# Relativistic rolling tank

Pete said:
No. The degree of strain is the gamma factor of the rim speed in the axle frame. It is not directly proportional to the rotation speed, and it is not directly related to the rim speed in any other frame.

Lorentz contraction means that the track won't physically fit around the wheels. The strain arises because the wheels push against the track.

Consider the barn and pole paradox: because of length contraction, the pole will physically fit in the barn in the barn's frame, but if the barn doors close around the pole, the pole pushes against the doors and is strained by the resulting stress. The strain is not a direct result of length contraction. The strain is the result of the stress experienced because the track no longer fits the tank, just like the pole won't fit in the barn. Real physical strain.

No. The curvature of the spokes is frame dependent - the spokes are not curved in the spokes rest frame, or the axle frame, for example.

A disk or wheel can't be rigidly spun up to relativistic speeds because the rim and spokes must be strained.

Relativistically rotating unstrained wheels are certainly incompatible with relativity theory.

2inq, your problem appears to be that you refuse to consider the possibility that the track is strained simply as an article of faith. If you allow the possibility that the track is stretched, then there is no problem.

A number of actual laboratory science experiments have been conducted by actual fizzists and reported in actual fizzist publications. Not ONE has detected ANY evidence supporting the Special Relativity claim of actual circumferential length contraction.

Hi CANGAS,
Another unsupported and badly spelled assertion?
If you can cite any physics journal articles that discuss experiments that test for strain in a rotating wheel, I would be very interested in reading them.

Pete said:
Hi CANGAS,
Another unsupported and badly spelled assertion?
If you can cite any physics journal articles that discuss experiments that test for strain in a rotating wheel, I would be very interested in reading them.
I believe CANGAS's statement was concerning a proof of the rim's length contraction in a rotating frame. Synchrotrons regularly accelerate particles to near the speed of light in their rings. The particles migrate to the outside of the ring, due to their angular momentum. Very powerful magnets are necessary to bend the path of the particles so they don't hit the outside of the ring's wall. The lab frame of the physicist is identical to the frame of the non-rotating axel, or tank, observer. The 'strain' on the spokes is angular momentum, acting to increase the diameter of the wheel. Replace the magnets with spokes connecting the rim with an axel, and it is very evident that the spokes and the rim will be stretched by angular momentum to a larger diameter. The 'strain' is resisting a centrifugal (spoke stretching) force on the spokes, not a centripetal (spoke compressing) force directed toward the axel.

Yes, there will certainly be some tension on the spokes due to their mass and the mass of the rim. This is a separate effect to that under discussion. In our gedanken, we're effectively assuming infinitesimal mass for spokes and rim.

I think my point was that the particles moving around the circumference of the ring do not follow a decreasing radius as they increase in velocity relative to the lab frame. As their relative velocity increases, they increase the diameter of their path around the ring. Greater and greater power is needed from the magnets to keep the particles from hitting the outer surface of the ring. Actually, little increase in power is needed to circulate (attract/repell across the acceleration gaps) the particles to greater and greater relative velocities, to essentially the speed of light. The great increase in power is needed by the magnets that bend the path of the particles inward to offset their increasing angular momentum.

Hi 2inquisitive,

I still don't get your point. All of that is according to the predictions of SR. Are you agreeing with SR or disagreeing? If you are disagreeing then why are you bringing up synchotrons when they are one of the best evidences for SR?

-Dale

Pete said:
I posted this in CANGAS's excellent [thread=56170]Next to last relativity thread[/thread], but the discussion has drifted beyond the thread's main topic. To avoid further hijacking, I'm making a new thread. It's also an instructive illustration of what Special Relativity does and doesn't say.

I've drawn up animations of a tank rolling along at 0.866c It gives interesting insights into the problem of the relativistic rotating disk, specifically that the outer rim of the disk (or in this case, the tank tread) must be physically stretched by a factor of gamma (unless the supporting structure is physically compacted). Notice how the portion of the track in contact with the ground is stretched to twice its proper tread spacing.

Macromedia Flash player required.

