To give a non mathematical example of a non-Abelian algebra, think of a Rubik’s cube where moves are the ‘numbers’ and composition of moves is the operation.
If you turn the right face clock wise and then turn the top face counter clockwise, that does not produce the same state as turning the top face counter clockwise and the turning the right face clockwise (try it out if you have one handy). Solving the cube in general requires exploiting this property by using what are called commutators, which are performing a move and then another move and then reversing the second move and reversing the first move. If it were Abelian, then that would leave you in the place where you started — which is to say you reversed time — but the state will actually have changed where the first and second move manipulated the same pieces — which makes it non Abelian and breaks ‘time symmetry’
So in this case, think of some physical operation that changes the state of the object somehow as being the same as a Rubik’s cube move, and assuming the operations have an inverse, that performing a commutator where you do one operation and then another and then invert the second and then the first, that leaves you in a new state, which would not be the case if it were time invariant.
edit: This is done consistently, and I think abelian is one of the few examples. I've never seen it capitalized before, which is why I made this post.
It seems to me that Abelian goes uncapitalized because few people know about Niels Henrik Abel, and it should properly be capitalized.
At the very least even with the knowledge that it refers to Abel they will still leave it in noun case.
Maybe it's just a post-rationalization of the phenomenon you're describing.
Examples of mathematical operators/functions that are always capitalized:
* Laplacian operator
* Gaussian distribution
* Lorentz factor
* Taylor series
* Bohr radius
This seems false.
"Time Reversal" would be better written as "Time-reversal" in title.
It obviously cares, because time slows down at high speeds and in gravitational dilation. I can't wrap my mind around it.
If you are very interested, I highly recommend Carlo Rovelli's 'The Order of Time.'
And 'Your Brain is a Time Machine', though I ultimately found it unsatisfying, goes directly at the apparent contradiction between our sense of the 'flow' of time, and the implications of general relativity. Although it doesn't have an answer, it states the problem clearly, and has a lot of other interesting facts about our perceptions of time.
Rovelli has also given some interesting talks on YouTube.
There are a lot of mysteries, even ones which arise in deceptively ordinary experiences, for example when we try to confront exactly how a gyroscope works(1).
My personal opinion is, to make an analogy, that we don't really know the source code of the universe. Every natural law is not really a law, but just a theory, or a mental model, articulated in maths, describing what we see, nothing more than that. This becomes obvious when you consider something famous like Newtonian gravity's obsolecense by GR. GR is also not the source code, just another really good mental model to describe behavioral patterns of the universe.
AFAIK time is something we really struggle with wrapping our minds around. There are questions which are so difficult I wonder if they're even worth asking -- such as about places where time would not exist, such as in places outside our universe.
I'm not a physicist but I've been pondering this sometime...
Time is like that. Pick a velocity, and then time is a distinguished axis in the coordinate system you overlay on spacetime.
In the same way speed depends entirely on your frame of reference, so does our perception of time.
What's weird about Relativity is that our experience leads us to expect that things like distance, mass, and time will be the same in every frame of reference. Instead, what's apparently the same in every reference frame is "how fast light appears to travel"; and that distance, mass, time actually warp to cause this law to be true.
Your conception of time care about the local time coordinate of the universe.
Your brain has a few clocks:
* Some are not very clear, like the time that the Sodium and Potassium needs to separate after a neuron has fired. It can't fire again until it has been recharged, so it is a clock that regulates the fire rate https://en.wikipedia.org/wiki/Na%2B/K%2B-ATPase
* Other clocks are more clear, for example there is a daily clock that counts approximately 24 hours. It has two substances that accumulate slowly and make the other substances get accumulated or get destroyed. It's tricky, but it's stable enough. https://en.wikipedia.org/wiki/Circadian_rhythm
These clock and all the other clocks and reactions of the brain are affected by the changes in the time coordinate, it's the same effect of a mechanical clock or an electronic clock or a water clock, or ...
If you go to a very fast space ship where there is a big time dilation, you will think more slowly, but the wall clock in the spaceship will be also more slowly, and the plants will grow more slowly, and the muons will decay more slowly, and the sound will move more slowly ...
