spinning and average their hydrogen's orentations.

 

We take a beam of the resolved left-left ion and boost it to 0.9999c in the Relativistic Heavy Ion Accelerator, then reverse the timing to decelerate it and collect as a salt. Give that the flying ions are randomly tumbling as viewed in our reference frame, billions and billions of potential flattenings and racemizations will (or will not) transpire to an equilibrium mixture of all three species. We then measure the optical rotation, [alpha]D, for the product vs. the starting material.

 

The Gedankenexperiment is mildly interesting. Reduction to practice is highly unlikely. Particle physics doesn't know organic chemistry exists.

[Damo2600]

Interesting. 'Do we really know how an atomic clocks work?' is a question I have already asked on this forum.

 

If I am flying toward you at v, and you are stationary, then you are flying toward me at v. The distance between us is equally shortened by both observations. Length contraction shows this. So how can you observe me to be younger? Perhaps atomic clocks are altered by velocity? Another question I have asked.

 

t = t'/(1 - v^2/c^2)

 

v = 0

 

t' = t

 

v = c/2

 

t = t'/3/4

 

Goes both ways doesn't it?

 

Hmmm...... curious....

 

Josie

[paultrr]

Lorentz-Fitzgerald, contraction equations used in relativity theory to change from a coordinate system or frame of reference in which the observer is at rest to a second frame that is moving at constant velocity with respect to the first frame are known as the Lorentz transformation. The Lorentz transformation will result in a stationary observer recording an effect "equivalent" to the Lorentz contraction when observing an object in uniform motion relative to his system of coordinates. Einstein himself showed, that this effect is not due to the actual deformation of the body in question, as Lorentz had originally supposed, but to a change in the way space and time are measured. It is a measuring rod change from one frame to the other. 1−v^2/c^2, where v is the velocity of the body and c is the velocity of light is the factor used to figure such out.

 

Of course, the effect works both ways. The length of a spaceship, for instance traveling at let's say .5C, will be shorter as viewed from the Earth than it is aboard the spaceship itself, because in this case the length in question is in the frame that moved with respect to the Earth. The sense of the contraction effect can be remembered by this mnemonic: Moving rulers are shorter. But if you really notice to the stationary observer at rest on the earth the craft is shorter, not to the crew on the ship. So the both ways issue has a qualifier because its the ruler that has changed from frame to frame. The same applies for time contraction. To the crew on a craft traveling near light speed time will seem to flow normally. But when one tries to compare their time to earth time the two clocks will not seem the same because again the ruler that is moving has changed.

[Damo2600]

Alas it can't be so.

 

The speed of light is the same for ALL observers. So if I (stationary) see you (moving)the distance between us appears decreased and has decreased. Vice-versa. You, according to your own reference frame, on the spaceship don't appear to be moving at all.

 

This is counter-intuitive on two levels:

 

It does not matter if you are moving away or moving closer the distance always appears shorter, and is shorter, due to velocity (regardless of whether you are the stationary body or the body moving). If you orbit me at v = 0.5c the distance remains the same as another stationary observer of equal distance. The actual time-dilation must be due to movement alone. The atomic clock must slow down therefore your body clock must also slow down.

 

Time dilation and length contraction is apparent and actual for both observers. A seperate time dilation occurs for the moving body alone.

 

(edit: Neither body is shorter in the sense that when they arrive they have lost length. Right? It is merely the distances that defines the two objects has shortened. Space, and the objects using said space, is not the Euclidean geometry we once thought it to be. The point where I am 1 mile from you is shorter depending on my velocity. Distance is relative.)

 

Josephine :( :( :( :( :(

[UncleAl]

Special Relativity works. We know there is no perceptible effect within a reference frame whether at rest or relativistic to an inertial observer. We know the Twin paradox - that time and space can be blended to give a permanent[/] disparity. "Flattening" parallel to the direction of velocity should be a trick of perspective only, and therefore fully reversible (nothing really happened!) without persistent result.

 

Can severe relativistic "flattening" have persistent results? Macroscopic bodies cannot be accelerated to large gammas much less be recovered thereafter. Brookhaven National Laboratory's Relativistic Heavy Ion Collider(RHIC) routinely accelerates gold nuclei to 100 GeV/nucleon for a 196.9 amu nucleus. If there were a low molecular weight ion that would be permanently structurally affected by "flattening" and repuckering, we have a thoughtexperiment.

 

A tetrahedral carbon atom bearing four different groups is chiral (handed: left-handed or S; right-handed or R). In solution it will rotate the plane of linearly polarized light clockwise or counterclockwise, detecable to nanoradians. If one were to sufficiently flatten the tetrahedron it might repucker in either direction. Tartaric acid has two such carbons allowing three optical isomers: two chiral mirror-image enantiomers (R,R) and (S,S) plus a third achiral structure, mesotartaric acid, wherein (R,S) and (S,R) are the same optically inactive molecule.

 

What is the smallest mass stable chiral cation we can build to run through the accelerator and recover? It will be a quaternary ammonium salt. I propose an elegant example, (N,N,2,5)-tetramethylpyrrolidinium with MW=128.24

 

http://www.mazeapth.com/uncleal/racem.png

 

Take the first or second chiral ion. Verify its enantiomeric purity and measure its optical rotation. Circulate an ion stream through the RHIC at gold nucleus energies, then reverse the acceleration to recover. That will give you many seconds of gamma about 107. The puckers will be flattened to less than 1% of rest geometry. Molecular tumbling is in the microwave region, billions of cycles/second. If there is a one in 10^9 chance of repuckering in the wrong direction the ion will scramble to all three isomers. Measure the optical rotation of recovered product.