This animation simulates what a distant camera moving parallel to the tank sees:
<object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="500" height="100" id="RollingTank" align="middle"><param name="allowScriptAccess" value="sameDomain" /><param name="movie" value="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTank.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#ffffff" /><embed src="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTank.swf" quality="high" bgcolor="#ffffff" width="500" height="100" name="RollingTank" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer" /></object>

This animation simulates what a camera fixed to the ground sees:
<object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="500" height="100" id="RollingTankGroundFrame" align="middle"><param name="allowScriptAccess" value="sameDomain" /><param name="movie" value="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTankGroundFrame.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#ffffff" /><embed src="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTankGroundFrame.swf" quality="high" bgcolor="#ffffff" width="500" height="100" name="RollingTankGroundFrame" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer" /></object>

Note that both cameras are filming at the same time, so they are recording exactly the same events. They look different because (according to Special Relativity), the relationship between events depends on the reference frame chosen to describe them (ie on the motion of the observer).

This weekend, I will add clock readings in both frames to the animation. This will make the time dilation of ground clocks in the tank frame easier to see.

Feel free to criticise, question, or comment.

Pete

This is the first opportunity I have been able to grasp to take in the tank tread thread. Hob nobbing on the forum pays me no money but consumes my time and energy. Personal profit oriented activities take precedence.

In your animation graphic, reproduced here for convenience, your interpretation of Special Relativity length contraction is apparently illustrated, but where is Special Relativity time dilation taken into account?

I never did get around to adding clocks to the animations, but I can if necessary.

For now, try this:

1) The time between events that occur in the same place in the tank frame is twice as long in the ground frame
In the tank frame, a cleat strikes the ground every six ticks.
In the ground frame, a cleat strikes the ground every 12 ticks.​
2) The time between events that occur in the same place in the ground frame is twice as long in the tank frame
In the ground frame, each cleat is on the ground for 30 ticks.
In the tank frame, each cleat is on the ground for 60 ticks.​

Your cute animations are totally worthless unless they show ( correctly ) the predictions of both Special Relativity length contraction and time dilation.

Your cute animations are totally worthless unless they show ( correctly ) the predictions of both Special Relativity length contraction and time dilation.

Which is exactly what they do.

Well done, Pete.

Pete said:
I posted this in CANGAS's excellent [thread=56170]Next to last relativity thread[/thread], but the discussion has drifted beyond the thread's main topic. To avoid further hijacking, I'm making a new thread. It's also an instructive illustration of what Special Relativity does and doesn't say.

I've drawn up animations of a tank rolling along at 0.866c It gives interesting insights into the problem of the relativistic rotating disk, specifically that the outer rim of the disk (or in this case, the tank tread) must be physically stretched by a factor of gamma (unless the supporting structure is physically compacted). Notice how the portion of the track in contact with the ground is stretched to twice its proper tread spacing.

Macromedia Flash player required.

This animation simulates what a distant camera moving parallel to the tank sees:
<object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="500" height="100" id="RollingTank" align="middle"><param name="allowScriptAccess" value="sameDomain" /><param name="movie" value="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTank.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#ffffff" /><embed src="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTank.swf" quality="high" bgcolor="#ffffff" width="500" height="100" name="RollingTank" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer" /></object>

This animation simulates what a camera fixed to the ground sees:
<object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="500" height="100" id="RollingTankGroundFrame" align="middle"><param name="allowScriptAccess" value="sameDomain" /><param name="movie" value="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTankGroundFrame.swf" /><param name="quality" value="high" /><param name="bgcolor" value="#ffffff" /><embed src="http://home.teegee.com.au/byrnes/Pete/Relativity/Images/RollingTankGroundFrame.swf" quality="high" bgcolor="#ffffff" width="500" height="100" name="RollingTankGroundFrame" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer" /></object>

Note that both cameras are filming at the same time, so they are recording exactly the same events. They look different because (according to Special Relativity), the relationship between events depends on the reference frame chosen to describe them (ie on the motion of the observer).

This weekend, I will add clock readings in both frames to the animation. This will make the time dilation of ground clocks in the tank frame easier to see.

Feel free to criticise, question, or comment.

Pete

Say, that's funny. Why is the top track ( in the view with camera fixed to the ground ) so much longer than me and my old friend Albert expected it to be?

