Does length contraction imply a superposition of particles? [answered: no]

[34student]

From what I understand about relativity, it seems as though the notion of superposition is unavoidable.  Whether it be for particles and worldlines or just particles, my question is quite simple.  If two different observers, travelling at different speeds relative to one another, are correct that two particles, at rest relative to one another, have different distances between each other, then how can this not be a superposition? 

[studiot]

18 minutes ago, 34student said:

From what I understand about relativity, it seems as though the notion of superposition is unavoidable.  Whether it be for particles and worldlines or just particles, my question is quite simple.  If two different observers, travelling at different speeds relative to one another, are correct that two particles, at rest relative to one another, have different distances between each other, then how can this not be a superposition? 

Quote

Does length contraction imply a superposition of particles?

 

The short answer to the headline question is no.

I don't know what you understand by superposition - perhaps you'd like to tell us.

 

Quite simply there are three frames involved in your scenario.

1) The frame of the two particles. Because they are in the same frame they must be at rest with respect to each other.

2) The frame of observer1

3) The frame of observer2

 

If frames 2 and 3 have different velocities relative to frame 1 then they will reckon the distance between the particles as being different.

 

[exchemist]

56 minutes ago, 34student said:

From what I understand about relativity, it seems as though the notion of superposition is unavoidable.  Whether it be for particles and worldlines or just particles, my question is quite simple.  If two different observers, travelling at different speeds relative to one another, are correct that two particles, at rest relative to one another, have different distances between each other, then how can this not be a superposition? 

For each observer all lengths, along the direction of relative motion, are affected equally. If we call it the x direction and say it is foreshortened for one observer, compared to the other, then it means that wherever x appears in the wave equation x is shorter. So the probability cloud of the particle is foreshortened, etc. Hence it does not cause anything to "overlap" that was not overlapping before. Quantum superposition, however, does not in any case refer to particles physically overlapping one another. That requires another discussion. 

Edited December 9, 2021 by exchemist

[34student]

2 hours ago, studiot said:

 

The short answer to the headline question is no.

I don't know what you understand by superposition - perhaps you'd like to tell us.

 

Quite simply there are three frames involved in your scenario.

1) The frame of the two particles. Because they are in the same frame they must be at rest with respect to each other.

2) The frame of observer1

3) The frame of observer2

 

If frames 2 and 3 have different velocities relative to frame 1 then they will reckon the distance between the particles as being different.

 

Yes, the case that I meant to present was to have a length contraction between the 2 particles as observed by the 2 observers.

If both distances between the 2 particles are correct, then at least one of the particles has 2 different locations.  How is this not a superposition?

[studiot]

22 minutes ago, 34student said:

Yes, the case that I meant to present was to have a length contraction between the 2 particles as observed by the 2 observers.

If both distances between the 2 particles are correct, then at least one of the particles has 2 different locations.  How is this not a superposition?

Actually there are three different reckonings to the distance between the two particles.

One corresponding to each of the three frames I listed.

Why do you think I said reckonings not observations or measurements ?

And why do you not cooperate by answering my questions ?
I am trying to find out what you understand superposition to be, so that I can help you simply.

22 minutes ago, 34student said:

How is this not a superposition?

Because it is not.

Because the situation you describe does not conform to the standard definition of superposition.

But I am not going to go through another 5 pages of argument with you about a definition which is not mine or yours to make.

Edited December 9, 2021 by studiot

[34student]

2 hours ago, exchemist said:

For each observer all lengths, along the direction of relative motion, are affected equally. If we call it the x direction and say it is foreshortened for one observer, compared to the other, then it means that wherever x appears in the wave equation x is shorter. So the probability cloud of the particle is foreshortened, etc. Hence it does not cause anything to "overlap" that was not overlapping before. Quantum superposition, however, does not in any case refer to particles physically overlapping one another. That requires another discussion. 

I am not saying that they overlap.  I am saying that the particle must be in two different locations, like QM superposition.

2 minutes ago, studiot said:

I am trying to find out what you understand superposition to be, so that I can help you simply.

 

Sorry, I missed that.

