Is Velocity Addition in Special Relativity Contradictory?

[DrGreg]

phyti and Ich are presenting equally valid perspectives and any choice between them is purely arbitrary and personal.

I've looked through all phyti's posts in this thread and here are all the reasons given for a top speed of 0.9c:

Caleb;
v: speed of tank
vb: speed of bottom tread
vt: speed of top tread
c = 1

The ground observer measures:
v = .45, vb = 0, vt = .9

The top track moves twice as fast as the tank.

the top track moves 2x the speed of the tank to function correctly,

That's it. These are just empty claims with no reasons behind them. Ich's posts actually give some explanation of how his conclusions are reached.

 

[phyti]

Phyti:
What's the reasoning that gets you from here:

to here:

In particular, I want to understand how you justify `the top track moves 2x the speed of the tank to function correctly', particularly in the light of the fact that, in the ground frame, the upper track is heavily lorentz contracted while the lower tread is not.

Using post7 from austino, if the tank is raised off the ground with the track running, to the driver, the top track is moving at +v and the bottom track is moving at -v.
If the tank is set onto the ground acquiring the speed v, then all components must increase speed the same amount so the tank moves as an integrated object. Thus the top track now moves at 2v, the bottom track at 0. Substitute .45c for v and this is the ground pov.
or;
With d=the center to center wheel distance and neglecting the wheel circumference, the driver sees the top move d,
then -d. On the ground the bottom is static, so the 2d motion must be in the top track.

While the top moves 2d forward, the tank moves d.

 

[phyti]

I can only refer to the 1st postulate, the physics is the same in all inertial frames.
If the tank works on Earth at slow speed, then moving it at some high speed shouldn't change the way it works, and definitely moving past it at some high speed cannot alter the way it works.

 

[yuiop]

Here is the problem analysed in terms of length contraction.

Let us say we have a simple tank with axle to axle proper length of 1.0 and a proper track length (considering only the horizontal portions of the track) of 2.0 when the tank engine is off.

In the tank frame (when the engine is on), the lower and upper parts of the track both have relative velocities of magnitude 0.45c so the half length of the track is 0.89302855 in the tank frame due to length contraction. One of the axles would have to have a tension control device to allow one of the axles to move inwards to prevent the track snapping under increased tension and so the axle to axle length in the tank frame would also have to be 0.89302855.

In the ground frame, the tank is moving at 0.45c and the axle to axle length is length contracted to 0.89302855*sqrt(1-0.45^2)= 0.7975.

The part of the track in contact with ground is stationary with respect to the ground frame so that part of the track has proper length 0.7975. The top part of the track also measures 0.7975 in the ground frame but because the top part of the track has relative velocity 0.7484407c in the ground frame (according to relativity), the proper length of the top part of the track is 0.7975/sqrt(1-0.7484407^2) = 1.2025. The total proper length of the track is therefore 0.7975+1.2025=2.0 in the ground frame.

Therefore a top track velocity of 0.7484407 is consistent with the relativistic addition laws and with relativistic length contraction if the total proper length of the track remains the same (2.0) in all frames. All this is totally consistent with relativity.

If the velocity of the top track was 0.9c, the total proper length of the track would not be 2.0 in both frames.

Therefore the velocity of the top track can not be 0.9c, if length contraction is a real physical effect and if proper length is invariant.

 

[phyti]

Let's assume that this is correct, just to see where it takes us. What you said implies that the bottom track is comoving with the ground. In the ground frame, the tank's velocity is v=0.45 (in units such that c=1). By symmetry (the principle of relativity), or by definition of the inertial frame we associate with the motion of an object, this implies that the velocity of the ground in the tank's frame is -v. So...relative to the tank, the bottom track has velocity -v=-0.45, and relative to the bottom track, the top track has velocity u=0.9 (according to your assumptions). Now the velocity addition formula tells us that the velocity of the top track relative to the tank is (-v+u)/(1+(-v)u))=(-0.45+0.9)/(1-0.45*0.9)=0.45/0.595≈0.756, while the velocity of the bottom track relative to the tank is -0.45. This contradicts your other claim:

So your assumptions can't all be correct.

Right, because I was too intent on making the drivers pov symmetrical. After making a rough space-time drawing, I see my mistake.

I have to apologize to Caleb, his original equation was correct. [(0-.45)/(1-0*.45) = -.45]

 

[calebhoilday]

This thread continues without me rather easily. When I made the thread i made the tank speed 0.45 C for a reason. This reason was to ensure that if one assumed to double the speed of the topside, the resulting speed will not equal or exceed C, revealing instantly the fault in the assumption (every other hypothetical use 0.5C).

I have not bothered to read this thread since my last post, but if there has been difficulty in understanding that post, it is equivalent to saying:
V= S/((1-(S^2/C^2))^0.5 +1)
S: the topside velocity
V: the velocity of the tank

As it has been difficult to explain my issue and also difficult for the people who have posted to explain a resolution, I will be watching some youtube edu lectures on special relativity. Hopefully then if a problem still exists then I will be typing in the appropriate discourse.

The Lorentz transformations that are length contraction, time dilation and mass increase I am familiar with, but it is relativity of simultaneity that is a source of difficulty when it comes to a comprehensive understanding. Using space-time to explain such things I feel is inadequate as space-time is formulated from the postulates. The challenge would be to explain how light speed is maintained in both directions with a thought experiment, like the ones Einstein used.

 

[yossell]

Phyti,

If the tank is set onto the ground acquiring the speed v, then all components must increase speed the same amount so the tank moves as an integrated object.

(a) This is question begging
(b) can you edit post 73 as that's not me you've quoted but austin0.

 

[phyti]

I've looked through all phyti's posts in this thread and here are all the reasons given for a top speed of 0.9c:







That's it. These are just empty claims with no reasons behind them. Ich's posts actually give some explanation of how his conclusions are reached.

This http://go.sharehub.com/shared/c6e7efb8-d0f3-4298-98bb-93038fb72b9b" shows why only .90c works.

