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I'll take weak equivalence principle in the formulation as given on Wikipedia page:

The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception.

Consider a wave function $\Psi(r,t)$ and suppose that the potential energy is constant. Now let's switch$^\dagger$ to a reference frame, which moves with respect to original one with velocity $V+At$ with $V$ and $A$ constant:

$$\Psi'(r,t)=\Psi\left(r-Vt-\frac{At^2}2,t\right)\exp\left[\frac i\hbar\left(m(V+At)r-\int_0^t\frac m2(V+At)^2dt\right)\right].$$

$\Psi'(r,t)$ is the wavefunction in accelerated (with acceleration $A$) frame.

If we assume Schrödinger's equation for free particle

$$i\hbar \partial_t\Psi(r,t)=-\frac{\hbar^2}{2m}\partial_{rr}\Psi(r,t),$$

we can get the effective potential energy for the $\Psi'(r,t)$ wave function:

$$U_\text{eff}(r)=\frac{i\hbar \partial_t\Psi'(r,t)+\frac{\hbar^2}{2m}\partial_{rr}\Psi'(r,t)}{\Psi'(r,t)}=-mAr.$$

But this is nothing than potential energy in uniform gravitational field:

$$U_\text{grav}(r)=mgh,$$

where we use $g=-A$ is free fall acceleration and $h=r$ is height.

What do we get from this? Indeed, it appears that motion in uniformly accelerated frame is indistinguishable from motion in gravitational potential, i.e. weak equivalence principle is satisfied, if we take the formulation I've cited above.

What do then papers like e.g. this talk about? They say about "strong quantum violation of weak equivalence principle"! The answer, as it seems to me, is that they confuse weak equivalence principle with mass-dependent effects. See, most of discussion is about dependence of some wave packet properties on particle mass. But this doesn't have anything to do with weak equivalence principle: we have mass-dependent wave packet broadening even without any gravitation — even in free space!

Maybe there's some inequivalent formulation of weak equivalence principle, which speaks about mass-dependent effects in cases where classical mechanics doesn't have them, but then it should be unrelated to gravity and general relativity theory at all.

_{$^\dagger$ The switch is similar to the one described in e.g. Landau, Lifshitz "Quantum mechanics. Non-relativistic theory" — in a problem after $\S$17, but taking time-dependent velocity into account (i.e. not forgetting to integrate $\frac12mV^2$ with respect to time instead of just multiplying by $t$).}

I'll take weak equivalence principle in the formulation as given on Wikipedia page:

The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception.

Consider a wave function $\Psi(r,t)$ and suppose that the potential energy is constant. Now let's switch$^\dagger$ to a reference frame, which moves with respect to original one with velocity $At$ with $A$ constant:

$$\Psi'(r,t)=\Psi\left(r-\frac{At^2}2,t\right)\exp\left[\frac {im}\hbar\left(Atr-\frac {A^2t^3}6\right)\right].$$

$\Psi'(r,t)$ is the wavefunction in accelerated (with acceleration $A$) frame.

If we assume Schrödinger's equation for free particle

$$i\hbar \partial_t\Psi(r,t)=-\frac{\hbar^2}{2m}\partial_{rr}\Psi(r,t),$$

we can get the effective potential energy for the $\Psi'(r,t)$ wave function:

$$U_\text{eff}(r)=\frac{i\hbar \partial_t\Psi'(r,t)+\frac{\hbar^2}{2m}\partial_{rr}\Psi'(r,t)}{\Psi'(r,t)}=-mAr.$$

But this is nothing than potential energy in uniform gravitational field:

$$U_\text{grav}(r)=mgh,$$

where we use $g=-A$ is free fall acceleration and $h=r$ is height.

What do we get from this? Indeed, it appears that motion in uniformly accelerated frame is indistinguishable from motion in gravitational potential, i.e. weak equivalence principle is satisfied, if we take the formulation I've cited above.

What do then papers like e.g. this talk about? They say about "strong quantum violation of weak equivalence principle"! The answer, as it seems to me, is that they confuse weak equivalence principle with mass-dependent effects. See, most of discussion is about dependence of some wave packet properties on particle mass. But this doesn't have anything to do with weak equivalence principle: we have mass-dependent wave packet broadening even without any gravitation — even in free space!

Maybe there's some inequivalent formulation of weak equivalence principle, which speaks about mass-dependent effects in cases where classical mechanics doesn't have them, but then it should be unrelated to gravity and general relativity theory at all.

_{$^\dagger$ The switch is similar to the one described in e.g. Landau, Lifshitz "Quantum mechanics. Non-relativistic theory" — in a problem after $\S$17, but taking time-dependent velocity into account (i.e. not forgetting to integrate $\frac12mV^2$ with respect to time instead of just multiplying by $t$).}

I'll take weak equivalence principle in the formulation as given on Wikipedia page:

The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception.

