# Problem Of Length Contraction At Cern Due To Special Theory Of Relativity.

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### #1 maheshkhati

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Posted 07 December 2017 - 04:10 AM

1) When I was in school & teacher was teaching Spe relativity to us. I had asked one question to the teacher. If I fixed four pulleys A, B, C & D in such a way that they would create rectangle & one thread is mounted on that pulleys & that thread is revolve on the pulleys with some velocity then what will happen. Length of thread would decrease due to length contraction as inter molecular distance get contracted (as per SR) but centersâ€™ of four pulleys would remain at same point. How would this possible?  My teacher said that velocity of thread is not much. So, this problem would not be created in actual life.

Now, same problem can be asked for CERN.

2) In CERN, 2808 bunches of protons are rotated in circular path, initial velocity of rotation is V1 = 0.9993 C at 25 GeV & final velocity of rotation V2 = 0.99999999 C at 6.5 TeV..

So, value of Y changes from Y1={(1-V1^2/C^2)}^-0.5 = 26.7308   to Y2 = 7071.068. This is very big change in Y. So, distance between any two bunches of protons will get decrease by 264.5288 times when velocity of protons increases in accelerator.

This will decrease the total circular path of proton from 27000 m (27 km) to just 102.0683 m (0.102 km).

& radius from 4299.363m to just 16.253 m.

How is this possible as accelerating magnets are at same position for rest observer?

Edited by maheshkhati, 07 December 2017 - 04:57 AM.

### #2 exchemist

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Posted 07 December 2017 - 05:21 AM

1) When I was in school & teacher was teaching Spe relativity to us. I had asked one question to the teacher. If I fixed four pulleys A, B, C & D in such a way that they would create rectangle & one thread is mounted on that pulleys & that thread is revolve on the pulleys with some velocity then what will happen. Length of thread would decrease due to length contraction as inter molecular distance get contracted (as per SR) but centersâ€™ of four pulleys would remain at same point. How would this possible?  My teacher said that velocity of thread is not much. So, this problem would not be created in actual life.

Now, same problem can be asked for CERN.

2) In CERN, 2808 bunches of protons are rotated in circular path, initial velocity of rotation is V1 = 0.9993 C at 25 GeV & final velocity of rotation V2 = 0.99999999 C at 6.5 TeV..

So, value of Y changes from Y1={(1-V1^2/C^2)}^-0.5 = 26.7308   to Y2 = 7071.068. This is very big change in Y. So, distance between any two bunches of protons will get decrease by 264.5288 times when velocity of protons increases in accelerator.

This will decrease the total circular path of proton from 27000 m (27 km) to just 102.0683 m (0.102 km).

& radius from 4299.363m to just 16.253 m.

How is this possible as accelerating magnets are at same position for rest observer?

The elementary principle, according to my limited understanding of relativity, is that time dilation and length contraction are complementary.

It is the proton that sees the path it takes as shrunken to ~100m.

We see the proton travel round a 27km circuit, but that time is running slow for it, such that the time elapsed for it to make a 27km circuit is the same as it would for it to complete a ~100m circuit, if time were running at "normal" rate.

I refer you to the well known atmospheric meson example. I think it is the same principle here.

### #3 maheshkhati

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Posted 08 December 2017 - 04:22 AM

You are true but time dilation & length contraction happen simultaneously.  For example, for man on platform  who is seeing event happen in moving train cabin find that event is slowing down & cabin length, other distances in cabin in direction of motion decreases simultaneously.

So, time dilation & length contraction  between two proton's bundles will  simultaneously happen for man at rest.

So, Initially if distance between two proton bundle =27000/2808 = 9.615 m

then it must get reduce to =0.036 m for man in rest at final increase velocity

So, total path of beam reduces to 102 m from 27000 m

example:- We consider electrons density contraction due to moving current in two wires in the direction of current for solving problem of attraction between two parallel wires having current in same direction by SR.

This solution is available everywhere for example

http://www.alternati...LCmagnetism.htm

So, length contraction between two particles (or particle bundles) in direction of motion is not new in SR.

Edited by maheshkhati, 08 December 2017 - 04:23 AM.

### #4 exchemist

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Posted 08 December 2017 - 12:04 PM

You are true but time dilation & length contraction happen simultaneously.  For example, for man on platform  who is seeing event happen in moving train cabin find that event is slowing down & cabin length, other distances in cabin in direction of motion decreases simultaneously.

So, time dilation & length contraction  between two proton's bundles will  simultaneously happen for man at rest.

So, Initially if distance between two proton bundle =27000/2808 = 9.615 m

then it must get reduce to =0.036 m for man in rest at final increase velocity

So, total path of beam reduces to 102 m from 27000 m

example:- We consider electrons density contraction due to moving current in two wires in the direction of current for solving problem of attraction between two parallel wires having current in same direction by SR.