Definition of superposition from Marriam-Webster,

"especially, physics : the combination of two distinct physical phenomena of the same type (such as spin or wavelength) so that they coexist as part of the same event.  Schrödinger perversely suggested that until the box was opened and the outcome of the experiment observed, the particle must remain suspended in a superposition of two states: simultaneously going through both holes.— George Johnson"

In our case the type of physical phenomena is location.

10 minutes ago, studiot said:

 

Why do you think I said reckonings not observations or measurements ?

I actually do not know.  What is the difference?

[studiot]

41 minutes ago, 34student said:

I am not saying that they overlap.  I am saying that the particle must be in two different locations, like QM superposition.

Sorry, I missed that.

Definition of superposition from Marriam-Webster,

"especially, physics : the combination of two distinct physical phenomena of the same type (such as spin or wavelength) so that they coexist as part of the same event.  Schrödinger perversely suggested that until the box was opened and the outcome of the experiment observed, the particle must remain suspended in a superposition of two states: simultaneously going through both holes.— George Johnson"

In our case the type of physical phenomena is location.

I actually do not know.  What is the difference?

 

OK the definition of superposition is largely correct but rather akward to work with and not totally correct.
In particular the physical phenomena do not have to be of the same type and the examples given could be difficul to apply without further informatuon.

Two or more causative or controlling agents act on the same body or in the same region of space or in the same electrical circuit they are siad to be in superposition.

a) So two voltage sources, one alternating and one direct, acting on the same electrical resistor are in electrical superposition.

b) Gravity and the thrust from a rocket engine are in mechanical superposition.

c) Two waves acting along a single string produce a combined wave by acting in superposition. An orchestra has many instuments acting in superposition to produce music in the concert hall.

These are examples of classical superposition.

d) Two quantum wavefunctions acting in the same space are may be in quantum superposition or they may not be depending upon circumstances.

Examples a and b are what are called linear superposition. This is good because you can simply add up the effects of each acting alone.

Example c may be linear or non-linear. You cannot simply add the wavelengths as suggested by your dictionary.

 

So back to your question.

Yes there is a region of space, but there are no causative agents acting.

An observation, calculation, measurement or reckoning is not a causative agent.

I said reckoning because direct observation or direct measurement of relativistic effects are generally not possible.

The effects have to be deduced from indirect measurements (called observables)

The two moving observers cannot directly observe the length they have to calculate or reckon it using the correct formulae for the frame concerned.
Of course relativity also says that a third observer located in the frame of the two points, frame 1 cannot directly observe what the other two observers see.

Does this help ?

Edited December 10, 2021 by studiot

[exchemist]

10 hours ago, 34student said:

I am not saying that they overlap.  I am saying that the particle must be in two different locations, like QM superposition.

 

OK I understand. But they are not in 2 locations. Each observer sees them in only one location.

Do not fall into the trap of thinking that one can somehow stand outside this scenario and see both at once, or that these observers are seeing two different "distortions" of some "true" version. A system always has to be analysed from one frame of reference or another. You can do QM in either reference frame and in neither of them will any superposition arise.  But you can't do QM in some imaginary space that stands outside reality and can see both perspectives at once.      

[swansont]

17 hours ago, 34student said:

From what I understand about relativity, it seems as though the notion of superposition is unavoidable.  Whether it be for particles and worldlines or just particles, my question is quite simple.  If two different observers, travelling at different speeds relative to one another, are correct that two particles, at rest relative to one another, have different distances between each other, then how can this not be a superposition? 

Superposition refers to quantum states, or the addition of certain quantities. Length is neither of those. To any observer, a length has a single value. A quantum superposition is a quality of the particle or system in question and choice of basis states, and does not depend on the observer. 

14 hours ago, 34student said:

In our case the type of physical phenomena is location.

The followup to this is: Is location an eigenstate?

No. So there is no quantum superposition.

As I believe you've been told before, length is not an intrinsic/inherent property; you keep treating this as some length having multiple values, and I think I've pointed out to you that we can look at the kinetic energy of a particle, which is another relative value. If you're at rest with respect to the particle, it has no KE. If there is relative motion, the KE is nonzero, and that value will depend on the relative speed, so it can have any positive value. But this doesn't seem to cause any conceptual issues (or maybe it does?), while length does.