Consider a wave function $\Psi(r,t)$ and suppose that the potential energy is constant. Now let's switch$^\dagger$ to a reference frame, which moves with respect to original one with velocity $V+At$:

$$\Psi'(r,t)=\Psi\left(r-Vt-\frac{At^2}2,t\right)\exp\left[\frac i\hbar\left(m(V+At)r-\int_0^t\frac m2(V+At)^2dt\right)\right].$$

$\Psi'(r,t)$ is the wavefunction in accelerated (with acceleration $A$) frame.

But, if we assume Schrödinger's equation for free particle

$$i\hbar \partial_t\Psi(r,t)=-\frac{\hbar^2}{2m}\partial_{rr}\Psi(r,t),$$

we can get the effective potential energy for the $\Psi'(r,t)$ wave function:

$$U_{eff}(r)=\frac{i\hbar \partial_t\Psi'(r,t)+\frac{\hbar^2}{2m}\partial_{rr}\Psi'(r,t)}{\Psi'(r,t)}=-mAr.$$

But this is nothing than potential energy in uniform gravitational field:

$$U_{grav}(r)=mgh,$$

where we use $A=g$ is free fall acceleration and $r=h$ is height.

What do we get from this? Indeed, it appears that motion in uniformly accelerated is indistinguishable from motion in gravitational potential, i.e. weak equivalence principle is satisfied, if we take the formulation I've cited above.

Why do then papers like e.g. this talk about? They say about "strong quantum violation of weak equivalence principle"! The answer, as it seems to me, is that they confuse weak equivalence principle with mass-dependent effects. See, most of discussion is about dependence of some wave packet properties on particle mass. But this doesn't have anything to do with weak equivalence principle: we have mass-dependent wave packet broadening even without any gravitation — even in free space!

Maybe there's some inequivalent formulation of weak equivalence principle, which speaks about mass-dependent effects in cases where classical mechanics doesn't have them, but then it should be unrelated to gravity and general relativity theory at all.

_{$^\dagger$ The switch is similar to the one described in e.g. Landau, Lifshitz "Quantum mechanics. Non-relativistic theory" — in a problem after $\S$17, but taking time-dependent velocity into account (i.e. not forgetting to integrate $\frac12mV^2$ with respect to time instead of just multiplying by $t$).}

I'll take weak equivalence principle in the formulation as given on Wikipedia page:

The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception.

Consider a wave function $\Psi(r,t)$ and suppose that the potential energy is constant. Now let's switch$^\dagger$ to a reference frame, which moves with respect to original one with velocity $V+At$ with $V$ and $A$ constant:

$$\Psi'(r,t)=\Psi\left(r-Vt-\frac{At^2}2,t\right)\exp\left[\frac i\hbar\left(m(V+At)r-\int_0^t\frac m2(V+At)^2dt\right)\right].$$

$\Psi'(r,t)$ is the wavefunction in accelerated (with acceleration $A$) frame.

If we assume Schrödinger's equation for free particle

$$i\hbar \partial_t\Psi(r,t)=-\frac{\hbar^2}{2m}\partial_{rr}\Psi(r,t),$$

we can get the effective potential energy for the $\Psi'(r,t)$ wave function:

$$U_\text{eff}(r)=\frac{i\hbar \partial_t\Psi'(r,t)+\frac{\hbar^2}{2m}\partial_{rr}\Psi'(r,t)}{\Psi'(r,t)}=-mAr.$$

But this is nothing than potential energy in uniform gravitational field:

$$U_\text{grav}(r)=mgh,$$

where we use $g=-A$ is free fall acceleration and $h=r$ is height.

What do we get from this? Indeed, it appears that motion in uniformly accelerated frame is indistinguishable from motion in gravitational potential, i.e. weak equivalence principle is satisfied, if we take the formulation I've cited above.

What do then papers like e.g. this talk about? They say about "strong quantum violation of weak equivalence principle"! The answer, as it seems to me, is that they confuse weak equivalence principle with mass-dependent effects. See, most of discussion is about dependence of some wave packet properties on particle mass. But this doesn't have anything to do with weak equivalence principle: we have mass-dependent wave packet broadening even without any gravitation — even in free space!

Maybe there's some inequivalent formulation of weak equivalence principle, which speaks about mass-dependent effects in cases where classical mechanics doesn't have them, but then it should be unrelated to gravity and general relativity theory at all.

_{$^\dagger$ The switch is similar to the one described in e.g. Landau, Lifshitz "Quantum mechanics. Non-relativistic theory" — in a problem after $\S$17, but taking time-dependent velocity into account (i.e. not forgetting to integrate $\frac12mV^2$ with respect to time instead of just multiplying by $t$).}

I'll take weak equivalence principle in the formulation as given on Wikipedia page:

The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception.