 

[Fredrik]

This http://go.sharehub.com/shared/c6e7efb8-d0f3-4298-98bb-93038fb72b9b" shows why only .90c works.

Huh. I thought what you said in #75 meant that you now understand that it isn't possible that the topside speed is 0.9. Does this mean that you still think it is?

I don't understand your drawing by the way. You should probably explain it if you want DrGreg to explain what's wrong with it. (I think I'm going to abandon this thread now. The correct answers have been given several times already).

 

[matheinste]

1------Imagine ‘the super-tank’ a tank capable of speeds of 0.45 C is being designed. Someone on the design team, raises a potential problem. When considering the tanks tracks, the tracks that are in-contact with the ground or the bottom-side tracks, have no velocity until the tank moves over them and pulls them to the top-side. The velocity they have according to a stationary observer is twice the speed of the tank.

2------The member of the design team states that if you treat the tank as the stationary observer, then what ever speed the top-side has the bottom-side needs to have, just in the opposite direction.

Another solution. As:-

1 Is false when viewed from the ground frame. (or the tank frame )

2 Is true. The speed of the top and bottom tracks, ignoring any slack in the system, will be opposite and equal with respect to the tank when viewed from the tank.

and if the same designer made both statements get rid of the designer.

Matheinste.

 

[Austin0]

I've looked through all phyti's posts in this thread and here are all the reasons given for a top speed of 0.9c:

Originally Posted by Austin0
phyti and Ich are presenting equally valid perspectives and any choice between them is purely arbitrary and personal.

Originally Posted by phyti
Caleb;
v: speed of tank
vb: speed of bottom tread
vt: speed of top tread
c = 1

The ground observer measures:
v = .45, vb = 0, vt = .9

Originally Posted by phyti
The top track moves twice as fast as the tank.

Originally Posted by phyti
the top track moves 2x the speed of the tank to function correctly,


That's it. These are just empty claims with no reasons behind them. Ich's posts actually give some explanation of how his conclusions are reached.

Post #8....Listen:
The top side does not have a speed of 0.9 c in the ground frame..

Post#1

The member of the design team states that if you treat the tank as the stationary observer, then what ever speed the top-side has the bottom-side needs to have, just in the opposite direction.
If this is not the case then the tank tracks would rip apart, as either the top-side or bottom-side tracks would not feed enough track to the other.

Post #8
From this (valid, btw) logic it is clear that the top side has v=0.45 and the bottom side has v=-.45.
From this, and the velocity addition formula, you get
"If i was on the ground, and the tank has a speed of 0.45C according to my frame of reference, the top-side has a speed of 0.74844C."
And then the subtraction formula works again.

Right here is the sum total of Ich's precise ,step by step logical derivation.
He simply adopted the logic of the OP's hypothetical engineers (who I wouldn't disagree with) , Inserted this assumption (which directly predetermined a unique conclusion) in as an argument and that's the end of the story.

So in fact the sole logical foundation of the argument is "it must be so or the tank won't work"

Later he added the following posts.

Poswt #21

2) Even if this assumption should be correct it still ignores the physics and measurement in the Earth frame.
If you apply the distance traveled according to the .74844 figure and then apply contraction on top of this you get a track point (segment) that has not traveled as far as the wheel base and gearing. The contraction figure for the base is .8930 and for the track is .6632.SO either something is amiss or the track should decompose.

There are the additional questions; in the tank frame both the top and bottom are moving and so would be equally contracted.In the earth frame the top would be contracted but not the bottom .

Post#23

Given: ...Ich's velocity figure is totally accurate.
....We start with a coordinate time and position measurement at the rear point on the track where it is equivalent to the rear wheel base.

...We take another measurement at the point where it is colocated with the topmost point of the front wheel (and base)

...From these two points we derive velocity for the track point and the wheel base.

...The distance traveled by the track is simply dx=dx_t

...for the wheel base it is dx-(wheel base...dx)=dx_b
...I think it is safe to say that geometrically dx_t=2 dx_b
...Using round geared wheels and geared track the forward motion of the base is $$\pi$$x 2r(radius of wheel) per revolution. The top track must advance by twice this value to maintain continuity with the wheel base and gear teeth.
.If there is some explanation why this would or could not be true ;great, But keep in mind it would have to apply in the track frame equally.

Post #32

The ground has v=-.45 by some basic principles, and since the lower track is at rest wrt the ground it has v=-.45, too.
Now imagine a virtual vertical plane separating the rear part from the front part of the tank. Call it the middle plane.
Now there's an equation of continuity that says that, in any given timespan, as many track segments have to cross said plane from back to forth as in the other direction, lest the segments accumulate somewhere.From symmetry principles it is evident that v=0.45 for the upper track fulfills the continuity condition. It can be shown mathematically that this is the only solution. .

What is this continuity equation??
WHere is the foundation for this bold and bald assertion that his is the only solution to fulfill this undefined continuity equation??

What is the justification that simply having gearing would not satisfy his unique continuity criteria?
I*.e. with gears, of course, the same number of segments would pass in either direction unless the system decomposes.

.

Post #23
...I think it is safe to say that geometrically dx_t=2 dx_b

...Using round geared wheels and geared track the forward motion of the base is $$\pi$$x 2r(radius of wheel) per revolution. The top track must advance by twice this value to maintain continuity with the wheel base and gear teeth.

Post #32
This is not entirely trivial, however.
For example, the segments all like to be Lorentz-contracted. If you have a fixed number of (well-fitting) segments and spin up the tank, this cannot be achieved. Either the track will break, or the segments all get stretched. You could also add more segments until the track fits again.

Ok, now we've established v_upper = 0.45 in the tank frame, and v_tank = 0.45 in the ground frame, we have that formula that tells us that v_upper in the ground frame is 0.74844.

If we observe the upper track, we see that it moves at v=0.74844, while the middle plane moves at v=0.45. We now invoke what has been dubbed the "closing speed" in recent threads. It is v1-v2=0.29844 for the upper track.
The closing speed for the lower track is 0-0.45 = -0.45.

