Groups > sci.physics.relativity > #625630

Re: The Helical Path Paradox

Newsgroups	sci.physics.relativity
Date	2023-12-12 11:28 -0800
References	<500ab0c4-e0fd-4dd9-8e00-6654a154e0cen@googlegroups.com>
Message-ID	<18f88b3a-b545-4e10-8cb8-e747a9de6b60n@googlegroups.com> (permalink)
Subject	Re: The Helical Path Paradox
From	patdolan <patdolan@comcast.net>

Show all headers | View raw

On Monday, December 11, 2023 at 10:19:39 PM UTC-8, patdolan wrote:
> Proxima Centauri is 4.2 light-years away from Big Ben. Two distant observers A and B are racing past Proxima Centauri on their way to Big Ben at .867c relative to the Big Ben--Proxima Centauri frame of reference. For these two observers Proxima Centauri and Big Ben are only 2.1 light-years apart due to Lorentz contraction. Both observers also note that the little hand of Big Ben rotates only 365.25 times per year of their proper time instead of 730.5 rotations, due to Lorentz time dilation. Now this slowing of Big Ben is not some illusion or artifact of speed. SR assures us that Big Ben REALLY IS RUNNING SLOWER in their frame of reference.
>
> Just as observer A passes Proxima Centauri he begins to count the 365.25 x 2.1 = 767 turns in the helical path of light emanating from the tip of Big Ben's little hand, which lie between Big Ben and Proxima Centauri at any given moment in that frame of reference. He also counts the 2.42 x 365.25 = 884 additional turns that Big Ben produces during the rest of his 2.42 year journey to Big Ben, for a total of 1651 turns during the entire trip.
>
> Meanwhile, observer B decides to use the relativistic doppler formula instead, which relies on the oscillator's own proper frequency (in this case 730.5 turns per year) as the input. So observer B gets 3.747 x 2.42 x 730.5 = 6624 total turns of the helix during the trip from Proxima Centauri to Big Ben.
>
> Observers A and B disagree on the total number of turns by a factor of 4 for the same helix on the same trip. The validity of the relativistic doppler formula is forever washed away.

There seems to be some reluctance in this forum to step up and take on this conundrum. So let's let ChatGPT break the ice. Chat, take it away!
_________________________________
Chat:

It appears there might be a misunderstanding or error in the calculations provided. Let's break down the scenario and the calculations to identify the source of the discrepancy.

Observer A is counting the turns directly using the Lorentz contraction and time dilation effects, while Observer B is using the relativistic Doppler formula. Let's reevaluate the calculations:

Observer A's calculation:
365.25
turns/year
×
2.1
light-years
=
767.625
turns
365.25 turns/year×2.1 light-years=767.625 turns
730.5
turns/year
×
2.42
years
=
1767.21
turns
730.5 turns/year×2.42 years=1767.21 turns
Total turns according to Observer A:
767.625
+
1767.21
=
2534.835
turns
767.625+1767.21=2534.835 turns
Observer B's calculation using the relativistic Doppler formula:
Total turns
=
Proper frequency
Observer B’s observed frequency
×
Total proper turns
Total turns=
Observer B’s observed frequency
Proper frequency

×Total proper turns
Total turns
=
730.5
turns/year
3.747
×
2.42
years
≈
6623.524
turns
Total turns=
3.747
730.5 turns/year

×2.42 years≈6623.524 turns
Now, let's compare the results:

2534.835
6623.524
≈
0.382
6623.524
2534.835

≈0.382

The factor by which the two observers disagree is approximately
0.382
0.382, not 4. There might be a mistake in the given values or calculations. Please double-check the numbers and the scenario to identify the discrepancy. If there's a specific part of the scenario or calculation that you'd like to focus on, feel free to point it out for further clarification.
_________________________________

Hm. Chat seems to be a little confused on the arithmetic details. But the important take-away is that ChatGPT understands and agrees in principle with the contradiction between the two methods. So I pressed Chat further with this question: "So you agree in principle with the contradiction between the two methods?" To which Chat answered:
_________________________________
Chat:

Yes, it seems there is a contradiction between the two methods in the provided scenario. Observer A and Observer B, using different methods to calculate the total number of turns of the helix between Proxima Centauri and Big Ben, arrive at significantly different results. The principle of relativity in Special Relativity asserts that physical laws are the same in all inertial frames of reference, but these calculations seem to indicate a discrepancy.

It's important to note that the scenario involves relativistic effects such as time dilation and length contraction, which can lead to counterintuitive results. These effects are well-established in the framework of Special Relativity and have been experimentally confirmed.

If there's a specific aspect of the scenario or calculation that you find confusing or if you suspect an error, please provide more details so that I can help clarify or identify any issues.

__________________________________
Me:

So in view of the foregoing, is there a possibility that the relativistic doppler formula is wrong?
__________________________________
Chat:

The relativistic Doppler formula is a well-established equation that describes the frequency shift of light due to relative motion between the source of the light and the observer. This formula has been tested and confirmed through experiments, and it is a fundamental aspect of Special Relativity.

The relativistic Doppler formula takes into account the effects of time dilation and length contraction, ensuring consistency with the principles of Special Relativity. It has been validated in various experimental scenarios, including observations of relativistic effects in high-speed particle physics experiments and astronomical observations.

If there appears to be a discrepancy in the scenario you presented, it's more likely that there might be an error in the specific values or calculations rather than a fundamental flaw in the relativistic Doppler formula itself. It's important to double-check the numbers, units, and the entire scenario to identify the source of the inconsistency.