Everything will happen more slowly, so inside the spaceship you will not notice the change. Everything will be normal. You will not experience "bullet-time" (like in the Matrix Movie) or "anti-bullet-time".
In this way it corresponds to the "change" in the universe. Whenever anything changes, it is moving time forward (and not the other way around). Therefore if we measure some rate of change, and give that rate of change a unit, we have ourselves a way of measuring time. For example, measuring the change in angle for shadows during the day, or measuring the changes in vibration in the Cesium atom. This count then becomes our "time".
Only to an external observer, right?
The more interesting thing is that "high gravity" is essentially acceleration (and interchangeable with acceleration in most relativity contexts+). This is why the classic "twins on a spaceship" scenario makes the twin on the spaceship the younger one, instead of them being totally interchangeable: the young one is the twin that experiences the acceleration. And you can tell all by yourself that you're undergoing acceleration; you don't need an external reference.
(+ if you accelerate forever, you can even make an acceleration event-horizon. light from beyond this horizon will never actually catch up with you, just like a black hole)
I'm sorry, I cannot really appreciate anything that plays with time and space. These are metrics to measure. I'm really not sure we can apply any thought process to imagine time reversal.
We can only imagine time reversal but that exists only in the mind not outside the head.
Another anology I would like to use "I have 100 litre of water, and I found a way to double it, compress it while keeping the mass volume unchanged".
That's how anything with space / time reversal / space wrap travelling machine all sounds!.
Stop encouraging these kind of flawed theories.
Spacetime is a unit, I cannot stand researchers providing theoritical proof that spacetime is flexible etc etc.
If I have a graph sheet with me and If I stick one edge to another edge drawing on the graph remains the same!
Lordy, I with these folks would speak english, but no, whats really important is saying things in a way only others in your field can comprehend. You can actually comprehend papers written even just 50 years ago because they written to be understood, not to confuse the granting body.
TL;DR: they setup a laser interferometer and twiddled the light in different ways through each path, the resulting interference pattern was evidence of the effect claimed.
On one path they polarized the light by running it through an LCD (a "crystal biased by powerful magnetic fields"). On the other path I'm less sure what they mean by "time-varying electrical signals", probably just means they were effectively pulsing it on and off. And somehow, by running each path through opposing winds of a fiber optic system they think they are getting results indicating "time reversal". I'll have to take them on their word on that, that's where I know less about the subject matter.
"Time-reversed human experience: Experimental evidence and implications" by Dean Radin is one that happens to be laying on my desk right now.
A new book by by Theresa Cheung and Julia Mossbridge, "The Premonition Code" gets into some of the science.
Ms. Mossbridge has published several papers and a few YouTube Videos about 'Time'.
The field of Parapsychology generally gets dismissed to easily. The top people know they will get criticized, so they tend to design their experiments and statistics to standards higher than most if not all fields of study.
If Parapsychologist presented the data that was given as 'Proof' of the Higgs boson, as shown by a small statistical bump in the data, they would have gotten their ass handed to them had they presented the same data has proof of any of their experiments.
Optical Phase Conjugation is also interesting in that it involves apparent negative time. Let you do things like a see through frosted glass. True Hacker material...
There is actually a science of studying Placebos. It is not as simple as most think. For example the strong the drug in many trials, the stronger the Placebo effect is.
Things like the total number of trials of the drug become relative. Spatial Separation does not necessary imply Independence.
To prove the placebo effect exists, you need to have a group that thinks it's getting a placebo, but actually gets nothing...
To be clear, I'm not just making a joke, I think the ideas people have about the placebo effect are deeply incoherent and harmful.
But... that is not at all what the linked essay is about? There's one paragraph in a 4.5k word essay explaining what a control group is that mentions the concept of a placebo because that's a concept related to control groups that the reader might be familiar with.
Here's the same author treating the subject of placebos more seriously: https://slatestarcodex.com/2018/01/31/powerless-placebos/
One lady did keep passing all of his tests, all day long, so they keep fiddling with the test to "improve it".
Until the lady was completely exhausted and failed the test.
Guess which test result they used?
After this no one took Randi seriously, so no one with skill bothered.
Randi's the worst kind of enemy science can have, someone who violates every principle of scientific inquiry for the sake of his own dogma, while claiming to care about the integrity of science.