Could you explain this to me why we are suddenly using gallilean addition here?

And what is the logical value or justification for using this figure in the ground frame where, whichever figure 0.9 or 0.7844 ,,you use, the top is defintiely moving faster than the bottom?

Post #32
Here's the point where some of you see the continuity equation violated, and claim that logic dictates both closing speeds be the same (up to the sign). It's easy to show how this is wrong.
How many segments ("n") do actually move from back to forth and otherwise in, say, 1 second?
Use some algebra to find that n = v/l * 1 second, where v is the closing speed and l the length of a segment.
The lower track is at rest in the ground frame. The're no relativity to be obeyed, and for the sake of simplicity we set the length of a segment in that frame to be 1 second. (Remember, c=1. If you want to use the usual dimensions: that means l = 1 lightsecond = ~300000 km.)
Then n_lower = 0.45/1 s = -0.45/s.

The upper segments are slower (lower absolute closing velocity), but contracted and thus more densely packed. From the Lorentz contraction formula, we get: l_upper = 0.6632 s.
And we find n_upper = 0.29844/0.6632 s = 0.45/s.

What is the supposed meaning of all of this.
If you posit gearing on both the front and back wheel this is all redundant as the reciprocal movement between top and bottom is guarenteed.
If on the other hand you posit a single geared wheel at the front then there is question whether this whole workup above would apply. If there is the possibility of slack through contraction then there is no guarantee that the velocity at the front which is being driven is going to be the same as at the back moving topside as it is free wheeling and would be determined by relative contraction and propagation of momentum.

It is also just one of many factors to be taken into account..

How is this supposed to show anyone wrong?? What is it supposed to prove that wasn't already acknowledged?? ANd how is it supposed to counter all the other factors and logics??

In either case this ignores my questions about the physical viability of the track given the difference in contraction between 1.0 on the bottom and .6632 on the top.

Post #36
There is the 1st P to consider also..

Post #36

Given your contraction figures which I am sure are accurate:

This would mean that not only the links were contracted but, if we assume gearing, then the number of links between wheels would be fixed and so the distance between the tops of the wheels would also have to be contracted relative to the ,bottom of the track, distance between the bottoms of the wheels. Yes??

WOuldn't you assume this would create intolerable stress on the wheels??

And wheelbase??

Would you maintain that this was a workable reality by the same criteria you applied to the tank frame??
.

Post #36 As far as I know the domain of applicability of the Addition of Velocities equation is limited to ;
Independant inertial frames or objects.

a) The track as a whole or as segments would not seem to be inertial.
It is under constant acceleration through force.

b) The track is not independant. It is physically connected to both the tank and the ground.
I don't just mean in contact but that the physics of both frames have direct causal effects.

SO it would seem there is doubt if it would apply to this situation at all.

This would seem to then raise some doubt whether the derived figure can be taken at its normally , factual value , without further ocnsideration.

Post #47
It is limited to inertial frames. "Independent inertial frames" makes no sense, as I can't imagine what a dependent inertial frame would be.

Well what would you call the case we examining?

YOu have two systems, ground and tank that are independant in that they have a singular relative velocitywrt each other.
You then have a third system the track which is physically connected to both through applied force ,acceleration,and axle to tank, and has four different relative velocities wrt the other two systems.

Post #47Each segment is inertial while it's moving linearly.

"Physical connectedness" is no criteria for something being inertial or not. If it's moving with constant velocity (speed and direction), it is inertial. ...Period.

Does anyone here doubt that it is possible to have a rocket move from a point on the surface to a point a mile high at a constant coordinate speed and direction??
Or an elevator?

Is there anyone here who would say these cases would be inertial??

Is there anyone who will tell me this is not just flat out wrong?? If so I would like to herar it and learn.

Post #36
Given your contraction figures which I am sure are accurate:

This would mean that not only the links were contracted but, if we assume gearing, then the number of links between wheels would be fixed and so the distance between the tops of the wheels would also have to be contracted relative to the ,bottom of the track, distance between the bottoms of the wheels. Yes??

Post #47
No..
This is a splendid example of logic vs preconception. Try to check what you can really be sure of, and what not. For example, the bottoms (and tops) of the wheels are stationary in the tank frame. They are points - as opposed to events. You know that distances between stationary points are Lorentz contracted. Both by the same factor, of course.
By similar arguments you should know that the top segments undergo contraction wrt the bottom segments.
So where does your logic fail and turn into preconception?

There's a single answer in more than 99% of all cases where "logic" clashes with reality: You forgot the relativity of simultaneity.

Counting the number of segments between wheels contains an assumption concerning the simultaneity of spatially separated events.

SO here I am being told of my lack of valid logic because I didn't consider simultaneity.
Well that is true I didn't.

But wait a sec! Neither did Ich. Not any previous mention in any post and now having put forth another ad hominem claim ,he doesn't provide any demonstration whatsoever of how this relates to anything specifiic I said or the question at large.

Once again he does not address any specific point but simply makes a meaningless blanket assertion that assumes and implies that my logic is flawed and I am missing basic priciples without ever actually demonstrating this.

In this case even more absurd as he is accusing a failure that he himself also commited

Post #36

WOuldn't you assume this would create intolerable stress on the wheels??

And wheelbase??

Would you maintain that this was a workable reality by the same criteria you applied to the tank frame??

The above was not addressed which normal.

I pointed out to phyti that his logical base was essentially the same as Ich's but in another frame.
SO can you point out where Ich's basis or demonstration is any more compelling or valid than phyti's?
Or where I have erred in my thinking?
Thanks

 

[Passionflower]

Does anyone here doubt that it is possible to have a rocket move from a point on the surface to a point a mile high at a constant coordinate speed and direction??
Or an elevator?

Is there anyone here who would say these cases would be inertial??

Is there anyone who will tell me this is not just flat out wrong?? If so I would like to herar it and learn.