If you have specific questions about the relativistic Doppler formula or if there are particular aspects of the scenario that you find confusing, please provide more details, and I'll do my best to help clarify.
___________________
Me:

But if I have not made errors, then what?
_____________________________
Chat:

If you've carefully checked the scenario and calculations, and there are no errors in your input, yet you are still observing a significant discrepancy between the two methods (Observer A's direct counting using Lorentz contraction and time dilation, and Observer B's use of the relativistic Doppler formula), then it would indeed be an interesting situation.

In the framework of Special Relativity, the relativistic Doppler formula is a well-established and experimentally validated formula. If there seems to be a contradiction, it would suggest a need for a deeper investigation or an alternative explanation.

Possible considerations:

Scenario Clarification: Recheck the details of the scenario to ensure there are no hidden assumptions or overlooked factors that could lead to the observed discrepancy.
Consistency with Special Relativity: Make sure that the scenario is consistent with the principles of Special Relativity. The Lorentz contraction and time dilation effects should be applied correctly.
Consultation with Experts: Discuss the scenario with experts in the field of relativity or physics. They may provide insights, identify any potential oversights, or offer alternative perspectives.
Alternative Explanations: Consider whether there might be an alternative explanation or interpretation of the scenario that aligns with the principles of Special Relativity.
Remember that the principles of Special Relativity have been extensively tested and confirmed through experiments, so any apparent contradiction would be unexpected. It's possible there could be a nuance in the scenario or an aspect that needs further clarification. If you can provide more specific details, I may be able to offer further assistance or insights.

_________________________
Me:

Might the same be said of Special Relativity?
____________________________
Chat:

The principles of Special Relativity, developed by Albert Einstein, have been extremely successful in explaining and predicting a wide range of physical phenomena. Special Relativity has undergone rigorous experimental testing over the years, and its predictions have been consistently confirmed.

Key aspects of Special Relativity include the invariance of the speed of light, time dilation, length contraction, and the equivalence of mass and energy (expressed by the famous equation
E
=
m
c
2
E=mc
2
). These principles have been validated through experiments in particle physics, high-speed observations, and various other domains of physics.

However, if there were ever to be a genuine contradiction or anomaly that could not be resolved within the framework of Special Relativity, it would certainly prompt a reexamination of the theory. Science is a self-correcting process, and if experimental evidence or observations were to challenge established theories, scientists would work to understand the discrepancies and potentially revise or extend the current understanding.

It's important to note that Special Relativity has passed many stringent tests and has been a cornerstone of modern physics for over a century. It is considered a well-established and robust theory that accurately describes the behavior of objects moving at high speeds or in strong gravitational fields.

If there were any doubts about Special Relativity, they would likely prompt further investigation, discussion, and experimentation within the scientific community to either refine or expand our understanding of the laws that govern the universe. As of my last knowledge update in January 2022, Special Relativity remains a fundamental and well-supported theory in physics.

Back to sci.physics.relativity | Previous | Next — Previous in thread | Next in thread | Find similar

Thread

The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-11 22:19 -0800
  Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-12 11:28 -0800
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-12 17:55 -0800
  Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-13 19:51 +1100
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 05:12 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 08:40 +1100
    Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-13 05:19 -0800
    Re: The Helical Path Paradox Ryker Habibulaev Balanda <enaa@brdaaeea.ye> - 2023-12-13 13:32 +0000
    Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-13 16:03 +0000
      Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 09:50 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 08:42 +1100
        Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-13 22:32 +0000
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 16:22 -0800
          Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 11:30 +1100
            Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-13 16:52 -0800
              Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 11:56 +1100
            Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-14 00:55 +0000
              Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 12:02 +1100
                Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-14 01:27 +0000
                Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-14 12:58 +1100
                Re: The Helical Path Paradox Athel Cornish-Bowden <me@yahoo.com> - 2023-12-14 13:56 +0100
                Re: The Helical Path Paradox Richard Hachel <r.hachel@frite.fr> - 2023-12-14 14:45 +0000
                Re: The Helical Path Paradox Athel Cornish-Bowden <me@yahoo.com> - 2023-12-14 18:17 +0100
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 10:03 -0800
            Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-13 17:00 -0800
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 12:07 -0800
      Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 12:49 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 11:10 +1100
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 19:21 -0800
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 19:23 -0800
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 19:33 -0800
          Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 15:07 +1100
            Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-14 20:40 -0800
              Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 16:07 +1100
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-15 00:26 -0800
                Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-15 19:45 +1100
                Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-15 14:45 +0100
                Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-15 12:06 -0800
                Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-16 10:24 +0100
                Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-16 01:47 -0800
            Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-15 13:37 -0800
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-16 13:20 -0800
      Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-17 16:13 -0800
        Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-18 11:25 +1100
          Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-17 16:48 -0800
            Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-18 13:09 +1100
              Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-17 18:31 -0800
                Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-18 14:14 +1100
                Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-18 06:29 -0800
        Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-18 20:43 +0100
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-18 06:19 -0800
      Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-19 09:59 +1100
        Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-18 15:28 -0800
          Re: The Helical Path Paradox Sylvia Else <sylvia@email.invalid> - 2023-12-19 11:01 +1100
        Re: The Helical Path Paradox Maciej Wozniak <maluwozniak@gmail.com> - 2023-12-18 21:17 -0800
  Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-15 14:45 +0100
    Re: The Helical Path Paradox patdolan <patdolan@comcast.net> - 2023-12-15 11:28 -0800
      Re: The Helical Path Paradox "Paul B. Andersen" <relativity@paulba.no> - 2023-12-16 10:24 +0100

csiph-web