Here's a statement from Randi about the dog ESP:
“I over-stated my case for doubting the reality of dog ESP based on the small amount of data I obtained,” he wrote. “It was rash and improper of me to do so. I apologise sincerely.”
Sounds like he's willing to revisit his initial claims. Has there been further evidence of dog esp that you're aware of?
As sincerely as when he said he'd replicated the experiment no doubt. And if he isn't capable of reproducing an experiment, what the frack was the prize supposedly for? I don't think he'd be capable of sincerity if he tried.
As for your other question, I saw a response Sheldrake posted about someone else's rebuttal stating that if the rebuttal's raw data were analysed the way his data was, it would have led to the same conclusion. That the attempt at replication looked at the first time the dog went to the window, rather than the average time it spent at the window. Don't have a link right now though.
Dog ESP is a pretty niche experiment though, I just brought it up because it's one of the more egregious lies Randi was caught in. If you're interested in psi data, there are much larger datasets with experiments into ganzfeld and skin conductivity precognition.
There are many people doing experiments with independent replication. Both experiments that succeed and fail. We learn from both. Sadly people would rather dismiss such things as impossible dogma rather than learn new things on the leading edge of science.
What does one do to qualify as one of the "top parapsychologists"? And how do you determine which bits are "the leading edge of science" and which are just bunk?
[Concetto R. Giuliano, 1981]
Concetto R. Giuliano, "Applications of optical phase conjugation," Physics Today, vol. 34, no. 4, pp. 27-35, Apr. 1981.
Abstract: Light waves that are, in effect, time-reversed images of their original can serve to restore severely aberrated waves to their original state.
This is just a mirror that keeps the shape of the wave intact, but moving the other way (but still forward in time).
Yoseph Imry and Richard A. Webb, "Quantum Interference and the Aharonov-Bohm Effect," Scientific American, vol. 260, no. 4, Apr. 1989.
Abstract: Can electrons be influenced by a nearby magnet so well shielded that its force field cannot be detected? The counter intuitive answer is yes:an energy emanation from the magnet known as the potential does indeed affect the electrons' wave function. This quantum-mechanical effect is being brought to bear on the development of new microelectronic devices.
Capt. Robert M. Collins (TQTR), "Soviet Research On The A-Vector Potential and Scalar Waves (U)," Unknown.
Abstract: Active in the areas of the Aharonov-Bohm effect as applied to the A-vector potential and scalar fields as applied to solving force related problems.
Capt. Robert M. Collins (TQTR), "Soviet Research On Unified Field Theories, False Vacuum States, and Antigravity (U)," Unknown.
Abstract: Theoretical progress in dealing with unified field theories...new concepts in weapons, transportation, propulsion.
Dr. Jack Dea, "Fundamental Fields and Phase Information," vol. 4, no. 3 Unknown.
Add to those the list of patents by Raymond C. Gelinas assigned to Honeywell from the 1980's and what today is being called Extended Electrodynamics as well:
L.M. Hively & G.C Giakos, “Toward a more complete electromagnetic theory”, Int. J. Signals & Imaging Syst. Engr., 5, 3-10(2012).
L.M.Hively, “Methods and Apparatus for Generating and/or Utilizing Scalar-Longitudinal Waves”, US Patent #9,306,527, (Apr. 6,2016).
L.M.Hively & O.Keller, “Electrodynamics in curved space-time: Free space longitudinal wave propagation”, Phys. Essays, 32 (3), Sept 2019.
Can't really get more up to date than a paper published this month. Sad that people will still be quick to down vote things without knowing what is going on in the world today. :-(
If we've changed topics to physics, I agree it's very interesting. The more we learn the stranger the universe seems.
I mixed the two subjects of Parapsychology and Optical Phase Conjugation under that heading. They have nothing to do with each other (as far as we know at the moment).
However in the case of psi it is about time, that is effect happens before the cause.
"... PAA [predictive anticipatory activity, an other term for Presentiment], the predictive physiological anticipation of a truly randomly selected and thus unpredictable future event, has been under investigation for more than three decades, and a recent conservative meta-analysis suggests that the phenomenon is real. ..."