Consider a wave function $\Psi(r,t)$ and suppose that the potential energy is constant. Now let's switch$^\dagger$ to a reference frame, which moves with respect to original one with velocity $V+At$:

$$\Psi'(r,t)=\Psi\left(r-Vt-\frac{At^2}2,t\right)\exp\left[\frac i\hbar\left(m(V+At)r-\frac{(V+At)^3}{6A}\right)\right].$$

$\Psi'(r,t)$ is the wavefunction in accelerated (with acceleration $A$) frame.

But, if we assume Schrödinger's equation for free particle

$$i\hbar \partial_t\Psi(r,t)=-\frac{\hbar^2}{2m}\partial_{rr}\Psi(r,t),$$

we can get the effective potential energy for the $\Psi'(r,t)$ wave function:

$$U_{eff}(r)=\frac{i\hbar \partial_t\Psi'(r,t)+\frac{\hbar^2}{2m}\partial_{rr}\Psi'(r,t)}{\Psi'(r,t)}=-mAr.$$

But this is nothing than potential energy in uniform gravitational field:

$$U_{grav}(r)=mgh,$$

where we use $A=g$ is free fall acceleration and $r=h$ is height.

What do we get from this? Indeed, it appears that motion in uniformly accelerated is indistinguishable from motion in gravitational potential, i.e. weak equivalence principle is satisfied, if we take the formulation I've cited above.

Why do then papers like e.g. this talk about? They say about "strong quantum violation of weak equivalence principle"! The answer, as it seems to me, is that they confuse weak equivalence principle with mass-dependent effects. See, most of discussion is about dependence of some wave packet properties on particle mass. But this doesn't have anything to do with weak equivalence principle: we have mass-dependent wave packet broadening even without any gravitation — even in free space!

Maybe there's some inequivalent formulation of weak equivalence principle, which speaks about mass-dependent effects in cases where classical mechanics doesn't have them, but then it should be unrelated to gravity and general relativity theory at all.

_{$^\dagger$ The switch is similar to the one described in e.g. Landau, Lifshitz "Quantum mechanics. Non-relativistic theory" — in a problem after $\S$17, but taking time-dependent velocity into account (i.e. not forgetting to integrate $\frac12mV^2$ with respect to time instead of just multiplying by $t$).}

I'll take weak equivalence principle in the formulation as given on Wikipedia page:

The local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception.

Consider a wave function $\Psi(r,t)$ and suppose that the potential energy is constant. Now let's switch$^\dagger$ to a reference frame, which moves with respect to original one with velocity $V+At$:

$$\Psi'(r,t)=\Psi\left(r-Vt-\frac{At^2}2,t\right)\exp\left[\frac i\hbar\left(m(V+At)r-\int_0^t\frac m2(V+At)^2dt\right)\right].$$

$\Psi'(r,t)$ is the wavefunction in accelerated (with acceleration $A$) frame.

But, if we assume Schrödinger's equation for free particle

$$i\hbar \partial_t\Psi(r,t)=-\frac{\hbar^2}{2m}\partial_{rr}\Psi(r,t),$$

we can get the effective potential energy for the $\Psi'(r,t)$ wave function:

$$U_{eff}(r)=\frac{i\hbar \partial_t\Psi'(r,t)+\frac{\hbar^2}{2m}\partial_{rr}\Psi'(r,t)}{\Psi'(r,t)}=-mAr.$$

But this is nothing than potential energy in uniform gravitational field:

$$U_{grav}(r)=mgh,$$

where we use $A=g$ is free fall acceleration and $r=h$ is height.

What do we get from this? Indeed, it appears that motion in uniformly accelerated is indistinguishable from motion in gravitational potential, i.e. weak equivalence principle is satisfied, if we take the formulation I've cited above.

Why do then papers like e.g. this talk about? They say about "strong quantum violation of weak equivalence principle"! The answer, as it seems to me, is that they confuse weak equivalence principle with mass-dependent effects. See, most of discussion is about dependence of some wave packet properties on particle mass. But this doesn't have anything to do with weak equivalence principle: we have mass-dependent wave packet broadening even without any gravitation — even in free space!

Maybe there's some inequivalent formulation of weak equivalence principle, which speaks about mass-dependent effects in cases where classical mechanics doesn't have them, but then it should be unrelated to gravity and general relativity theory at all.

_{$^\dagger$ The switch is similar to the one described in e.g. Landau, Lifshitz "Quantum mechanics. Non-relativistic theory" — in a problem after $\S$17, but taking time-dependent velocity into account (i.e. not forgetting to integrate $\frac12mV^2$ with respect to time instead of just multiplying by $t$).}