When the rocket fires its engine it is not traveling inertially, when the rocket engine is turned off it is traveling inertially.

Whether the rocket travels with a constant coordinate speed entirely depends on the chosen coordinate chart.

 

[matheinste]

Austin0,

Your error lies in assuming that the top track speed is twice the tank speed when viewed from the ground frame. It is not. the value is correctly arrived at using the relativistic velocity addition formula.

Until you accept this point, which has been explained several times, you will be unable to see how to relate frames to each other.

The difference between phyti's approach and Ich's approach is that ich is correct and phyti is wrong regarding the top track velocity relative to the ground.

Matheinste.

 

[Ich]

Great. In https://www.physicsforums.com/showpost.php?p=2814757&postcount=81", after a long and stagnant discussion, you confess that you didn't understand anything of what I wrote in this thread. And you ask the general public - rhetorically - a whole lot of concrete questions concerning my derivations. But didn't ask me a single one when I posted all this stuff.

I'm done with this.

 

[Ken Natton]

Possibly against all wisdom, I am going to butt my ore into this thread one more time. Not because I imagine for one moment that I can offer any resolution to the discussion, but just to see of there is any consensus on an issue that has been a surprise to me on this thread – this notion that the tank track is subject to any physical tension as a result of unequal length contraction.

It may well be that you are all going to tell me that it has no connection at all, but I have only just come across this notion known as the Ehrenfest paradox. A quick search of this specific forum shows up a large number of previous threads that have mentioned it, not a few of which refer to the Wikipedia article and its example of a circular train linked by elastic couplings. By that account, as the train accelerates and the individual carriages contract, the elastic couplings are stretched. The Wikipedia article mentions that this paradox remains an unresolved controversy among the people that, I certainly, would have supposed would know.

So, taking it back to Einstein’s measuring rod lying along the x-axis of the co-ordinate system and accelerated along the x axis. Surely it was never the relativity case that the rod is subject to any kind of compression? There is no rearrangement of the constituent molecules, or atoms or even subatomic particles of the rod. It is simply made to appear to have length contracted because of its relative deflection in spacetime. The observer sat on the rod still finds it to be exactly the same rod it always was.

I cannot explain the resolution of the paradox, but it seems clear to me that the individual carriages and all of the elastic couplings must be length contracted according to the appropriate formula. In the original case of the rigid disc, the whole system must be homogenous.

And whatever the appearance to the ground observer due to conflicting length contractions, the reality in the frame of the tank itself is that the peripheral scalar speed of the tank track is constant and no undue tension is caused.

 

[Austin0]

Austin0,

Your error lies in assuming that the top track speed is twice the tank speed when viewed from the ground frame. It is not. the value is correctly arrived at using the relativistic velocity addition formula.

Until you accept this point, which has been explained several times, you will be unable to see how to relate frames to each other.

The difference between phyti's approach and Ich's approach is that ich is correct and phyti is wrong regarding the top track velocity relative to the ground.

Matheinste.

Where did this come from. WHere did I ever state any quantitative speed for the top track?

I did logical analysis working explicitly with Ich's firgure of .7844c

I never anywhere did any analysis or attempted derivation of 0.9c.

I did mention that this would have problems too.

I did show reason for assuming that in the ground frame the distance would be twice the wheel base but drew no quatitative conclusions from this.

I never in any place said phyti's resolution was correct. In fact I specifically wrote him pointing out that he was using the same logical basis that Ich was, just using it in another frame.

My point wasn't that either one was right or wrong but rather that both solutions had problems and created situations which seemed to negate the basis of both view's logical premises:
i.e. " It must be this way or the tank won't work"

I am at a loss how you have misread the explicit meaning of what I have written.
Have somehow drawn a conclusion or reinterpretation that has no basis in what is actually there in black and white.
DO you have any awareness of recognized logical fallacies?

 

[Ich]

this notion that the tank track is subject to any physical tension as a result of unequal length contraction.

Not as a result of unequal length contraction. We're talking here essentially about the Ehrenfest paradox (which is solved, of course). If the track is moving in the tank frame, all its segments are shorter, but the number of segments is the same. So you have to do something about it. Which I described https://www.physicsforums.com/showpost.php?p=2810402&postcount=32".
It is not important for the rest of the problem, because we're going to fix the segments' length in the tank frame to an arbytrary (and irrelevant) number anyway.

 

[Austin0]

When the rocket fires its engine it is not traveling inertially, when the rocket engine is turned off it is traveling inertially. Whether the rocket travels with a constant coordinate speed entirely depends on the chosen coordinate chart.

This my point exactly. When under acceleration whether it is hovering underthrust in gravity or being accelerated upward at a constant speed it is not inertial.

 

[matheinste]

Where did this come from. WHere did I ever state any quantitative speed for the top track?

I did logical analysis working explicitly with Ich's firgure of .7844c

I never anywhere did any analysis or attempted derivation of 0.9c.

I did mention that this would have problems too.

I did show reason for assuming that in the ground frame the distance would be twice the wheel base but drew no quatitative conclusions from this.

I never in any place said phyti's resolution was correct. In fact I specifically wrote him pointing out that he was using the same logical basis that Ich was, just using it in another frame.

My point wasn't that either one was right or wrong but rather that both solutions had problems and created situations which seemed to negate the basis of both view's logical premises:
i.e. " It must be this way or the tank won't work"

I am at a loss how you have misread the explicit meaning of what I have written.
Have somehow drawn a conclusion or reinterpretation that has no basis in what is actually there in black and white.
DO you have any awareness of recognized logical fallacies?

My apopogies for any upset caused. I am finished here. Life's too short to peel mushrooms ( in the frame of reference in which I am at rest ).

Matheinste.

 

[Ken Natton]

Austin0, nobody’s logical premise is that ‘it must be this way or the tank won’t work.’ It is a perfectly valid point that the fact that the tank does work is a big clue to the reality that any explanation that requires impossible conditions must be wrong. But that is not the same holding that to be a logical premise. The only logical premise is that relativity as introduced to us all by Einstein is mathematically proven and supported by a wealth of experimental evidence. The true explanation of this problem lies within it.