 

If "flattening" is only perspective, recovered ion (as a salt, of course) will be as enantiomerically pure as it started. If there is inversion of chiral centers it is easily dectectable and very interesting.

[Qfwfq]

As Paul says, it's but a coordinate transformation.

We know the Twin paradox - that time and space can be blended to give a permanent[/] disparity..

Which of the two twins will be younger, after they meet again?

 

Can severe relativistic "flattening" have persistent results? Macroscopic bodies cannot be accelerated to large gammas much less be recovered thereafter.

No, for the first question. Why can't macroscopic bodies travel near c? According to which observers can't they? That assert is in contradiction of the principle of relativity.

 

We are all travelling at velocities near c, all the time, for some observers.

[Mac]

Just a question. In your thought experiment have you considerred the more recent view that what you are calling Lorentz Contraction is actually a "Rotation". That is a rod will appear to shorten but only because the view is rotated (imagine a ruler orthogonal to your line of sight measures 12 inches but if you rotate it in the plane of view it shortens and at 90 degrees no longer has length).

 

It is claimed in this view that a sphere does not flatten at all but still appears as a perfect sphere because it is spherical from any viewed angle.

 

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

[paultrr]

Just a question. In your thought experiment have you considerred the more recent view that what you are calling Lorentz Contraction is actually a "Rotation". That is a rod will appear to shorten but only because the view is rotated (imagine a ruler orthogonal to your line of sight measures 12 inches but if you rotate it in the plane of view it shortens and at 90 degrees no longer has length).

 

It is claimed in this view that a sphere does not flatten at all but still appears as a perfect sphere because it is spherical from any viewed angle.

 

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

 

Very good point, Mac. Its actually the more standard view today on Lorentz contraction making the clock effect a rotational effect itself. A friend of mine utilized some of that to answer partly an objection often raised about a GR type Alcubierre field and control of such. There is a rotational effect within the front portion of such a field that provides a partial boost so that part of the frontal portion of a warp field is controled by the craft's own control signal even though the field as a whole appears superluminal. It just happens to lie in a region where one could turn the field off. On a personal note I've read his paper. I see what he is saying. But it still does not fully solve the problem there as far as navigation goes, etc. However that rotational aspect does get born out in that approach.

[paultrr]

Alas it can't be so.

 

The speed of light is the same for ALL observers. So if I (stationary) see you (moving)the distance between us appears decreased and has decreased. Vice-versa. You, according to your own reference frame, on the spaceship don't appear to be moving at all.

 

This is counter-intuitive on two levels:

 

It does not matter if you are moving away or moving closer the distance always appears shorter, and is shorter, due to velocity (regardless of whether you are the stationary body or the body moving). If you orbit me at v = 0.5c the distance remains the same as another stationary observer of equal distance. The actual time-dilation must be due to movement alone. The atomic clock must slow down therefore your body clock must also slow down.

 

Time dilation and length contraction is apparent and actual for both observers. A seperate time dilation occurs for the moving body alone.

 

(edit: Neither body is shorter in the sense that when they arrive they have lost length. Right? It is merely the distances that defines the two objects has shortened. Space, and the objects using said space, is not the Euclidean geometry we once thought it to be. The point where I am 1 mile from you is shorter depending on my velocity. Distance is relative.)

 

Josephine ;) ;) ;) ;) ;)

 

The speed of light is measured the same for all observes in vacuum. Everything about relativity stipulates as a whole a certain medium with certain properties. If any of those properties are different in a frame then one can have a measured difference in the speed of light. STR and GTR are a whole. One builds upon the other. But as a complete picture one derives the actual case situation. We do not measure the local speed of light in our atmosphere the same as we measure it in a vacuum. Inside of a conductor the speed of light is different than it is in air or the vacuum. All of these differences have been measured over and over again. But none of these differences violates relativity since a specific medium is spoken of in relativity as a whole. Even in GRT there is the stress energy tensor which has different aspects that form the whole. If any aspect of that stress energy tensor changes so does the local measurable speed of light. If one goes back to Einstein himself and his own writtings he knew C in the atmosphere was different than C in the vacuum. The difference within experimental limits had already been measured in his time. Relativity as stated deals with C in a vacuum, not in any other medium. One difference someone failed to notice earlier on was where I stated its invarient within a specific medium. If you compare one medium to another C is not invarient. In one medium it will have one velocity and in another a different velocity. But within each medium that velocity remains constant. If one could compare a Universe that had the properties of our atmosphere to a universe composed of a vacuum the measured speed of light between both universes would not be the same. Only within each universe could one say the measured speed of light was constant.

[Qfwfq]

have you considerred the more recent view that what you are calling Lorentz Contraction is actually a "Rotation".

This isn't a "more recent view", it has been around since Minkowski.

 

It is claimed in this view that a sphere does not flatten at all but still appears as a perfect sphere because it is spherical from any viewed angle.

Not correct for a sphere. The shape to have this property would be defined by t^2 - x^2 - y^2 - z^2 < r^2 and it wouldn't have a finite extension even for small r.