I Because of length contraction, does absolute position exist?

[student34]

I know that I have heard that GR proves that there is no absolute time, so does this go for location too?

If so, could it be said that particles have a superposition in position/location the same way that particles do in QM?

 

[Orodruin]

There is no such thing as absolute position. Not in relativity nor in classical mechanics.

Note that this is not at all the same issue as that of positional uncertainty in quantum mechanics.

 

[Ibix]

I know that I have heard that GR proves that there is no absolute time, so does this go for location too?

Galileo showed that there was no absolute notion of position, but Einsteinian relativity agrees, yes.

If so, could it be said that particles have a superposition in position/location the same way that particles do in QM?

No. Position and length are well defined. Different frames measure different aspects of a 4d object but both call it length. It's closely analogous to slicing a sausage perpendicular to its length and seeing a circular cross-section and somebody else slicing it diagonally and seeing an elliptical cross section. The sausage is not in a superposition of circular and elliptical - the different people are just making different measurements on it.

 

[Orodruin]

It's closely analogous to slicing a sausage perpendicular to its length and seeing a circular cross-section and somebody else slicing it diagonally and seeing an elliptical cross section. The sausage is not in a superposition of circular and elliptical - the different people are just making different measurements on it.

I am stealing this analogy for future classes.

 

[student34]

Galileo showed that there was no absolute notion of position, but Einsteinian relativity agrees, yes.

No. Position and length are well defined. Different frames measure different aspects of a 4d object but both call it length. It's closely analogous to slicing a sausage perpendicular to its length and seeing a circular cross-section and somebody else slicing it diagonally and seeing an elliptical cross section. The sausage is not in a superposition of circular and elliptical - the different people are just making different measurements on it.

But wouldn't one of the measurements be of different parts of the sausage than the other?

 

[Nugatory]

But wouldn't one of the measurements be of different parts of the sausage than the other?

Yes, because we can’t slice a sausage twice at the same place. That just shows us that the analogy is not exact which isn’t surprising because all analogies are, by definition, not the exact real thing.

 

[Ibix]

But wouldn't one of the measurements be of different parts of the sausage than the other?

Yes. Likewise, two length measurements made using different frames' simultaneity conventions are not made at the same time. Each frame will describe the other frame measurement as having a duration, and its own as being instantaneous. So they measure different sections of the 4d object.

 

[Dale]

But wouldn't one of the measurements be of different parts of the sausage than the other?

That is the point. Different measurements of length similarly measure different parts of the 4D object.

 

[vanhees71]

I am stealing this analogy for future classes.

The same here :-).

 

[anuttarasammyak]

But wouldn't one of the measurements be of different parts of the sausage than the other?

Say a measure is at rest in an IFR. The two ends draw two world lines in spacetime. Space distance between the lines so to say space distance between the ends depends on in which IFR the observer is.　Observers in different IFRs observe the same lines with different space distance. He or she in the original IFR observes the longest distance.

 

[student34]

Say a measure is at rest in an IFR. The two ends draw two world lines in spacetime. Space distance between the lines so to say space distance between the ends depends on in which IFR the observer is.　Observers in different IFRs observe the same lines with different space distance. He or she in the original IFR observes the longest distance.

Ok, so for Bob standing next to a meter stick, the particles on the ends of the meter stick are a meter stick apart. For Alice traveling fast, parallel to the meter stick, the meter stick is, say, half the size, and thus the particles are 50 cm from each other.

According to GR, there exist 2 real sizes of meter stick here. How can the particles at the ends of the meter stick possibly be in the same location in space for each frame of reference?

 

[Ibix]

According to GR, there exist 2 real sizes of meter stick here. How can the particles at the ends of the meter stick possibly be in the same location in space for each frame of reference?

They aren't. The frames don't agree on simultaneity so their measurements of where at least one end of the meter stick is aren't taken at the same time, and the meter stick is moving in at least one frame. So according to each frame at least one end of the rod isn't in the same place when measurements are made by the other frame.

This is the point we've been trying to make to you. What one frame measures as "length" is a different measurement of the object from what the other frame measures as "length".

 

[PeroK]

According to GR, there exist 2 real sizes of meter stick here. How can the particles at the ends of the meter stick possibly be in the same location in space for each frame of reference?

If you are in a train, looking at your cellphone. To you, your cellphone is stationary. It's not moving and you can operate it easily. To domeone on the platform, your cellphone is moving at 150 km per hour, say.

How can your cellphone be moving and not moving at the same time? How can you and the person on the platform possibly be describing the same physical object?

 

[Nugatory]

According to GR….

SR as well. We are running out of ways of saying that the two measurements are of different things.

 

[student34]

They aren't. The frames don't agree on simultaneity so their measurements of where at least one end of the meter stick is aren't taken at the same time, and the meter stick is moving in at least one frame. So according to each frame at least one end of the rod isn't in the same place when measurements are made by the other frame.

Okay, I hope you don't mind if I try to really nail this down here with the following 2 questions. Is the meter stick truly 50 cm for Alice? Is the meter stick truly 100 cm for Bob?

 

[student34]

SR as well. We are running out of ways of saying that the two measurements are of different things.

Let's say that the meter stick is on the x coordinate for Bob's frame of reference. Will the meter stick be on the x coordinate for Alice's frame of reference?

 

[Ibix]

Okay, I hope you don't mind if I try to really nail this down here with the following 2 questions. Is the meter stick truly 50 cm for Alice? Is the meter stick truly 100 cm for Bob?

Yes. They are measuring the spatial extent of different 3d slices through a 4d object.

