# A Implications of quantum foundations on interpretations of relativity

#### Demystifier

2018 Award
Summary
If the Bell theorem is interpreted as nonlocality of nature, then what does it tell us about the meaning of Einstein theory of relativity?
Physicists often discuss interpretations of quantum mechanics (QM), but they rarely discuss interpretations of relativity. Which is strange, because the interpretations of quantum non-locality are closely related to interpretations of relativity.

The field of interpretations of relativity is not so rich as the field of quantum interpretations. As far as I am aware, basically there are 4 major interpretations of relativity.

1. Operational interpretation. According to this interpretation, relativity is basically about how the appearance of space, time and some related physical quantities depends on motion (and current position) of the observer. Essentially this is how Einstein originally interpreted relativity in 1905.

2. Spacetime interpretation. According to this interpretation, relativity is not so much about the appearance of space and time to observers, as it is about the 4-dimensional spacetime that does not depend on the observer. This interpretation was first proposed by Minkowski. Einstein didn't like it in the beginning, but later he embraced it in his formulation of general theory of relativity. The spacetime interpretation naturally leads to the block-universe interpretation of the world, according to which time does not flow, meaning that the past, the presence and the future exist on an equal footing.

3. Ether interpretation. This is not really one interpretation but a wide class of different physical theories. One simple version of the ether theory was developed by Lorentz, before Einstein developed his theory of relativity in 1905. According to ether theories, there are absolute space and absolute time, but under certain approximations some physical phenomena obey effective laws of motion that look as if absolute space and time did not exist. The original Lorentz version of ether theory was ruled out by the Michelson-Morley experiment, but some more sophisticated versions of ether theory are still alive.

4. Spacetime+foliation interpretation. This interpretation posits that in addition to spacetime, there is some timelike vector field $n^{\mu}(x)$ that defines a preferred foliation of spacetime, such that $n^{\mu}(x)$ is orthogonal to the spacelike hypersurfaces of the foliation. This preferred foliation defines a preferred notion of simultaneity.

What different interpretations of QM can tell us about those interpretations of relativity? Which interpretations of relativity seem natural from the perspective of which interpretations of QM?

Related Quantum Interpretations and Foundations News on Phys.org

#### DarMM

Gold Member
Well a simple example might be Copenhagen and the Blockworld, what you call the spacetime interpretation. In Copenhagen measurement results don't exist prior to the measurement (made more concrete by things like the Kochen Specker theorem) which can be hard to square with the view that all of four dimensional history "already exists" in some sense.

#### Demystifier

2018 Award
Well a simple example might be Copenhagen and the Blockworld, what you call the spacetime interpretation. In Copenhagen measurement results don't exist prior to the measurement (made more concrete by things like the Kochen Specker theorem) which can be hard to square with the view that all of four dimensional history "already exists" in some sense.
The operational interpretation of relativity is very much in spirit of Copenhagen interpretation of QM. But still, there is no direct contradiction between blockworld interpretation of relativity and the idea that a measurement result doesn't exist prior to the measurement. One can simply say that the measurement result exists at the spacetime point at which the measurement is performed.

An amusing historical fact is that Einstein, who was so much against Copenhagen interpretation of QM, embraced (at least in the beginning in 1905) the operational "Copenhagen-like" interpretation of relativity. Indeed, the categorical statement that "there is no ether" is very much in spirit of the categorical statement that "there are no hidden variables".

#### Demystifier

2018 Award
One related subquestion is this. The Bell's famous book "Speakable and Unspeakable in Quantum Mechanics" contains the chapter called "How to teach special relativity". What's the point of this chapter in the context of the whole book?

#### DarMM

Gold Member
The operational interpretation of relativity is very much in spirit of Copenhagen interpretation of QM.
David Mermin has a bit on this in his "Why Quark rhymes with Pork" essay collection.

But still, there is no direct contradiction between blockworld interpretation of relativity and the idea that a measurement result doesn't exist prior to the measurement. One can simply say that the measurement result exists at the spacetime point at which the measurement is performed.
Very true. Christopher Timpson says a bit about this in this paper:

He basically says that one can consider 4D spacetime to simply be laid out in advance, but events in each 3D slice don't follow dynamically from those on the previous 3D slice. So from the perspective of the prior slice events in the future are utterly unpredictable. Of course one must still add something like contextuality as otherwise it would simply be a classical stochastic process. Essentially a contextual adynamical view somewhat like @RUTA 's relational blockworld.

