B A well defined thought experiment

[Mikael17]

You seem to accept that Alice and Bob mke different measurements of the same thing, but you then get hung up on some imagined process after them dividing one number by the other. Stop inventing extra steps.

I consider d = t * v mathematically, and that v= m (meter) per s (second) .
I realized that t is variable, and I understand that when v is not equal, for Alice and Bob, - then mathematical consequence, can only be that m is not equal either. Sorry this is not my "invention" this i math.

 

[Ibix]

also understand that the concept of "speed" then "must" have a stange schizophrenic or multi-schizophrenic nature

The thing is, this bit is totally mundane. Your speed if you are sitting in your chair is zero. Or it's several hundred miles per hour (the Earth surface rotation speed at your latitude) if you take the Earth's rest frame. Or it's about twenty kilometres per second (Earth's orbital speed) if you take the Sun's rest frame. That's just a consequence of different definitions of "at rest".

A lot of students do struggle with this notion, but it underlies Newtonian physics too - which suggests a review of classical kinematics is probably necessary before you even try Einstein's relativity.

Sorry this is not my "invention" this i math.

It is completely your invention.

Speed is literally the answer to "how many meters did this thing travel in one second". If Alice and Bob agree on the distance travelled but not the time taken then they disagree on the number of meters travelled in one second. That's it. There's no need to redefine the meter. In your scenario they can even both use the same meter rule to measure the distance travelled, in which case they can't possibly be using a different definition.

 

[Motore]

I consider d = t * v mathematically, and that v= m (meter) per s (second) .
I realized that t is variable, and I understand that when v is not equal, for Alice and Bob, - then mathematical consequence, can only be that m is not equal either. Sorry this is not my "invention" this i math.

d = 1000m, tA = 10s, tB = 5s
vA = d/tA = 1000m/10s = 100m/s
vB = d/tB = 1000m/5s = 200m/s
So the distance is the same, the speeds and times measured by Alice and Bob are not.
What is bothering you exactly?

 

[Dale]

the concept of "speed" then "must" have a stange schizophrenic or multi-schizophrenic nature depending on who and how many observers in different gravity levels measure this speed

This is unacceptable language for this forum. Nowhere in any professional scientific literature is speed described as schizophrenic. This is untrue and pejorative, and it trivializes a severe mental illness.

Furthermore, this is standard fare for ordinary Newtonian physics. Speed has always been frame variant (the correct term). Even in normal Newtonian physics the speed of a person walking in the aisle of a bus is maybe 1 kph relative to the bus and 101 kph relative to the ground. So your objection is not specifically relativistic.

Frame variant things are frame variant. Not schizophrenic. And the list of what things are frame variant differs between relativity and Newtonian physics, but the idea of frame variance is a standard and you cannot do even classical physics without it. You need to accept that idea if you wish to learn physics.

I realized that t is variable, and I understand that when v is not equal, for Alice and Bob, - then mathematical consequence, can only be that m is not equal either. Sorry this is not my "invention" this i math.

This is illogical. If the difference in $t$ explains the difference in $v$ then there is no need to additionally posit some weird variation in $m$. Furthermore, physics can be done in other units besides SI units. So positing some weird variation in $m$ wouldn’t resolve the issue anyway.

 

[PeterDonis]

Neither the mouse nor the photon can travel at two speeds simultaneously (depending on who is observing them).

Yes, they can. Speed in relativity is observer dependent.

I understand Einstein explained a lot that depended on how different observers perceive something that happens in other frames of reference and the consequences of that.

Einstein may have used the term "perceive" (his original writings are in German so we'd have to look at the German word he used), but if he did, he did not mean by it what you mean by it. The observer-dependent speeds in relativity are not subjective perceptions but objective measurements; different observers make different objective measurements that are the "speed" according to them.

You have been given the correct answer multiple times now in this thread, by multiple experts on the subject. If you don't want to accept it, we can't help you any further. Thread closed.

 

[Dale]

As an appendix, if we start with the usual Schwarzschild line element $$ds^2=-\left(1-\frac{R}{r}\right)dt^2 +\left(1-\frac{R}{r}\right)^{-1}dr^2+ r^2d\theta ^2+ r^2 \sin ^2(\theta )d\phi ^2$$ And we define the perspective of an observer hovering at $r_0$ to be given by the transformation $$t \rightarrow \left( 1-\frac{R}{r_0} \right)^{-1/2} T$$ Then for the vertical light pulse we can set $d\theta=d\phi=0$ and $ds^2=0$ and solve for $dr/dT$ to get the coordinate speed of light in the radial direction for a given observer which is $$\frac{dr}{dT}\bigg|_{\text{radial light}}=\left(1-\frac{R}{r} \right) \left( 1-\frac{R}{r_0}\right)^{-1/2}$$ Note that this depends on $r_0$, so different observers hovering at different radii will disagree about the speed of light, as mentioned above many times. This fully accounts for all of the disagreements between Alice and Bob. There is nothing left over to explain. I leave it as an exercise to the interested reader to show that this definition of the perspective of a hovering observer will agree on spatial distances.