 

[Ibix]

Let's say that the meter stick is on the x coordinate for Bob's frame of reference. Will the meter stick be on the x coordinate for Alice's frame of reference?

Do you mean "on the x axis"?

 

[student34]

Do you mean "on the x axis"?

Yes

 

[Ibix]

Yes

Then yes, the rod can lie completely in the $xt$ and $x't'$ plane.

 

[student34]

Yes. They are measuring the spatial extent of different 3d slices through a 4d object.

So the particles exist in the objective universe as being 50 cm apart and 100cm apart. Is that correct?

 

[Ibix]

So the particles exist in the objective universe as being 50 cm apart and 100cm apart. Is that correct?

50cm along one axis and 100cm along a different axis, yes. That was the point of the sausage analogy - the edges of the sausage are different distances apart if you look along different directions. Similarly, the distance between the particles depends if you measure along Alice's x-axis or Bob's x' axis.

 

[Nugatory]

Is the meter stick truly 50 cm for Alice? Is the meter stick truly 100 cm for Bob?

Instead of tossing around words like “truly” (what would it mean to say the rod is “not truly”?)we should state the objective facts.

Using Bob’s simultaneity convention the ends of the rod are 100 cm apart. Using Alice’s simultaneity convention the ends of the rod are 50 cm apart. These are facts about which there is no dispute and can (in principle) be measured directly with suitable lab equipment.

So those are the facts. If you want to consider those facts as equivalent to saying “the meter stick is truly 50 cm long for Alice and truly 100 cm long for Bob”, or not….either way it says more about what you mean by “truly” than about the rod.

 

[sdkfz]

Cross ref in case it's useful: https://www.scienceforums.net/topic...ply-a-superposition-of-particles-answered-no/

 

[jbriggs444]

A meter stick is not a line segment the exists only as a snapshot in time. It has extent in time and is more like a parallelogram extending indefinitely into the past and into the future. When you measure its length, you are taking a snapshot at an instant in time according to some chosen frame.

When you measure the length of the stick in frame A, you are measuring from event a1 to event a2 such that a1 and a2 are simultaneous according to frame A.

When you measure the length of the stick in frame B, you are measuring from event b1 to event b2 such that b1 and b2 are simultaneous according to frame B.

 

[Ibix]

So, @student34, the diagram in @jbriggs444's post is a spacetime diagram. The x position of something is shown horizontally and the t position vertically. In this frame, then, the length of the rod is the Minkowski interval along the horizontal line. In a different frame with a different x-axis (call this x') which slopes down the page, though, the length of the rod is the Minkowski interval along the sloped line. It isn't the same as the length measured by the other frame, but there's no superposition going on here. The two frames are just measuring along different 1d cross sections of the 2d rod.

 

[PeroK]

Okay, I hope you don't mind if I try to really nail this down here with the following 2 questions. Is the meter stick truly 50 cm for Alice? Is the meter stick truly 100 cm for Bob?

This is what happens when you unify space and time into spacetime. It's the spacetime interval between events that is invariant; and not both the space interval and the time interval.

If you insist that space and time are distinct and unrelated, then SR will forever remain perplexing and a source of consternation.

 

[student34]

50cm along one axis and 100cm along a different axis, yes. That was the point of the sausage analogy - the edges of the sausage are different distances apart if you look along different directions. Similarly, the rod.

Okay thanks a lot. This next part will really answer my question about whether or not there is a superposition of position.

Let's say that Alice goes flying past Bob right at his feet causing the meter stick to contract to 50cm. So an x value of Bob's frame will intersect with an x value of Alice's frame as she goes past Bob. And the meter stick is on the x-axis lying in front of Bob with one end touching his feet.

When Alice and Bob were together on the ground before her flight, their clocks were synchronized at say 1:00pm. Alice flies directly over Bob's head at 5:00pm as per Bob's clock.

The particle at the end of the meter stick 100cm from Bob's feet we will call Bf (B for Bob's frame and f for far). So when Alice is at Bob's feet, the particle 100cm from Bob we can say that it is an event at some value Bf(x,y,z,t). And the other particle will be Bc(x,y,x,t) where c is for close. For Alice, similarly, we can use Ac(x,y,z,t) and Af(x,y,z,t)

When Af(x) = Bf(x), Af(z) = Bf(z) right?

 

[jbriggs444]

Let's say that Alice goes flying past Bob right at his feet causing the meter stick to contract to 50cm.

Is the meter stick at rest on the sidewalk that Bob is standing on? Or is it at rest strapped to the rocket that Alice is riding on?

 

[Ibix]

This next part will really answer my question about whether or not there is a superposition of position.

No there is not a superposition. Please read that sentence repeatedly until it sinks in. We have all told you this and the posters at scienceforums.net have told you this. I get that you don't understand what is going on, but desperately hoping that it's actually something every subject expert is telling you it's not is not going to help you.

I can't make sense of your scenario. I think what you are doing is having Bob at rest in some frame and Alice moving at some speed in the +x direction. Two particles also move in the +x direction, at rest with respect to one another. Both Bob and Alice have identical meter rules that they use to measure the distance between the particles.

Let's say that the back particle, Alice, Bob, and the zero end of both their rulers pass at one time (you called this 5pm). To measure the distance between the particles, both Bob and Alice make note of where the front particle is at the same time as the back particle passes them. But they do not have the same idea of what "at the same time" means, so both will say that they measured the front particle's position at time zero, but that the other did not. Thus the other includes some timelike separation in their length measure.

This is what is illustrated in jbriggs444's diagram on the previous page shows - both frames use the same event to measure the location of one end, but use different events for the other end.