This solution is available everywhere for example

http://www.alternati...LCmagnetism.htm

So, length contraction between two particles (or particle bundles) in direction of motion is not new in SR.

### #5 sluggo

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Posted 08 December 2017 - 01:26 PM

In the left figure, the earth observer E records the travel time of the muon at .95c, for the distance 5 (altitude to ground) as 5.26. E calculates the travel time for M the observer moving with the muon as 1.64, resulting from time dilation. Since M experiences time dilation to the same degree as his clock, his sense of time agrees with his clock.

In the right figure, M calculates the altitude as .95*1.64=1.56.

If time dilation and length contraction are motion induced phenomena, then

this large scale length contraction is not a consequence of em field deformation, but the interpretation of the observers own time dilation. The observer's motion cannot alter the behavior of distant objects, but can alter his perception of them.

### #6 maheshkhati

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Posted 11 December 2017 - 03:53 AM

Do not apply any transformation of frames for time, This is simple one observer problem. So, in this prime frame time remain same. (for proton, this will change)

here is only one observer is present, which is at rest with CERN magnets (may be scientist of CERN). Velocity of 2808 bundle of protons are increasing from 0.9993c to 0.99999999 C for this observer & distance between two bundles will decreases from 9.615 m to 0.036 m due to length contraction.

(No of bundles remain same in circular path)

Now, only problem is this, decrease in above distances will not decrease the circular path of protons or remain same.

because position of magnets will remain as it is for this prime observer.

Do not go to proton bundle frame for change in time because observer are not changing the frame.

This is just same frame observation problem.

1) This is simple as if any train is moving with more velocity, observer find its length get contracted.

Edited by maheshkhati, 11 December 2017 - 04:11 AM.

### #7 maheshkhati

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Posted 12 December 2017 - 12:44 AM

Length contraction formula derived from formula

dx' = Y(dx-vdt)

We can measure length when we know position of two points at the same instant

so, dt = 0

& dx= dx'/Y

So, time slow down does not have any effect on length contraction because this is known position of two points at same instant in prime frame.

& this formula has only two variables dx' & Y.

(not dt)

So, if Y increases dx decreases

Edited by maheshkhati, 12 December 2017 - 12:52 AM.

### #8 sluggo

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Posted 12 December 2017 - 12:40 PM

1) When I was in school & teacher was teaching Spe relativity to us. I had asked one question to the teacher. If I fixed four pulleys A, B, C & D in such a way that they would create rectangle & one thread is mounted on that pulleys & that thread is revolve on the pulleys with some velocity then what will happen. Length of thread would decrease due to length contraction as inter molecular distance get contracted (as per SR) but centersâ€™ of four pulleys would remain at same point. How would this possible?  My teacher said that velocity of thread is not much. So, this problem would not be created in actual life.

Now, same problem can be asked for CERN.

2) In CERN, 2808 bunches of protons are rotated in circular path, initial velocity of rotation is V1 = 0.9993 C at 25 GeV & final velocity of rotation V2 = 0.99999999 C at 6.5 TeV..

So, value of Y changes from Y1={(1-V1^2/C^2)}^-0.5 = 26.7308   to Y2 = 7071.068. This is very big change in Y. So, distance between any two bunches of protons will get decrease by 264.5288 times when velocity of protons increases in accelerator.

This will decrease the total circular path of proton from 27000 m (27 km) to just 102.0683 m (0.102 km).

& radius from 4299.363m to just 16.253 m.

How is this possible as accelerating magnets are at same position for rest observer?

The space between bunches does not contract. That would only happen if the accelerator was moving relative to the scientist.

### #9 maheshkhati

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Posted 13 December 2017 - 02:43 AM

Two bundles of protons are moving with velocity V1 with related two you.
In protons frame of reference distance between two bundles in direction of motion is dx' then
when V1 = 0.9993 c
dx1 = dx'/Y1 = dx'/26.7308
Now, velocity increases to V2 = 0.99999999 c
then, for you
dx2 = dx'/Y2 = dx'/7071.068
So, dx2 = dx1/ 264.5288

This clearly shows that dx2 is less than dx1 i.e. length between two bundles after increasing velocity of protons get contracted.
If two nearer dots in circle get contracted then whole circle will have to be get contracted.

Edited by maheshkhati, 13 December 2017 - 02:44 AM.

### #10 sluggo

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Posted 14 December 2017 - 09:53 AM

The bunches contract per gamma, (increase in electric field strength measurements). The accelerator is at rest, so it does not experience lc, thus the circuit traveled remains constant.Spacing of bunches is approx. 27km/3k=9m. The bunches are individual objects moving through space, not one continuous object.

At v1, 1 cycle requires t1. At v2, 1 cycle requires t2. The scientist observes a decrease in cycle time t1-t2. The particles are closer in time, but not distance.