Ich, you understand that I do not hold that there is any unequal length contraction, but I have demonstrated that my opinion is only based on the kind of supposition that Physics Forums frowns upon. I believe that it can be proven mathematically, I just can’t do it myself.

I confess that I don’t exactly understand how your post #32 resolves it, and whether you are saying that the track (or Einstein’s measuring rod) does or does not undergo some physical change. I am tantalised by your assertion that the Ehrenfest paradox is solved. That certainly does not appear to be what the Wikipedia article says, though the article is flagged as being one that is not up to standard. Can you refer me to an explanation of the resolution of the Ehrenfest paradox? Or do I just labour through all the existing threads here on Physics Forums in the hope of finding that explanation somewhere? I have the strongest feeling that the resolution of it is the same as the resolution to this problem.

 

[Austin0]

Sorry, but as long as you don't take the time to read what I've written, it'd be a waste of time to write more. We're exactly where we've started.

Great. In https://www.physicsforums.com/showpost.php?p=2814757&postcount=81", after a long and stagnant discussion, you confess that you didn't understand anything of what I wrote in this thread. And you ask the general public - rhetorically - a whole lot of concrete questions concerning my derivations. But didn't ask me a single one when I posted all this stuff.

I'm done with this.

You had last written it would be a waste of time to write more to me.

DrGreg posted a full history of phyti's derivation and logic as a demonstration of its weakness compared to yours, so in the interests of equitable search for truth I did the same with your history. Did I leave anything out??
Is this not an accurate presentation of your derivation and logic??

I did not say I didn't understand what you did, just that I didn't understand the logical justification for some of it or the strength , as any kind of proof, for other parts.

This was addressed directly to DrGreg but I opened it up for anyone to explain specifically points where I was misunderstanding or logically in error.

This of course includes you if you care to, I assumed from what you had written you didn't

I have read very carefully eveything you have said in this question. You ignore the many times I have agreed with you. Ignored that I took your figure and spent time working its logical and physical implications.
I made an effort to make a direct point by point responce to your ideas.
You continually come out with these unspecified claims that carry an implicit assumption and an explicit insinuation that if I don't agree with everything you say I obviously don't understand basic SR principles or am incapable of valid logic or reasoning.

This is a recognized logical fallacy: It does not address my logical arguments but instead attacks my qualification to question your assertions.Avoiding any actual logical argument because you have a priori decided my logic is false becaue I am not qualified to possibly have valid points. ALso completely circular.

It is an appeal to authority , in this case mainly your own.

It is poisoning of the well in that it seeks to undermine any future arguments I may have.

Care to comment or do you think this isjust more of my "games"

 

[yossell]

O! Austin0,

I make that three down, about five more to go. But that's just from my reference frame, of course.

edit: hey! $$13^2$$ posts!

 

[matheinste]

O! Austin0,

I make that three down, about five more to go. But that's just from my reference frame, of course.

[/tex] posts!

OK so I can't resist peeling another mushroom.

Numbers (of departing posters?) are frame invariant.

Matheinste.

 

[Austin0]

Austin0, nobody’s logical premise is that ‘it must be this way or the tank won’t work.’ It is a perfectly valid point that the fact that the tank does work is a big clue to the reality that any explanation that requires impossible conditions must be wrong. But that is not the same holding that to be a logical premise. The only logical premise is that relativity as introduced to us all by Einstein is mathematically proven and supported by a wealth of experimental evidence. The true explanation of this problem lies within it.

Ich, you understand that I do not hold that there is any unequal length contraction, but I have demonstrated that my opinion is only based on the kind of supposition that Physics Forums frowns upon. I believe that it can be proven mathematically, I just can’t do it myself.

I confess that I don’t exactly understand how your post #32 resolves it, and whether you are saying that the track (or Einstein’s measuring rod) does or does not undergo some physical change. I am tantalised by your assertion that the Ehrenfest paradox is solved. That certainly does not appear to be what the Wikipedia article says, though the article is flagged as being one that is not up to standard. Can you refer me to an explanation of the resolution of the Ehrenfest paradox? Or do I just labour through all the existing threads here on Physics Forums in the hope of finding that explanation somewhere? I have the strongest feeling that the resolution of it is the same as the resolution to this problem.

This the specific logic in the original post. The engineers decided that the tracks must move at equal velocity in both directions ,I have repeatedlu stated I agree with this logic.

Ich also explicitly stated he agreed with this logic and that was the sum total logical justification for the assumption of .45 top track speed in his derivation.

Phyti also used a variation of this as justification for assumptions.

I certainly agree with the statement about SR . ANd I haven't in any way ruled out a resolution. I have just stated my opinion that we haven't arrived there yet. Perhaps simultaneity does have to be figured in. I can't feel there has been a satisfactory and clearcut resolution so far. Thats all.

I do think that your assumption that the tank would neccessarily work would take some real proof IMHO

 

[Austin0]

O! Austin0,

I make that three down, about five more to go. But that's just from my reference frame, of course.

edit: hey! $$13^2$$ posts!

OK I give up . This thread may be done anyway as you have all decided the question is answered.

I will just sit back and direct my flawed logic to other things . SO that's now just four more to go.

 

[Ken Natton]

Okay, I have found a paper for myself, it is here:

http://www.wbabin.net/physics/hynecek7.pdf


Of course, I must confess that the explanation is largely over my head. Although, what I take from the abstract is that the heart of the resolution is that the paradox bases itself in special relativity, which applies to inertial reference frames and a spinning disc is not an inertial reference frame. Anybody else thinking, ‘well I could have told you that?!’ I do also understand that Hynecek does refer to a ‘New Space-Time Metric’. I just don’t necessarily understand the mathematics behind his new metric.