An amusing historical fact is that Einstein, who was so much against Copenhagen interpretation of QM, embraced (at least in the beginning in 1905) the operational "Copenhagen-like" interpretation of relativity. Indeed, the categorical statement that "there is no ether" is very much in spirit of the categorical statement that "there are no hidden variables".
Again I believe Mermin points this out as well.

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#### atyy

An amusing historical fact is that Einstein, who was so much against Copenhagen interpretation of QM, embraced (at least in the beginning in 1905) the operational "Copenhagen-like" interpretation of relativity. Indeed, the categorical statement that "there is no ether" is very much in spirit of the categorical statement that "there are no hidden variables".
Again I believe Mermin points this out as well.
Heisenberg & Einstein's conversation
https://www.informationphilosopher.com/solutions/scientists/heisenberg/talk_with_einstein.html

"But you don't seriously believe," Einstein protested, "that none but observable magnitudes must go into a physical theory?" "Isn't that precisely what you have done with relativity?" I asked in some surprise. "After all, you did stress the fact that it is impermissible to speak of absolute time, simply because absolute time cannot be observed; that only clock readings, be it in the moving reference system or the system at rest, are relevant to the determination of time."

"Possibly I did use this kind of reasoning," Einstein admitted, "but it is nonsense all the same. Perhaps I could put it more diplomatically by saying that it may be heuristically useful to keep in mind what one has actually observed. But on principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe.

#### EPR

Gold Member
Summary: If the Bell theorem is interpreted as nonlocality of nature, then what does it tell us about the meaning of Einstein theory of relativity?

That we can only talk meaningfully about observed(measured) quantities. The Copenhagen interpratation connects well with relativity some assumptions notwithstanding.

#### atyy

What different interpretations of QM can tell us about those interpretations of relativity? Which interpretations of relativity seem natural from the perspective of which interpretations of QM?
All of the above? From "State vector reduction in relativistic quantum mechanics: An introduction" by Breuer and Petruccione https://doi.org/10.1007/BFb0104397:

"There is a second possibility which has been first proposed by Aharonov and Albert [8]. This possibility consists in the assumption that the state vector reduction takes place instantaneously in all inertial flames. ...

Covariance requires only the equivalence of all inertial systems, hence the independence of all physical statements from a special coordinate system. And exactly this point has been made obvious in what we have discussed above: Performing a Lorentz transformation from an inertial system to another one has to transform the states of the quantum system as well as the observer who ascribes a history of state vectors to his equal-time hypersurfaces."

#### Demystifier

2018 Award
"Possibly I did use this kind of reasoning," Einstein admitted, "but it is nonsense all the same."

#### PrashantGokaraju

There are very close analogies between relativity and complementarity in their epistemological aspects. In relativity, properties of objects like position and velocity are only defined with respect to a frame of reference. This is analogous to the fact that in quantum mechanics, a 'phenomenon' is definable only in the context of a particular experimental arrangement. Because of this fact, we can treat the measuring bodies in an idealization in which their mass is so large compared to the electrons or other quantum mechanical systems that their velocities are not affected by collisions with the electrons. The point is that this idealization is the only basis for the definition of a phenomenon.

This is similar to the fact that in thermodynamics, the use of the concept of temperature is only possible in an idealization in which the second law of thermodynamics is exactly valid. The idea that the second law is only statistically valid does not contradict classical thermodyanmics because of this fact.

The analog of this in relativity is the fact that the reference frame is defined by objects which must be considered rigid, i.e. they are not subject to the lorentz contractions. This means that there is a sharp seperation between space and time in the interpretation of measurements, similar to the fact that in quantum theory, we can attach meaning to measurements only by using classical concepts. In relativity, a phenomenon such as length contraction has to be interpreted in terms of the forces within the rod. For example, take a rubber band. The energy density of the band is its tension. If the rubber band is moving, its mass increases due to its kinetic energy (m = KE/c2), and therefore contracts because of the greater tension.

Imagine sending a light signal to an event at time -t and receiving the reflected signal at time t'. The event is then characterized by the coordinates (t, t'). We can define an inertial frame (x, T) by

2x = t + t'
2T = t - t'

Under a lorentz transformation,

t' → (1/f(v)) t'
t → f(v) t

the invariant distance squared between (0,0) and (t,t') is s2 = tt' = T2 - x2. The idea of a light-signal seems to be more basic than the idea of x and T. the measurement of the speed of light therefore must consist of comparision of measurements obtained by different observers, similar to the fact the the measurement of plank's constant implies the comparision of measurements obtained under mutually exclusive arrangements.