[34student]

On 12/9/2021 at 4:56 PM, studiot said:

 

OK the definition of superposition is largely correct but rather akward to work with and not totally correct.
In particular the physical phenomena do not have to be of the same type and the examples given could be difficul to apply without further informatuon.

Two or more causative or controlling agents act on the same body or in the same region of space or in the same electrical circuit they are siad to be in superposition.

a) So two voltage sources, one alternating and one direct, acting on the same electrical resistor are in electrical superposition.

b) Gravity and the thrust from a rocket engine are in mechanical superposition.

c) Two waves acting along a single string produce a combined wave by acting in superposition. An orchestra has many instuments acting in superposition to produce music in the concert hall.

These are examples of classical superposition.

d) Two quantum wavefunctions acting in the same space are may be in quantum superposition or they may not be depending upon circumstances.

Examples a and b are what are called linear superposition. This is good because you can simply add up the effects of each acting alone.

Example c may be linear or non-linear. You cannot simply add the wavelengths as suggested by your dictionary.

 

So back to your question.

Yes there is a region of space, but there are no causative agents acting.

An observation, calculation, measurement or reckoning is not a causative agent.

I said reckoning because direct observation or direct measurement of relativistic effects are generally not possible.

The effects have to be deduced from indirect measurements (called observables)

The two moving observers cannot directly observe the length they have to calculate or reckon it using the correct formulae for the frame concerned.
Of course relativity also says that a third observer located in the frame of the two points, frame 1 cannot directly observe what the other two observers see.

Does this help ?

To be honest I am more confused.  I was really just referring to the superposition that a particle can be in when it is travelling in two different paths at the same time.  Length contraction seems to demonstrate this too. 

On 12/10/2021 at 3:24 AM, exchemist said:

OK I understand. But they are not in 2 locations. Each observer sees them in only one location.

Do not fall into the trap of thinking that one can somehow stand outside this scenario and see both at once, or that these observers are seeing two different "distortions" of some "true" version. A system always has to be analysed from one frame of reference or another. You can do QM in either reference frame and in neither of them will any superposition arise.  But you can't do QM in some imaginary space that stands outside reality and can see both perspectives at once.      

Yes, but there is still a superposition in QM.  I am trying to say that length contraction seems to imply a superposition also.

On 12/10/2021 at 4:35 AM, swansont said:

Superposition refers to quantum states, or the addition of certain quantities. Length is neither of those. To any observer, a length has a single value. A quantum superposition is a quality of the particle or system in question and choice of basis states, and does not depend on the observer. 

 

Are you saying that length contraction depends on the observer?  I don't think it does.

[studiot]

4 minutes ago, 34student said:

To be honest I am more confused.  I was really just referring to the superposition that a particle can be in when it is travelling in two different paths at the same time.  Length contraction seems to demonstrate this too. 

 

You have asked this question in the relativity section, so you should expect answers pertinent to relativity.

Objects in relativity theory do not travel two different paths at the same time.

 

I was deliberately brief on quantum superposition as it has some quite different characteristics from classical superposition.

I suggest you forget mixing the two.

 

I have litrally dozens of textbooks describing superposition in electrical engineering, structural engineering, civil engineering, and several other disciplines.

The technique goes back to the catapault where two pieces of elastic are used in superposition to fire a projectile.

[34student]

On 12/10/2021 at 4:35 AM, swansont said:

 

As I believe you've been told before, length is not an intrinsic/inherent property;

It depends for what context.  The length between points A and B in an equilateral tringle defined by points ABC is definitely an intrinsic property to the triangle.

 

In the case of the change in length from length contraction, if we want to say that the contraction is real and not just an illusion, then there must be a change in distance that is intrinsic to the structure and shape of the universe.  

[swansont]

55 minutes ago, 34student said:

Are you saying that length contraction depends on the observer?  I don't think it does.

You would be wrong. How did you get this far in discussions of relativity without knowing this?

