Einstein equations don't work at large scale?

[PeterDonis]

I have attempted to substitute $dt = dt' = t_P$ into the Lorentz transformations

The Lorentz transformations you wrote down in post #118 don't have $dt$ (or $dx$, for that matter), in them anywhere. So this makes no sense.

 

[PeterDonis]

would it be tenable to set $dt = dt' = t_P$?

Since time intervals between events are different in different frames, obviously this would contradict standard SR.

 

[PeterDonis]

@WatsonWangShuai are you aware of Doubly Special Relativity?

https://en.wikipedia.org/wiki/Doubly_special_relativity

This is a family of speculative models that attempt to find transformations that reduce to the standard Lorentz transformations at low energy, but are very different at energies approaching the Planck scale, so that, heuristically, the Planck energy is invariant, the same in all DSR "frames". What you appear to be describing looks to be more along these lines, since you can't do what you're describing with standard Lorentz transformations.

 

[WatsonWangShuai]

@WatsonWangShuai are you aware of Doubly Special Relativity?

https://en.wikipedia.org/wiki/Doubly_special_relativity

This is a family of speculative models that attempt to find transformations that reduce to the standard Lorentz transformations at low energy, but are very different at energies approaching the Planck scale, so that, heuristically, the Planck energy is invariant, the same in all DSR "frames". What you appear to be describing looks to be more along these lines, since you can't do what you're describing with standard Lorentz transformations.

PeterDonis Mentor

I appreciate the reference to DSR. DSR suffers from the well‑known locality paradox: whether multi‑particle events occur "simultaneously" becomes frame‑dependent. It remains a speculative model with no experimental confirmation to date. DSR modifies the Lorentz transformations themselves via a non‑linearly deformed Poincaré group, enforcing the Planck scale to be invariant across all frames.

By contrast, this formula effectively yields a minimum spatial interval $$dx'(v)$$, that varies with relative velocity. The Planck length is merely its high‑speed limit, rather than an invariant quantity across reference frames.This is also what puzzles me.

 

[Dale]

Do you have a professional scientific reference about this concept? If not, then we wont be avle to discuss it further here