### #11 maheshkhati

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Posted 15 December 2017 - 03:53 AM

I have already proved that contraction is only depend on value of Y (not on dt).
Continuous object is also made up of discrete particles like electrons, protons , neutrons & space between them. Here, dx' stand for all distances in moving frame in x-direction. Now, it is your choice to measure what. It may be length of rod in X-direction. Here not only molecules get contracted in X-direction but space between two molecules get contracted in X-direction. (if this is not happen contraction of rod can not be even as molecules get more contracted & space between remain same).
Here dx' stand for distance in X-direction in non prime frame. It may be distance between two particles or end particles of any substance.
Remember distance is always measure between two points x1 & x2. If one proton is at x1 & other proton stand at x2 then dx'=x2-x1 measure in non prime frame then it definitely get contracted in prime frame.
I have already given example of free electron flow in conductors which shows that contraction of space between two particles is not new for SR.
1)SR says dx' get contracted
& i.e. distance between two points in X-direction get contracted (that points may be marked in that frame by proton bundles).
You can't say that points comes together but protons remain at same distance.

Edited by maheshkhati, 15 December 2017 - 04:08 AM.

### #12 maheshkhati

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Posted 15 December 2017 - 04:15 AM

I like this statement.
You can't say that points comes together but proton bundles remain at same distance.

Edited by maheshkhati, 15 December 2017 - 04:17 AM.

### #13 sluggo

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Posted 15 December 2017 - 10:46 AM

How can two particles have an em effect when separated at 9m?

### #14 maheshkhati

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Posted 18 December 2017 - 02:07 AM

1)Length contraction formula derived from formula
dx' = Y(dx-vdt)
We can measure length when we know position of two points at the same instant
so, dt = 0
& dx= dx'/Y
here, dx' is distance in non-primary frame may distance between two points, two particles or two ends of rod in x-direction.
in non-primary frame.
2)You increase the velocity of particle then time to complete one cycle will reduce
& t2 will be less than t1.
This is simple kinematics i.e. when velocity increases time require to travel the same distance decreases.
This has not time slow down effect.
dt = dx/v, So, when v increases dt decreases.
Time remain same for that observer frame until you change the observer, you will not find that slow down effect.

Edited by maheshkhati, 18 December 2017 - 03:26 AM.

### #15 Vmedvil

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Posted 18 December 2017 - 10:50 AM

You are missing the fact that the length is only different within the object that has the velocity as soon as you leave the matter field of the particle of the particle with velocity the length contraction is no longer there, only in that reference frame with the velocity is that length contraction valid.

It is not like gravity where the effects are felt outside the reference frame though the particle will have increased gravity because of increased Energy-mass, but the Time Dialation and Length Contraction does not effect outside reference frames that are not contained within the object with velocity.

So, my point is the path does not shrink outside the particle's matter field unless the particle has a large amount of energy-mass for gravity, length contraction does not effect outside the object in motion.

Edited by Vmedvil, 18 December 2017 - 11:15 AM.

### #16 maheshkhati

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Posted 19 December 2017 - 01:36 AM

Just consider one situation
One Truck is moving with velocity V1 has two bikes A & B loaded on it & placed at distance dx on it.
Now, two Biker with Bikes C & D are also moving in same direction on same road with same velocity V1 with same distance dx in such away that ABCD are creating rectangle.
Now, If this velocity V1 increases to V2 then that will happen.
According to you:- Length of truck with both bike loaded get contracted as it is part of one object.
So, d(AB) decreases
But distance between C & D bikes will not decrease as they are different objects.
So, d(CD) not decreases.
& now, ABCD is not rectangle for rest observer.
This is wrong. You can not change the physics by velocity with observer.
If this is true then contraction of length will not be even in x-direction.
Some where it is contracted & some where it is not contracted.
This will create the problem of continuity of space.
1)When I was in school. I have read the book of Gammon on relativity. He consider the world when C is very less.
In this world if you move with certain velocity. You will find that whole world get contracted in that direction of your velocity.
Tree get contracted, house get contracted, man standing get contracted, distance between two house get contracted.
Here matter get contracted & distance between them also get contracted.
This will create the even reference frame.

Edited by maheshkhati, 19 December 2017 - 05:09 AM.

### #17 maheshkhati

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Posted 19 December 2017 - 05:08 AM

This is just shrinking of one co-ordinate system with relative to other co-ordinate system due to SR. That co-ordinate system may present matter also.
Refer https://en.wikipedia...tion#Derivation
here, one good diagram of red rods & blue rods are given. Both are relatively moving with one another. Here not only length of other color rods get contracted but distance between them also get contracted.
Due to SR.
https://en.wikipedia...kontraktion.png

Edited by maheshkhati, 19 December 2017 - 05:56 AM.