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Catastrophe

"There never was a good war, or a bad peace."
Unc, you got me on the second sentence:

"So, if a pair of say, electrons were "entangled" so that they had opposite spins, then sent flying in opposite directions"

I don't understand. Are we looking through a souped up electron microscope to see these entangled electrons? Can we see the opposite hands they fit (their opposite spins) and then we gently give them a shove in opposite directions?

Sorry. I am a scientist, but not a physicist. I stopped at Advanced Level Scholarship Level School Physics (which I passed). But that was long ago.

Since this is not happening on a macroscopic level, then there must be assumptions involved, and I guess, teeny side issues like division by zero, which seems to be a plague vide mathematics in science.

And, as I suggested, what about Heisenberg in this problem? We seem to be glibly measuring these particles, and knowing their past trajectories?

Sorry. Like others, I suspect, I am just trying to understand this "paradox".

Cat :)
 
Feb 7, 2022
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Regarding the apparent paradox, perhaps this explanation will help. Here

The last paragraph is interesting as it takes a Doppler approach. This is a little like the business analogy where “add-on” and “mark-up” differ. A 50% add-on to $1 is $1.50, but a 50% mark-up is $2, allowing the seller to make 50% profit. [I think this applies.]

iPhone with rib sauce. :)
Helio, That is a really good pictorial explanation of the time difference effect for a round trip, as described by Special Relativity. This result is counter-intuitive, because it shows that a person would age less due to traveling fast, even though he ends up back at the starting point at zero velocity.

But, that in itself is not the "twin paradox" that people keep talking about. That twin paradox tries to use the idea or "relativity" to imply that a calculation done the same way for the twin who stays at the starting point should be considered to be moving in the other direction while the actual traveling twin is assumed to be at-rest. The problem with that is, as you have pointed out, the twin that is accelerated can be determined to be different from the twin that remains at rest because the forces involved are detectable, and while they are being applied, violate the condition of Special Relativity that it applies to observations between two inertial frames of reference. I agree with that, but the problem is that the calculation does not include the effects of the accelerations on the mathematical result.

So, we are left in the situation where we agree that the Theory of Special Relativity cannot be applied to this whole experiment without modification, but we do not have the formula that we think does apply to the whole experiment. That is what leaves in-doubt that veracity of the result.

However, I seem to remember that some experiments were done by putting clocks in orbit around the Earth, and comparing them to clocks left on earth once the orbiting clocks were returned to Earth, and that those experiments verified the time difference calculated by "relativity". Unfortunately, that would involve both Special and General Relativity, and the media reports that I remember were not really adequate to describe the details of the experiment.

But, we currently use those theories to make verifiable predictions with our satellite GPS systems. See https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gps.html . That says Special Relativity makes the clocks in the GPS satellite orbits seem to run 7 microseconds per day slower than our clocks here on Earth's surface, but General Relativity says that clocks here on Earth's surface should run 45 microseconds per day slower than the clocks in orbit because of the difference in the gravitational field force at the two different altitudes. The net effect is that the clocks on the GPS satellites need a 38 microsecond per day correction to avoid the calculated positions on Earth shifting by 10 kilometers per day! That does seem like good experimental validation of the theories, as applied together, for observations of things in 2 different locations.

But, that is really not represented by the out-and-back time lines in your example, because the distance between the sender and receiver is not being monotonically increased and decreased by the velocity in orbit. So, I am having a hard time thinking about it as vectors. The Special Relativity part is really a scalar calculation, so it seems to work no matter what direction(s) the travel is going in, compared to the observer.

The problem is that an orbit is not an inertial frame of reference. It is a constant acceleration frame of reference with the acceleration vector changing the direction of travel along the constantly shifting radial direction (relative to an actual inertial frame of reference).

So the same criticism (motions of subjects not always being in inertial frames of reference) that applies to the "twin paradox" seems to also apply to this experimental verification for Special Relativity. It seems inconsistent to use the same concept in 2 diametrically opposite ways, logically.

So, I am still looking for a pure empirical demonstration that a clock that is sent into orbit and returned to Earth has actually shown less time passage than a clock left on Earth when the difference is corrected for the altitude effects of General Relativity.

Because that seems like an experiment that can be done, I expect that it has been done. I just have not found it, yet. This link https://en.wikipedia.org/wiki/Time_dilation talks about experimental verifications using things like sub atomic particle half-life measurements. It also claims a solution to the twin paradox with Minkowski diagrams, but I am not following that clearly, (yet?).
 
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But, that in itself is not the "twin paradox" that people keep talking about. That twin paradox tries to use the idea or "relativity" to imply that a calculation done the same way for the twin who stays at the starting point should be considered to be moving in the other direction while the actual traveling twin is assumed to be at-rest.
Yes, we assume relativity should work from the view of any inertial frame, but....