Also, I will mention again that you continue to avoid answering my question about kinetic energy

1 hour ago, 34student said:

To be honest I am more confused.  I was really just referring to the superposition that a particle can be in when it is travelling in two different paths at the same time.  Length contraction seems to demonstrate this too. 

Your OP said nothing about this.

22 minutes ago, 34student said:

It depends for what context.  The length between points A and B in an equilateral tringle defined by points ABC is definitely an intrinsic property to the triangle.

 

In the case of the change in length from length contraction, if we want to say that the contraction is real and not just an illusion, then there must be a change in distance that is intrinsic to the structure and shape of the universe.  

No, the length depends on who observes it, as it always is with relativity. There is no intrinsic length.

 

[34student]

8 minutes ago, swansont said:

You would be wrong. How did you get this far in discussions of relativity without knowing this?

A muon does not have to observe the length contraction of its surroundings for length contraction to happen.  Observation shouldn't play a part in length contraction.

27 minutes ago, swansont said:

Also, I will mention again that you continue to avoid answering my question about kinetic energy

Well that's kinetic energy, not length.  We are talking about length, not kinetic energy.  I gave an example of how length can be an intrinsic property of a structure.  

[exchemist]

1 hour ago, 34student said:

 

Yes, but there is still a superposition in QM.  I am trying to say that length contraction seems to imply a superposition also.

 

You are not making much sense now. I have tried to explain to you why length contraction does not imply any superposition. Nothing is changed, as far as QM is concerned, by one spatial dimension appearing foreshortened in one frame of reference relative to another one. You can't do QM outside a frame of reference, any more than you can do any other physics outside one. A frame of reference is always presumed, either explicitly or implicitly. So in your example, you are in one or the other and your QM maths will come out the same in both, with, say, the x dimension a bit squashed in one compared to the other. That's all.   

From your other response it looks as if you are labouring under the misapprehension that there is some "intrinsic" or "real" length and that observations made from other frames of reference are an illusion or distortion. This is wrong. I think it is the source of your confusion.

 

Edited December 11, 2021 by exchemist

[studiot]

11 minutes ago, exchemist said:

I think it is the source of your confusion.

confused or not listening ?

 

On 12/9/2021 at 11:16 PM, studiot said:

But I am not going to go through another 5 pages of argument with you about a definition which is not mine or yours to make.

 

I'm done with this thread.

[34student]

2 minutes ago, exchemist said:

You are not making much sense now. I have tried to explain to you why length contraction does not imply any superposition. Nothing is changed, as far as QM is concerned, by one spatial dimension appearing foreshortened in one frame of reference relative to another one. You can't do QM outside a frame of reference, any more than you can with any other physics. A frame of reference is always presumed, either explicitly or implicitly. So in your example, you are in one or the other and your QM maths will come out the same in both, with, say, the x dimension a bit squashed in one compared to the other. That's all.   

But there can be a frame of reference in my argument.  I am not saying there can't be.

For example, from one observer's frame of reference, he sees particle C a meter from particle B.  But from another frame of reference, particle C is 2 meters from particle B.  Then, it would be true to say that particle C is 1 meter away from particle B, and it would be true to say that particle C is 2 meters away from particle B.

Clearly that must be a superposition of position. 

1 hour ago, studiot said:

 

Objects in relativity theory do not travel two different paths at the same time.

 

How can there not be two different worldlines of a particle that exists, say 1 meter away from me, and that also exists 2 meters away from me (say from some other observer)?

[exchemist]

18 minutes ago, 34student said:

But there can be a frame of reference in my argument.  I am not saying there can't be.

For example, from one observer's frame of reference, he sees particle C a meter from particle B.  But from another frame of reference, particle C is 2 meters from particle B.  Then, it would be true to say that particle C is 1 meter away from particle B, and it would be true to say that particle C is 2 meters away from particle B.

Clearly that must be a superposition of position. 

 

"Clearly", ballocks. If you change reference frames you start your QM analysis again, with the length ruler appropriate to that frame.

You only have a superposition if you have 2 states that are mixed. But in either reference frame, you have only one state.