Perhaps it is because your expectation was incorrect.
Why did you expect it to be shorter?

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CANGAS said:
Say, that's funny. Why is the top track ( in the view with camera fixed to the ground ) so much longer than me and my old friend Albert expected it to be?
Because you and Albert didn't check with Lorentz like you should have.

-Dale

Pete said:
Perhaps it is because your expectation was incorrect.
Why did you expect it to be shorter?

Because the Fitzgerald/Lorentz/Einstein/ Special Relativity length contraction says so. Did you not, up to this moment, ever calculate the length contraction for anything in all of your posts and pretty pictures?

DaleSpam said:
Because you and Albert didn't check with Lorentz like you should have.

-Dale

Dale, dear sir you cur; I have performed a considerable number of calculations regarding the Fitzgerald/ Lorentz/ Einstein/ Special Relativity length contraction both in relation to the the tank thread and to the bike thread. For you and Pete to give glib but non substantial responses proves that neither of you have executed any additional wear upon your slide rules and abacuses. Or fingers and toes.

Take a deep breath and try again. The top tread as copied onto my hard drive some time ago is much longer than Special Relativity allows it to be. Why was it shown in gross error in what was apparently intended to be a serious science exposition? Or were Pete and Dale's responses only really intended as jokes?

CANGAS said:
Dale, dear sir you cur; I have performed a considerable number of calculations regarding the Fitzgerald/ Lorentz/ Einstein/ Special Relativity length contraction both in relation to the the tank thread and to the bike thread. For you and Pete to give glib but non substantial responses proves that neither of you have executed any additional wear upon your slide rules and abacuses.
CANGAS you are such a clown. I greatly enjoy your amusing antics. You certainly did many silly calculations, and not a single Lorentz transform among them. On the other hand I have done three exhaustive calculations here each with multiple Lorentz transforms, and each one clearly demonstrating that there is no paradox here. You have yet to address any of those with any substantial response.

When will you quacks learn the Lorentz transform? You cannot determine what SR predicts without it. Unless you can use the Lorentz transform and obtain a contradiction you have not found a SR paradox. All you have demonstrated here is that your typical crackpot tactics are worthless.

-Dale

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CANGAS said:
Because the Fitzgerald/Lorentz/Einstein/ Special Relativity length contraction says so. Did you not, up to this moment, ever calculate the length contraction for anything in all of your posts and pretty pictures?
I certainly did, CANGAS, and it's clear that you haven't.

All the tempestuous talk about the tank top track topic tempted me to try to get to the bottom of the top track issue. Pete's pretty pictures provided a profusion of perplexities partnered with a penury of precise answers. I decided to deal with the top track problem first. First I had to get my hands on a tank to observe reliable measurements of its top track and other stuff. Knowing he wouldn't mind, I borrowed Pete's tank while he was away. With my assistant Mimi's assistance, I measured the distance between the axle center lines of the front and rear track guide pulleys. Exactly 20.0 feet. I had always believed tanks were longer than that. Or shorter. Mimi used the same yardstick Fitzgerald used to measure the contraction of his length, according to the pawn shop she borrowed it from after mistakenly going there, so we can be confident that my top track measurement is accurate, and you can take it from me that goes for the bottom track too. Next we measured the vertical seperation of the top and bottom tracks. Exactly just a foot or two. I had always believed tank tracks were taller than that. Or shorter. That was the last straw. I decided to completely ignore the length of track vertically hugging the arc of the front hemicircle of the front guide pulley and the length of track vertically hugging the arc of the hemicircle of the rear guide pulley. Thereby all references hereby to track length refer to the relatively flat portions happening to fall between the guide pulley center lines.

An observer who is fixed to the ground, such as a stationary observer who is sitting still in the station area in an easy chair watching the tank whizz by, will observe the bottom track to have zero velocity, the tank itself to have a specific velocity v, and the top track to have a specific velocity 2v. Therefore, the observer must expect Special Relativity to predict length contractions in those specific objects according to the different length contraction factors ( the inverses of the gammas ) germane to the specific velocities of the specific objects.