The problem with that is, as you have pointed out, the twin that is accelerated can be determined to be different from the twin that remains at rest because the forces involved are detectable, and while they are being applied, violate the condition of Special Relativity that it applies to observations between two inertial frames of reference. I agree with that, but the problem is that the calculation does not include the effects of the accelerations on the mathematical result.
I don't see a violation during acceleration, though I'm no expert. Acceleration involves GR, but SR can work fine by doing the math for incremental increases in velocity. The key is that only one person is experiencing acceleration and, somehow, time dilation gets assigned to this person (ie traveler). [Perhaps some see this event as some sort of symmetry break.] The math during acceleration (& deceleration) will show that there is very little time dilation during acceleration. The real time dilation (or length contraction if one wishes) is in the long travel times at relativistic speeds.

So, we are left in the situation where we agree that the Theory of Special Relativity cannot be applied to this whole experiment without modification, but we do not have the formula that we think does apply to the whole experiment. That is what leaves in-doubt that veracity of the result.
I'm saying SR can be made to work effectively even during the brief time period of accelerations. I suspect the math will show very little time dilation difference in accounting for acceleration for those long trips, if one wants to do the slice -method of SR.

However, I seem to remember that some experiments were done by putting clocks in orbit around the Earth, and comparing them to clocks left on earth once the orbiting clocks were returned to Earth, and that those experiments verified the time difference calculated by "relativity". Unfortunately, that would involve both Special and General Relativity, and the media reports that I remember were not really adequate to describe the details of the experiment.
Correct.

But, we currently use those theories to make verifiable predictions with our satellite GPS systems. See https://www.astronomy.ohio-state.edu/pogge.1/Ast162/Unit5/gps.html . That says Special Relativity makes the clocks in the GPS satellite orbits seem to run 7 microseconds per day slower than our clocks here on Earth's surface, but General Relativity says that clocks here on Earth's surface should run 45 microseconds per day slower than the clocks in orbit because of the difference in the gravitational field force at the two different altitudes. The net effect is that the clocks on the GPS satellites need a 38 microsecond per day correction to avoid the calculated positions on Earth shifting by 10 kilometers per day! That does seem like good experimental validation of the theories, as applied together, for observations of things in 2 different locations.
Yes, SR and GR dilations work against one another to produce the 38 microsecond delay.

Many other experiments support relativity. The muon story is a common one used. The muon should never have time to reach our surface, but relativity demonstrates, accurately, what actually happens. [Oddly, the story is told in terms of length contraction rather than time dilation. There is very little evidence that length contraction is "real", but I did learn of one likely demonstration.]

But, that is really not represented by the out-and-back time lines in your example, because the distance between the sender and receiver is not being monotonically increased and decreased by the velocity in orbit.
You are referring to the Doppler point of view as noted in that link, no doubt. I have not given that view a lot of thought, but there must be something to it because the traveler must necessarily receive the same no. of radio pulses as those sent, but the difference is the rate they are received. There will be a blueshift/redshift difference by the link's simple math shown, apparently.

The problem is that an orbit is not an inertial frame of reference. It is a constant acceleration frame of reference with the acceleration vector changing the direction of travel along the constantly shifting radial direction (relative to an actual inertial frame of reference).
That's a good point because that too involves GR. I'm curious if the simplified method (slicing velocity units) for SR is used.

So the same criticism (motions of subjects not always being in inertial frames of reference) that applies to the "twin paradox" seems to also apply to this experimental verification for Special Relativity. It seems inconsistent to use the same concept in 2 diametrically opposite ways, logically.
Only when all the relativistic effects are included will the result match the experimental result. I don't understand it that well, admittedly, since it isn't intuitive in the slightest.

This questioning is (or was) common. There were 100 prominent Germans (authors and at least one scientist) that sent a letter out stating Einstein's relativity was wrong. Einstein was shown this letter and his response was that why would you need 100 when only 1 is necessary (falsifying the theory). :)

So, I am still looking for a pure empirical demonstration that a clock that is sent into orbit and returned to Earth has actually shown less time passage than a clock left on Earth when the difference is corrected for the altitude effects of General Relativity.
Some of the many experiments include the wavelength shift for light when pointed from a higher elevation towards the ground. Even when done at extreme precisions, relativity, and nothing else, shines.

I've tried to think of SR using the analogy of a boat at a high speed. Speed racing often only has the prop in the water as the hull no longer is emersed in water creating wake. If relativistic speeds of a spacecraft traveling faster and faster were to skip over more and more Planck time pulses (just like the boat over fewer and fewer waves of water), then we would have a more intuitive solution. Unfortunately, this idea is incorrect, though I still like it since it can assume the Hubble Flow is the ocean. :)
 
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Cat:
1. I thought all electrons have a spin number of 1/2, no matter its orientation.
2. Electron microscopes don't look at electrons, they use electrons to bounce off and create images of other small stuff.

But, somehow, I have a sneaking suspicion that you knew all that! :) :) :)
 
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May 14, 2021
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The bartender tells the tachyon before he arrives,
Werner Heisenberg was stopped by a police officer for speeding, Werner said 'Well, if you knew where I was when I was driving, you could not possible know how fast I was going.'
 

Catastrophe

"There never was a good war, or a bad peace."

Catastrophe

"There never was a good war, or a bad peace."
Pogo,
"Are we looking through a souped up electron microscope to see these entangled electrons? Can we see the opposite hands they fit (their opposite spins) and then we gently give them a shove in opposite directions?" Shhhhh. It was a rhetorical question. ;)

Cat :)
 
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