‘The centrifugal and centripetal forces resulting from the rotation are always present and need to be included into considerations. Using the previously derived metric for a centrally gravitating body the effect of the centrifugal and centripetal forces can be included. When this is correctly done no paradox is obtained and it is shown that the spinning disc has flat space-time geometry.’​

So, my contention now is that the explanation given here explains exactly what happens to the tank track as it goes around the wheels at either end. The peripheral speed that it has at it comes off at a tangent to top dead centre of the rear wheel is the speed it maintains throughout the forward motion, and the peripheral speed that it has at it comes off at a tangent to bottom dead centre of the front wheel is the speed it maintains throughout the rearward motion.

 

[Ich]

Ich, you understand that I do not hold that there is any unequal length contraction

Not in the tank frame. All segments have the same speed there.

I confess that I don’t exactly understand how your post #32 resolves it, and whether you are saying that the track (or Einstein’s measuring rod) does or does not undergo some physical change.

There is physical change. The segments are contracted, the circumference of the wheel (in the tank frame) is not. They no longer fit, unless they get stretched.

I am tantalised by your assertion that the Ehrenfest paradox is solved. That certainly does not appear to be what the Wikipedia article says

The Ehrenfest paradox may be the most basic phenomenon in relativity that has a long history marked by controversy and which still gets different interpretations published in peer-reviewed journals.

I don't think they want to say it is unsolved.

Can you refer me to an explanation of the resolution of the Ehrenfest paradox?

I think the first reference in the Wikipedia article is good.
However, I fail to see what the paradox is supposed to be. You can't spin up a rigid cylinder? Well, rigid bodies are incompatible with SR anyway. The measured circumference is longer than the radius suggests? Why should it?

Okay, I have found a paper for myself, it is here:
http://www.wbabin.net/physics/hynecek7.pdf
Of course, I must confess that the explanation is largely over my head.

There's a problem: wbabin is a crackpot site, and the paper is a crackpot paper. It's not only over your head, typically no one except the author understands these papers. Well, no, the authors don't understand them either.

The peripheral speed that it has at it comes off at a tangent to top dead centre of the rear wheel is the speed it maintains throughout the forward motion, and the peripheral speed that it has at it comes off at a tangent to bottom dead centre of the front wheel is the speed it maintains throughout the rearward motion.

Yes.

 

[yuiop]

It may well be that you are all going to tell me that it has no connection at all, but I have only just come across this notion known as the Ehrenfest paradox. A quick search of this specific forum shows up a large number of previous threads that have mentioned it, not a few of which refer to the Wikipedia article and its example of a circular train linked by elastic couplings. By that account, as the train accelerates and the individual carriages contract, the elastic couplings are stretched. The Wikipedia article mentions that this paradox remains an unresolved controversy among the people that, I certainly, would have supposed would know.

There are no genuine paradoxes in Relativity. A genuine paradox constitutes a valid counterproof to SR and no such counterproof exists. There are only "apparent paradoxes" that reflect popular misconceptions in people's understanding of SR. In the Ehrenfest paradox, the couplings are under increasing tension as the velocity of the circulating train increases due to length contraction. Anyone who does not understand this, does not understand SR. This comes about from a popular misconception that length contraction is not a physical effect and is just some mathematical notion that comes about from coordinate measurements. This is similar to Bell's rocket paradox, which confuses some people, because they can not accept that a string connecting two accelerating rockets that maintain a constant distance apart as measured in an inertial frame, will eventually snap due to tension induced in the string due to length contraction.

I cannot explain the resolution of the paradox, but it seems clear to me that the individual carriages and all of the elastic couplings must be length contracted according to the appropriate formula.

.. and therefore the carriages and coupling will be under increased tension that is measurable/physical and possibly destructive.

And whatever the appearance to the ground observer due to conflicting length contractions, the reality in the frame of the tank itself is that the peripheral scalar speed of the tank track is constant and no undue tension is caused.

If the wheelbase of the tank remains constant, then the track will be under increased tension. You could put pressure sensors on the axles of the tank and measure this increased tension. That is a fact.

Can you refer me to an explanation of the resolution of the Ehrenfest paradox? Or do I just labour through all the existing threads here on Physics Forums in the hope of finding that explanation somewhere? I have the strongest feeling that the resolution of it is the same as the resolution to this problem.

I am curious as what you imagine is not explained in the Ehrenfest paradox? The only way that the Ehrenfest paradox might seem paradoxical is if you ask why relativistic effects can not be explained by Newtonian or Galilean physics. Or you might ask why it is that when we live in a Relativistic universe, things don't behave as if we don't live in a Relativistic universe? The resolution is that we live in a universe that obeys relativistic laws, that are only approximated by Newtonian laws at low relative velocities.

Here is another physical example. Let us say we have a relativistic chain saw. The cutting chain of the saw is mounted on a spring loaded, free wheeling sprocket at the end of the saw furthest from the handle that keeps the tension of the chain constant. When the engine is running, the chain length contracts and the total length of the chainsaw visibly shrinks in the rest frame of the chainsaw. With a chain speed of 0.9c, you could for example fit the chainsaw comfortably in a box that is half the size of the box that would be required when the chainsaw engine is off.

 

[Ken Natton]

Okay Kev and Ich, many thanks for the responses. Please understand that I make no absolute assertions and I offer no stubborn refusals to listen to what you are saying. I am genuinely only trying to flag up what I don’t understand in the hope of creating a conversation that might be informative for other neutral parties reading the thread – not to mention achieving a better understanding for myself in the process!

Kev, I’ve seen disputes on other threads about what is and what is not ‘a paradox’, and again I don’t think it adds anything. Believe me, I belong to the school of thought that says that one of the key difficulties with the popular perception of relativity is all the coffee table philosophical discussions of obscure implications of the theory that get presented as if they were the theory itself. But the moment I saw this Ehrenfest paradox I recognised its connection with (at least my perception of) this problem. I never sought to suggest that it offered any serious challenge to relativity theory, I just sought to understand it because I knew it would offer insight into the tank track problem.