1. The bottom track itself will contract according to the contraction factor for zero v; 1.0.
2. The tank itself, therefore the distance between guide pulley center lines, will contract according to the contraction factor for v.
3. The top track itself will contract according to the contraction factor for 2v.

Just randomly selecting some velocities v and their specific Special Relativity contraction factors:
0.0c; contraction factor = 1.0
0.866c; contraction factor = 0.50
1.0c; contraction factor = infinitely shortened to zero length
1.732c; contraction factor = HOLY MOLY! shorter than zero length

When Pete's tank is whizzing by at 0.866c, the bottom track is relatively motionless at 0.0c and the top track at 2v is really whizzing at 1.732c. Gamma for v = 1.732c is off the gauge; the top track is contracted to much less than zero length. Perhaps it turns into a black hole and sucks the rest of the track into Riemann hyperspace. According to Special Relativity it would have no real physical length, leading me to guess that it would not be visible. Guessing that it would not be visible coerces me to expostulate that it looks funny in Pete's pretty picture because it should look shorter than being visible at all.

It is important to note that I have not yet addressed the issue of Special Relativity time dilation nor the issues of track lengths at velocities other than the thread standard 0.866c, in keeping with the example provided by the thread starter.

It is also important to note that this post has laid groundwork for such further exploration, hopefully as soon as taking care of ( real ) business will allow me.

CANGAS said:
An observer who is fixed to the ground, such as a stationary observer who is sitting still in the station area in an easy chair watching the tank whizz by, will observe the bottom track to have zero velocity, the tank itself to have a specific velocity v,
All good so far...
CANGAS said:
and the top track to have a specific velocity 2v.
You might be a bit hasty reaching that conclusion.
That would indeed be the case if the easy-chair observer saw all parts of the track to be equally expanded or contracted. But SR suggests that the parts of the track in the top section are length contracted while the bottom parts are not.
Being a consistent theory, SR also suggests that the parts of the track in the top section have a velocity of 2v/(1+v&sup2.

Taking this correction through to the remainder of your post (I actually did this already, back in the first page or two of the thread):

1. The bottom track itself will contract according to the contraction factor for zero v; 1.0.
2. The tank itself, therefore the distance between guide pulley center lines, will contract according to the contraction factor for v.
3. The top track itself will contract according to the contraction factor for 2v/(1+v&sup2.

Just randomly selecting some velocities v and their specific Special Relativity contraction factors:
Bottom parts of track: 0.0c; contraction factor = 1.0
Tank structure: 0.866c; contraction factor = 1/2
Top parts of track: 0.9897c; contraction factor = 1/7

Take a look at the animations, and you'll find that they exactly match these figures.

Pete, according to CANGAS's scenario, the length of the track is 20 feet, from centerline of the axel to centerline of the other axel. We can change this to 20 meters to make it easier for you. Assume the cleats are one meter apart. You state: (1) the bottom of the tread will contract according to the contraction factor for 0 v; 1.0. Therefore the bottom of the tread will remain 20 meters long. You display this length as contracted by a factor of 1/2 in your animation (10 meters) and the distance between cleats as stretched to two ground meters.
(2) the contraction factor for the body of the tank, and the distance between the axels, is 1/2. Therefore the distance between the axels is 10 meters according to the ground observer.
I am using two synchronized clocks located on the ground to determine lengths. One clock will start recording time when a single cleat, while it is located below the centerline of the axel, trips a laser beam projected slightly above the ground and record until that same cleat lifts off the ground. The second clock will start recording time when an axel trips a laser beam as the first axel passes, and then stop when the second axel trips the laser beam a second time. The clocks are sitting on top of each other, and the laser beams are as well, one slightly above the ground and the other at axel-heigth. You are the mathematician, can you tell me how many nanoseconds will be recorded on each clock? I get 7.698 nanoseconds recorded on each clock, assuming a speed of .866c for the tank and Newtonian physics. What does Special Theory predict? We could add another laser beam and clock to record the number of cleats passing, and the total time taken, for the top of the tread. Each cleat would simply break the laser beam as it passed. Newton says this clock will also record 7.698 ns and would record 20 cleats, of course.