#### Prathyush

In relativity, a phenomenon such as length contraction has to be interpreted in terms of the forces within the rod. For example, take a rubber band. The energy density of the band is its tension. If the rubber band is moving, its mass increases due to its kinetic energy (m = KE/c2), and therefore contracts because of the greater tension.
Length contraction/time dilation in relativity is a purely kinematic phenomenon(in the sense that it only defined in terms of transformation of co-ordinates and their relationships) and does not have a dynamic interpretation in any obvious sense.

The rest mass of a rubber band can be a completely independent of the tension. Or alternatively tensile strength of a material can also be completely independent of its weight.

I don't think it would be correct to think about greater tension because of mass/energy increase. Forces in a rubber band are electromagnetic and follow lorentz force law and hence co-variant. The idea that dynamical law is co-variant will imply what ever force that applied in frame 1 must transform in way that it would give identical behavior upto transformation in frame 2 also.

#### PrashantGokaraju

See chapter 15 of the Feynman lectures, volume one.

The whole content of relativity as far as the description of phenomena in a single frame goes is contained in the statement that the mass of a body is given by

m = m0/√1 - v2

This is the only change needed, and Newton's laws remain

F = dp/dt

p = mv

Therefore all relativistic effects are derivable from, or attributed to the increase of mass with velocity, or in other words, the equivalence between mass and energy. Another way to say it is that the momentum is

pc = Ev/c

(the "flux of energy"), where E = mc2.

If you substitute this in the first formula, you get

(p/v)2 - p2 = m02

and (p/v)2 = E2. This is just the familiar formula E2 - p2 = m02

#### weirdoguy

The whole content of relativity as far as the description of phenomena in a single frame goes is contained in the statement that the mass of a body is given by

m = m0/√1 - v2
And this is not true - relativistic mass is not used in physics for ages. See this insight article:

#### Demystifier

2018 Award
relativistic mass is not used in physics for ages.
I think it's related to the fact that the interpretation 2. (in the first post on this thread) is today much more popular than the interpretation 1.

What I find surprising is that today most adherents of Copenhagen interpretation of QM are not at the same time adherents of the interpretation 1. of relativity. Does anyone has idea why is that? Perhaps we still wait for someone who will do for QM what Minkowski has done for relativity?

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#### Prathyush

The whole content of relativity as far as the description of phenomena in a single frame goes is contained in the statement that the mass of a body is given by

m = m0/√1 - v2

This is the only change needed, and Newton's laws remain
It is true that all consequences of relativity(dynamical aspects) can be inferred from the mass changes however its more naturally formulated in the 4 vector language. And how the mass changes is obvious in this picture by defining 3 momentum from 4 momenta.

$$p^\mu = m \frac{\partial u^\mu}{\partial \tau}$$
$$f^\mu = \frac{\partial p^\mu}{\partial \tau}$$

This is a natural generalization of newton's force law. This is all you need apart from natural kinematic concepts that follow constancy of speed of light. I don't think Feynman was implying something along the lines of what you are suggesting.

For example, take a rubber band. The energy density of the band is its tension. If the rubber band is moving, its mass increases due to its kinetic energy (m = KE/c2), and therefore contracts because of the greater tension.
Also this point remains unexplained.

and (p/v)2 = E2. This is just the familiar formula E2 - p2 = m02
How?
Edit:
3 momentum $p_i = \gamma m v$ which is just $p_i = E v_i$ . I don't see why anything else is needed.

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#### PrashantGokaraju

In relativity, forces are not derived from scalar potentials F = -dU, but from a vector potential F = dA. This is because in relativity, forces can depend not just on the positions, but also on the velocities. The reason for this is that scalar potentials like U cannot be used to describe gravity in relativity, because of the equivalence principle. In relativity, gravity is described by a tensor potential g. The gravitational poisson equation

dδU = 4πGρ

is replaced by an equation of the form δF = j in the linear approximation. If p is the 4-momentum, then the covariant version of F = dp/dt is of the form

dpa/dτ = eFabvb

This is the force law of electrodynamics dp/dt = e(E + v ∧ B) where E and B are the electric and magnetic fields.

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#### atyy

And this is not true - relativistic mass is not used in physics for ages. See this insight article:
What you said is not correct. The article you linked to disagrees with what you claimed. @PrashantGokaraju referenced the Feynman lectures in his post, which does give correct physics on this point.

#### martinbn

What you said is not correct. The article you linked to disagrees with what you claimed. @PrashantGokaraju referenced the Feynman lectures in his post, which does give correct physics on this point.
The Feynman lectures were written ages ago.