This is why I keep telling you that you can't somehow stand outside these frames of reference when you apply your QM, and say "Look, there are 2 different states".

I repeat: any application of physics has to assume some frame of reference, from which it takes its dimensional  yardsticks. You cannot use two different ones at once.   

Edited December 11, 2021 by exchemist

[swansont]

1 hour ago, 34student said:

A muon does not have to observe the length contraction of its surroundings for length contraction to happen.  Observation shouldn't play a part in length contraction.

You’re taking “observe” literally. It’s a frame dependent quantity.

 

1 hour ago, 34student said:

Well that's kinetic energy, not length.  We are talking about length, not kinetic energy. 

KE is a relative property, just as length is. Why do you accept one but not the other?

1 hour ago, 34student said:

I gave an example of how length can be an intrinsic property of a structure.  

It was incorrect. 

[34student]

4 hours ago, exchemist said:

"Clearly", ballocks. If you change reference frames you start your QM analysis again, with the length ruler appropriate to that frame.

You only have a superposition if you have 2 states that are mixed. But in either reference frame, you have only one state.

This is why I keep telling you that you can't somehow stand outside these frames of reference when you apply your QM, and say "Look, there are 2 different states".

I repeat: any application of physics has to assume some frame of reference, from which it takes its dimensional  yardsticks. You cannot use two different ones at once.   

But we know that there is a contraction from B to C, and we know that there is not a contraction from B to C.  Is this is or is this not correct?

3 hours ago, swansont said:

KE is a relative property, just as length is. Why do you accept one but not the other?

Because for the purposes of my argument - in this case - length is an intrinsic property.  Just like in my example about the equilateral triangle, the length is intrinsic.

[exchemist]

20 minutes ago, 34student said:

But we know that there is a contraction from B to C, and we know that there is not a contraction from B to C.  Is this is or is this not correct?

Incorrect. What you "know" is that, due to the relative motion between your 2 reference frames, you expect a difference in these measured lengths, depending on the reference frame  choose to consider.

You do not "know" 2 incompatible things, for the simple reason that you cannot be simultaneously in both reference frames at once. Rather obviously.  

Edited December 11, 2021 by exchemist

[swansont]

22 minutes ago, 34student said:

But we know that there is a contraction from B to C, and we know that there is not a contraction from B to C.  Is this is or is this not correct?

I don’t follow this. There is contraction for any observer (or frame) moving relative to it.

 

22 minutes ago, 34student said:

Because for the purposes of my argument - in this case - length is an intrinsic property.  Just like in my example about the equilateral triangle, the length is intrinsic.

But it’s not true, so any conclusion drawn from it is invalid.

Further, the thread is about superposition in relativity; relativity is taken as being true. If you have some alternative to SR, like a concept of intrinsic length, it needs to go in a thread in speculations 

[34student]

19 minutes ago, exchemist said:

Incorrect. What you "know" is that, due to the relative motion between your 2 reference frames, you expect a difference in these measured lengths, depending on the reference frame  choose to consider. 

So does measuring two different lengths (as you put it) mean that there are two different lengths? 

20 minutes ago, swansont said:

I don’t follow this. There is contraction for any observer (or frame) moving relative to it.

Yes, I know.  So if there is a contraction for one observer and not a contraction for the other observer, then does that mean that there are two lengths?

[Bufofrog]

51 minutes ago, 34student said:

So does measuring two different lengths (as you put it) mean that there are two different lengths?

If there are 2 observers in different reference frames they will measure the lengths as being different, so yes the same ruler (for instance) will have 2 different lengths, one for one reference frame and another for the other reference frame.  I think that has been said multiple time in this thread.  Are you going to just keep asking the same question?

[34student]

24 minutes ago, Bufofrog said:

If there are 2 observers in different reference frames they will measure the lengths as being different, so yes the same ruler (for instance) will have 2 different lengths, one for one reference frame and another for the other reference frame.  I think that has been said multiple time in this thread.  Are you going to just keep asking the same question?

I put stress on "are".  "Are" means exist.  So the two lengths exist with particles at the ends of each.  It seems to mean that at least one of the particles exists in two different positions.  This is what I am asking in the OP.