Having said that, I want to ask both of you to put the tank track problem aside and just answer me on this one simple issue. I can project your answer forward to its implications for the tank track problem perfectly well, so please, for a moment, just stick with Einstein’s measuring rod with me.

If I have the measuring rod static in front of me, and load it into one of those machines they use for testing the compressive capabilities of materials, and squash it such that it is no longer 1 metre long but it is now 0.995 metres long, all of us understand that I have done something pretty serious to the rod. To decrease its length, I will have subjected to some serious kind of distortion. When I take it out of the machine, it doesn’t spring back to 1 metre long, it remains squashed. I have damaged the measuring rod.

If I lie it along my Cartesian x-axis and accelerate it up to something close to the speed of light along the x axis, it contracts to some small fraction of the length it used to be. But if I stop it, it goes back to being 1 metre long. Moreover, if I had been riding on it while it was accelerated up to speed, I would have seen no change at all occur to the measuring rod.

Am I right? Is it your case that the measuring rod is subjected to a compressive force when it is accelerated?

 

[jtbell]

If I lie [a measuring rod] along my Cartesian x-axis and accelerate it up to something close to the speed of light along the x axis, it contracts to some small fraction of the length it used to be. But if I stop it, it goes back to being 1 metre long. Moreover, if I had been riding on it while it was accelerated up to speed, I would have seen no change at all occur to the measuring rod.

Correct. Note also that you observe the same effects on the rod if you accelerate yourself instead of the rod, in which case no forces are exerted on the rod at all!

 

[Ken Natton]

Ah ha! Excellent point jtbell. Just perfect. So. Let’s leave the tank and its track stationary on planet Earth and accelerate me up to 0.45c. Does the tank track rip itself apart then? Is it subject to any kind of tension at all in that circumstance? Of course not.

There is physical change. The segments are contracted, the circumference of the wheel (in the tank frame) is not. They no longer fit, unless they get stretched.

So this then is what I don’t understand. I don’t think any of us are confused about what happens in the reference frame of being on board the tank. My case is that whatever the perceptions of the ‘ground observer’ of the relative speeds of the top and the bottom sections of the track, it is not actually subjected to any undue force likely to cause it to fail. Is that right or is it wrong?

 

[yuiop]

Ah ha! Excellent point jtbell. Just perfect. So. Let’s leave the tank and its track stationary on planet Earth and accelerate me up to 0.45c. Does the tank track rip itself apart then? Is it subject to any kind of tension at all in that circumstance? Of course not.

Moving at 0.45c relative to a tank with a stationary track (case a) is not at all equivalent to a tank moving at 0.45c with its wheels and tracks turning (case b). In the case a, the top and bottom tracks are at rest with respect to each other and in case b the top and bottom tracks are moving relative to each other, so this is a bad counter example. Of course when the observer is moving at 0.45c relative to the stationary tank with stationary tracks, the length contraction of the tank's wheelbase is exactly the same as the length contraction of the track length and of course there will be no stress on the track in that situation, but that is not relevant to the moving tank, moving track scenario.

So this then is what I don’t understand. I don’t think any of us are confused about what happens in the reference frame of being on board the tank. My case is that whatever the perceptions of the ‘ground observer’ of the relative speeds of the top and the bottom sections of the track, it is not actually subjected to any undue force likely to cause it to fail. Is that right or is it wrong?

Wrong. The track will fail at high enough velocity if we have a fixed wheelbase tank, due to length contraction of the track.

If I have the measuring rod static in front of me, and load it into one of those machines they use for testing the compressive capabilities of materials, and squash it such that it is no longer 1 metre long but it is now 0.995 metres long, all of us understand that I have done something pretty serious to the rod. To decrease its length, I will have subjected to some serious kind of distortion. When I take it out of the machine, it doesn’t spring back to 1 metre long, it remains squashed. I have damaged the measuring rod.

It is possible to compress a rod without applying any undue forces to it. I can take a rod and cool it and it will shrink to its natural unstressed length for the lower temperature. If one the other hand I clamp the two ends of the rod in a very strong structure and wrap a cooling jacket around the rod (but the vice structure) then when the rod is cooled it will be under serious tension and if cooled enough will snap, because the rod is not being allowed to contract to its natural length for the temperature it is at. The same is true for a relativistic rod. If it is somehow prevented from contracting to its natural length for the velocity it is at, then it will be under tension and may snap. Do you agree that the example I gave of the relativistic chain saw is a valid prediction of relativity?

Am I right? Is it your case that the measuring rod is subjected to a compressive force when it is accelerated?

If you understood my arguments above, then you will understand that my position is that the measuring rod is not subjected to a compressive force when it is accelerated. It simply shrinks to its natural unstressed length. It is only stressed if it is not allowed to attain its natural unstreessed length. A fixed wheelbase tank with a track moving at relativistic speeds does not allow its track to attain its natural length contracted length and the track will be under tension that will destroy the track in the extreme case.

You should bear in mind that if a measuring rod and an observer are at rest with respect to each other, accelerating the observer to 0.45c is not equivalent to accelerating the rod to 0.45c relative to the observer. In the first case, the observer feels proper acceleration and in the second case, the rod experiences proper acceleration. Accelerometers will reveal whether it was the rod or the observer that really changed velocities. Even without accelerometers, clocks in the frame of the onbject that really changes velocity will go out of sync and will have to be re-synchronised at the final velocity. From the Lorentz Ether Theory (LET) point of view, when the observer accelerates relative to the rod, changes in the observers clocks and rulers cause him to measure the length of the unaccelerated rod as length contracted without any actual physical change in the length of the rod. If the rod is accelerated relative to the observer, then the change in the length of the rod is real. LET is completely equivalent to SR mathematically in its predictions. It is only the philosophical interpretation that is different.

 

[Austin0]

I would like to understand velocity addition and subtraction in special relativity, more than I currently do. It would be greatly appreciated if one could comment on the outcome of the following thought experiment.