#### weirdoguy

What you said is not correct.
So can you give any example of paper on HEP, relativity or cosmology written in last, say, 30 years that explicitly uses relativistic mass? I know that some people use it in teaching, but teaching physics should prepare students to use physics in their work and I see no point in teaching relativistic mass if barely anyone use it in their scientific work.

#### vanhees71

Gold Member
The Feynman lectures were written ages ago.
It's still an enigma for me, why Feynman used the "relativistic mass" concept. Though among the best textbooks on physics ever written, not everything is perfect!

#### Demystifier

2018 Award
It's still an enigma for me, why Feynman used the "relativistic mass" concept. Though among the best textbooks on physics ever written, not everything is perfect!
Perhaps it is not such a nonsense even from a modern point of view. Consider a big object at rest made of many small objects moving relatively to the center of mass of the big object. (For instance, the small objects can be atoms in thermal motion.) The mass of the big object is larger than the sum of individual invariant masses of its constituents, which can be hard to understand without introducing the concept of relativistic mass for each of the constituents.

#### atyy

So can you give any example of paper on HEP, relativity or cosmology written in last, say, 30 years that explicitly uses relativistic mass? I know that some people use it in teaching, but teaching physics should prepare students to use physics in their work and I see no point in teaching relativistic mass if barely anyone use it in their scientific work.
You claimed correct physics was wrong - that was the point I was disputing. Infrequent usage does not mean wrong. Anyway, if you wish to see an example in the literature, there are many, as Jaramillo and Gourhoulhon note: "In the literature, references are found where the term ADM mass actually refers to this length of the ADM 4-momentum and other references where it refers to its time component, that we have named here as the ADM energy. These differences somehow reflect traditional usages in Special Relativity where the term mass is sometimes reserved to refer to the Poincar´e invariant (rest-mass) quantity, and in other occasions is used to denote the boost-dependent time component of the energy-momentum." https://arxiv.org/abs/1001.5429

#### martinbn

You claimed correct physics was wrong - that was the point I was disputing. Infrequent usage does not mean wrong. Anyway, if you wish to see an example in the literature, there are many, as Jaramillo and Gourhoulhon note: "In the literature, references are found where the term ADM mass actually refers to this length of the ADM 4-momentum and other references where it refers to its time component, that we have named here as the ADM energy. These differences somehow reflect traditional usages in Special Relativity where the term mass is sometimes reserved to refer to the Poincar´e invariant (rest-mass) quantity, and in other occasions is used to denote the boost-dependent time component of the energy-momentum." https://arxiv.org/abs/1001.5429
I don't think that this is relevant. If anything it shows that people are a bit behind on the convention for the ADM mass and energy. That doesn't mean that the convention for invariant mass and relativistic mass currently in use is not a good one.

#### vanhees71

Gold Member
Perhaps it is not such a nonsense even from a modern point of view. Consider a big object at rest made of many small objects moving relatively to the center of mass of the big object. (For instance, the small objects can be atoms in thermal motion.) The mass of the big object is larger than the sum of individual invariant masses of its constituents, which can be hard to understand without introducing the concept of relativistic mass for each of the constituents.
The point is that you define mass as a Lorentz scalar. If you have a closed composed system it's its energy measured in its center-momentum frame (divided by $c^2$).

If you introduce relativistic mass, then you should be honest and define it as a function of the velocity of the object and the relative angle between this velocity and its acceleration. It's utmost complicated. Writing the equations of motion down in a manifestly covariant way, using manifestly covariant definitions of intrinsic properties like mass, charge, temperature, pressure/stress, etc. makes everything much more simple.

#### martinbn

May be people lost interest in this thread, but I will say what my opinion is anyway. First, I don't think that relativity needs any interpretation. It doesn't have anything remotely similar to the measurement (and related) problems. Second, I disagree that what you wrote are interpretations.

For me the fact that space-time has the structure of Minkowski space is not an interpretation but a consequence. No matter what your preferred formulations of special relativity is, it implies that space-time is Minkowskian. Just as in classical physics the space-time has a specific structure that is implied by the laws of classical physics.

So 1) is just the original formulation. 2) is also not an interpretation, but a better understanding of the colloraries. 3) you, yourself say that these are a class of different theories, so not interpretations either. 4) is a bit strange, but not and interpretation. It just adds something additional, that is completely unnecessary. You may as well pick a point in the universe and call it the centre, and claim that the universe isn’t homogeneous. Completely unnecessary and equally silly.

I also must say that I am puzzled by the very first sentence. You say "If the Bell theorem is interpreted as nonlocality of nature...", well what if it isn’t?