[jeffreyH (OP)]

Time is dilated in a frame moving with respect to a rest frame. Since reactions are observed to slow in the moving frame does this affect the probability of quantum mechanics? If so then what implications does this have?

[Colin2B]

If the probability is time related eg atomic decay, then yes the probability of an event occurring in a given time will change

[jeffreyH (OP)]

There is an article on time dilation and decoherence.  Although it is thought to play a very minor role at best. Unless the field is strong.
https://arstechnica.co.uk/science/2015/06/relativitys-time-dilation-may-limit-the-quantum-world/

[guest4091]

Time is dilated in a frame moving with respect to a rest frame. Since reactions are observed to slow in the moving frame does this affect the probability of quantum mechanics? If so then what implications does this have?

Isn't that the reason for the extended half-life of muons?

[jeffreyH (OP)]

Time is dilated in a frame moving with respect to a rest frame. Since reactions are observed to slow in the moving frame does this affect the probability of quantum mechanics? If so then what implications does this have?

Isn't that the reason for the extended half-life of muons?

Yes. That was the reason behind posting the question. I am pondering some things to do with relativity. It is always good to ask questions. It can bring to light things that haven't been considered before.

[puppypower]

Time is dilated in a frame moving with respect to a rest frame. Since reactions are observed to slow in the moving frame does this affect the probability of quantum mechanics? If so then what implications does this have?

Probability, statistics and the assumption of random is a human mathematical invention; applied science, and not a fact of reality; pure science. A quantum universe only allows certain distinct states, whereas random implies all state are possible, albeit some are very remote but finite. Statistics is a useful tool that helps us estimate complex quantum states associated with a large number of units and variables.

For example, if we had a mole of hydrogen molecules; 6.02x 10²³, existing as a gas, although at any instant all the molecules and the entire system will exist in a quantum state, there are too many molecules and quantum interactions to keep track of, even with the most powerful modern computers. Statistics was developed as a way to estimate, even before there were computers. 

After many generations of scientists using this useful tool and getting good testable results, the original understanding, that this was only a tool, was lost. The convention started to define the universe as random, and not random a good approximation for the quantum complexity of reality. The result is the cart started to lead the horse. This can work going down hill, but not up hill or going around corners. The other way has more flexibility.

Random is more connected to manmade things, but not to natural things, which is defined by quantum principles. For example, if we had a deck of cards, it takes the same energy to flip any card, even though they all have different face values. But in terms of natural states, each quantum states; face value, requires its own unique energy to flip it. One energy quanta; dealer, cannot flip all the energy states of hydrogen, like we can flip cards.

With dice, of we throw the dice each time with the same energy, the symmetrical die can land on land on each side with the same probability. If each side of the die was defined as the energy level of an electron in a hydrogen atom, that dice will no longer act randomly, because all the side are loaded differently. The random assumption will assume average energy, which is useful as an approximation, but does not hold up to reality.

Getting back to the original question, the question is about how the random tool approximates SR conditions. The dice may appear to slow or speed up, but since each side uses the same energy, the odds will not change. Wha till change is  the time needed to reach the final state. In a quantum universe, since there are only certain states and the laws of physics are the same in all references, we will still get the same final quantum state at steady state. The tool will still work with SR.

[Colin2B]

Probability, statistics and the assumption of random is a human mathematical invention; applied science, and not a fact of reality; pure science.

This is untrue. The science of probability and statistics comes from careful observation of the natural world. The mathematics describes systems no less real than does Pythagoras's maths for right angled triangles.

[jeffreyH (OP)]

We can consider the effects of gravity on a freely falling body. The body accelerates in the field with a changing rate of acceleration. At the same time a remote viewer will see any clocks on the object to slow. The interaction of the object with the gravitational field will be seen to be stretched out over time. Does this imply a change in the action potential of the field itself?

[jeffreyH (OP)]

Note that by action potential I am not referring to the biological term.

[jeffreyH (OP)]

I am currently thinking about circular orbits at various radial distances and ground based signalling to the orbiting objects. I may have more to say on this.

[yor_on]

No, I don't think it does. The probability of something is a locally observed quantity. It's like Collin says, it's facts from where we build experimental, mathematical and philosophical frameworks. Time dilation's, length contractions etc are observables created through your 'local anchor', your clock, your definitions of length, and whatever other forces you involve.
=

If you're thinking that probability is frame dependent you should be correct, but that is not the way we reach statistics, neither a repeatable experiment. As far as I know everything is frame dependent, the only common nominator being local. Locally you can define statistics, repeatable experiments, nature constants etc.
=

there is a very simple test whether my proposal being correct. Just get into a same frame of reference as what you found to differ from another frame, then test whatever statistics etc again.

[jeffreyH (OP)]

@yor_on The point of view I am considering has to be remote. Yes, locally, this doesn't occur but if you consider the action of gravity this brings up some interesting considerations. A simple harmonic oscillator will appear to run slower in the remote frame. Since time dilation is a physical reality, as shown by GPS, then the slowing of the oscillator is also a physical reality. This has other implications involving the acceleration in a gravitational field.

You have to remember I am still learning this stuff and thinking about the implications of it.

[jeffreyH (OP)]

Since gravity must affect quantum mechanics then to unite the two that effect has to be studied in detail. Unfortunately for me that means I now have to study quantum mechanics in more depth.

[jeffreyH (OP)]

BTW It may be that when viewed from a rest frame time slows down due to velocity change but particle spin may be unaffected. This sounds like it should be important to verify if possible.

This is my starting point of investigation.
https://en.m.wikipedia.org/wiki/Quantum_reference_frame

N.B. The above should include unaffected isospin.

[yor_on]

"Since time dilation is a physical reality, as shown by GPS, then the slowing of the oscillator is also a physical reality. "

Depends on how you define 'reality' Jeffrey. If you you use 'repeatable experiments' locally made then it's not true as different observers will find different observations. What we do is to presume that a 'universe' is a coherent experience, that we all share. And it's true, but it's a partial truth if you go by observer dependencies.