Imagine ‘the super-tank’ a tank capable of speeds of 0.45 C is being designed. Someone on the design team, raises a potential problem. When considering the tanks tracks, the tracks that are in-contact with the ground or the bottom-side tracks, have no velocity until the tank moves over them and pulls them to the top-side. The velocity they have according to a stationary observer is twice the speed of the tank.

The member of the design team states that if you treat the tank as the stationary observer, then what ever speed the top-side has the bottom-side needs to have, just in the opposite direction. If this is not the case then the tank tracks would rip apart, as either the top-side or bottom-side tracks would not feed enough track to the other.

It is then shown that the tank will not have the same but opposing velocity for its tracks, in the reference frame of the tank, based on the velocity of the bottom-side tank relative to the ground observer being 0 and the top-side 0.9C.

U = (S-V) / (1-(SV/C^2))
U: The velocity of the tracks according to the tanks frame of reference.
S: The velocity of the tracks according to the ground frame of reference.
V: The velocity of the tank according to the ground frame of reference.
C: the speed of light in a vacuum.

Bottom-side velocity according to the tank
U = (0 - 0.45C) / (1-(0C*0.45C/C^2))
= -0.45C / 1
= -0.45C

Top-side velocity according to the tank
U = (0.9 - 0.45C) / (1-(0.9*0.45/C^2))
= 0.45C / (1-0.405)
= 0.45C / 0.595
= 0.7563C

How can this difference exist considering the concerns of the designer?

Hi calebholiday
You definitely provided a provocative ,even if not unsolvable scenarioo.

Some thoughts:

From the ground frame the clocks at the front wheelbase of the tank are running behind the clocks at the rear.
This would mean that measurement of track speed of the upper track would be faster than that measured for the bottom track.
As we know the bottom track velocity is 0.45c this would mean that the top track velocity must be greater than 0.45c
From the tank frame the reciprocal situation prevails.

The rear clocks are running behind so the measurement of the wheel base velocity must be lower. This is symmetrical with the clocks on the tank and both derive 0.45c as expected.

But in this case the top track is moving in the same direction as the wheel base so the desynchronization does not change the measurement as it is the exact same clocks measuring both.
So in this case the geometry and mechanics would seem to indicate twice the distance covered and hence twice the velocity i.e. 0.9c

So it would appear that in the light of simultaneity you may have been right all along.

There still remains the problem of reciprocal contraction:

It can be seen that in the tank frame the number of segments counted for the upper track would be increased due to simultaneity and therefore the conclusion would be they were contracted.
If there is a marked segment to start the velocity measurement and the rear observer starts counting segments from that point, he will count more segments passing in the time it takes the clock in the front to catch up as that first segment reaches his position.
But of course the opposite would seem to pertain wrt the bottom track where they would count fewer segments.

Likewise in the ground frame I can see no way that the count starting in the rear, where the clock is running behind could not count fewer segments in the interval between time there and the same time at the front where the clock is running ahead.

So there is still seems to be good reason to think that your question has yet to be fully or satisfactorily resolved.
There remains the purely SR question of reciprocal contraction as well as the engineering/physics question of whether such a system is possible or would decompose before ever attaining such velocities.
The fundamental question of the meaning of contraction i.e. kinematic vs physical , itself appears to be unresolved and far from concensus.

If I have brought disruption inot your otherwise rational and objective thread I apologize
it was not my intention
Thanks for bringing forth interesting problem

 

[Ken Natton]

Kev, I have to say, to me, the point about the tracks being stationary is a red herring. Okay, how about this then. I’m still going to leave the tank and its tracks here on earth, but I’m going to dangle it from a crane so that its tracks are not in contact with the ground. Then I am going to run the tracks up to speed such that the top track is going 0.45c forwards, and the bottom track is going 0.45c backwards. The tank itself is going nowhere. No unequal length contraction, no confusion about what happens to the top or the bottom of the track.

Now I’m going to get into a spacecraft and accelerate myself to 0.9c. I understand that it is clear that it is me that accelerates, not the tank, but I am not interested in what happens during the acceleration phase. I’m interested in what happens once I am up to a steady 0.9c. I’m in an inertial reference frame at 0.9c relative to the tank dangling from the crane on planet earth. We’re back to confusion about what the top and bottom tracks are doing relative to me. Their velocities, relative to me are not the same and thus their length contractions are not the same. But no-one is going to suggest that the change in my velocity is going to put any added strain on the tank track.

Maybe I am completely wrong about this and I stand to be educated if I am, but my understanding is that the length contraction that occurs due to differences in relative speed is not of the same nature as that that occurs doe to physical compression or even due to reducing temperature, when it is clear that the reduction in length occurs because the molecules are slowing down and getting closer together. If I lie my measuring rod along my Cartesian x-axis and take a view perfectly square to the x-y plane, if I then rotate the measuring rod into the z plane, it appears to get shorter in the x direction. It isn’t really getting any shorter, it is just rotated into the z plane. Likewise, length contraction due to differences in relative velocity is just a question of deflections in spacetime. Right or wrong? If you are going to say wrong, then I do need an explanation for why the stationary observer sees the tank track fail due to length contraction but the observer on board the tank sees no such problem.

 

[Ich]

If I lie my measuring rod along my Cartesian x-axis and take a view perfectly square to the x-y plane, if I then rotate the measuring rod into the z plane, it appears to get shorter in the x direction. It isn’t really getting any shorter, it is just rotated into the z plane. Likewise, length contraction due to differences in relative velocity is just a question of deflections in spacetime. Right or wrong?

That's a very accurate view of length contraction.

If you are going to say wrong, then I do need an explanation for why the stationary observer sees the tank track fail due to length contraction but the observer on board the tank sees no such problem.

Nobody ever said that.
It has nothing to do with observers, and nothing to do with different length contractions in different frames.
If you spin up the track, it gets stretched, and the observer on board the tank sees a problem, too. Which he/she can handle on the engineering level, this is nothing which make the rest of the Gedankenexperiment invalid.