The Twin Paradox/How To WinThe Debate

The Twin Paradox: Brief Background

Einstein derives symmetric time dilation

“Therefore”, if two clocks start together and one makes a round trip, a net proper time difference (NPTD) will result

Quickly led to the “Clock Paradox” - How Does One Get An Asymmetric Effect From Symmetric Causes?

How has the Debate Been Handled?

Mainstream: “There is no paradox or problem”

Wikipedia Echoes That View: I tried to enter one line in Twin Paradox article about Dingle and was “burned at the stake”

Mainstream: Accepts a wide variety of “reconciliation arguments” (RAs) – many of which are mutually exclusive

Post Dingle: Papers rebutting any of these RAs are explicitly banned from mainstream journals

1-On-1 debates with professors are unsatisfactory

Confident in their position even if they were backed into a corner, they resort to “You don’t understand SRT”

New Technique For Debating Twin Paradox

Get opponent to convince himself by his own statements

For each class of RA, get opponent to answer specific, non-controversial questions up front

Keep opponent from mixing “observed time” with “proper time” - limit discussion to “pairs of events” and the “associated proper time” – Don’t compare traveler’s proper time to Stay-At-Home’s clock readings

Ask opponent to specify how much proper time accumulates for each segment of the “traveling” twin’s round trip

After opponent has defined his position in detail, ask him to address specific problems

Optional: Slightly modified scenarios

RA # 1: NPTD Accumulates During Constant Velocity Segments

Cause is relative velocity or relative simultaneity which are symmetric

Mixes Observed Time with Proper Time

Unconscious Assumption that Starting Frame is Unique Frame

Key Up Front Points

1/2 the NPTD accumulates in outbound and 1/2 in inbound

The NPTD accumulates smoothlyAll clocks in a frame tick at the same rateIf a clock accumulates a NPTD versus one

clock in another frame, then it also accumulates the same NPTD versus all other clocks in that other inertial frame

Sample ScenarioV = 0.866c, time dilation factor = ½

Stay-At-Home 200,000,000,000 “ticks”

Traveler 50,000,000,000 out & in

Periods of acceleration made arbitrarily small wrt constant velocity segments

Twin Paradox Scenario Events

E1-E2 (Traveler’s outbound trip) E3 V--------------------------------------------------------------V S(Stay-At-Home remains at rest ) E4 V--------------------------------------------------------------V E7-E6 (Traveler’s inbound trip) E5

Argument

Agreeing that NPTD accumulates equally and smoothly for constant velocity segments implies that the clock in the T-out frame loses proper time vs all clocks in S for all of E2-E3

However, if one adds a 2nd Twin Paradox scenario where T-out now also plays the role of the stay-at-home twin and the “new traveling triplet” is at rest in S during the outbound leg and the whole 2nd scenario begins at E2 and ends at E3, then RA #1 leads to a contradictory conclusion that the T-out clock gains vs all clocks in S for part of E2-E3 

Optional Argument

• Replace initial acceleration (E1-E2) with arbitrarily near miss

• Then for the outbound constant velocity segment, the time dilation effect occurs before one determines who will be the traveling twin!?!

RA # 2: NPTD Accumulates During Turnaround AccelerationCause is asymmetric, turnaround

acceleration, changing frames, virtual gravitational field, or rel. simultaneity

NPTD calculations use distance of separation between twins at turnaround

Key Up Front Points

1/2 the NPTD accumulates in E3-E4 and 1/2 in E4-E5

All clocks in a frame tick at the same rate

If a clock accumulates a NPTD versus one clock in another frame, then it also accumulates the same NPTD versus all other clocks in that other inertial frame

Argument – Fill In Table

Traveler’s Event Pairs # of Proper Time Ticks

E1-E2 (Initial Acceler’n) 500

E2-E3 (Outbound @ v) (50,000,000,000 - 1,000)

E3-E4 (Turnaround - 1) 500

E4-E5 (Turnaround - 2) 500

E5-E6 (Inbound @ v) (50,000,000,000 - 1,000)

E6-E7 (Final Deceler’n) 500

Stay-At-Home # of Proper Time Ticks

E1-E7 (Whole scenario) 200,000,000,000

Optional Argument

Add a 2nd scenario, also starting in S with T accelerating to 0.866c, but have 1/10th the duration and arrange it so the turnaround for both scenarios will be at virtually the same place and time

Ask, “How can same turnaround parameters yield radically different effects?”

RA #3: Minkowski Spacetime, Invariance of the Interval

RA #3 is really RA #1 – it’s just the relative velocity argument in disguise

SRT’s Time Dilation Equation is used with an implied meaning that’s compatible with LAT not SRT

Mixes Observed Time and Proper Time

Notes

• http://TwinParadox.net (all the details)

• Designed Experiment Where Traveling Twin Gains Proper Time

• NPA Sponsored (Public) Debate

Part – IIImplications For SRT –

Observations From A Long Odyssey

Thoughts From My Odyssey

Physical, Asymmetric Time Dilation As A Function of Velocity WRT A Unique Frame Is The Only Viable Cause For the NPTD

Tried To Derive Alternative to SRT And (unknowingly) Derived LAT-like (w/o ether) -Called it ESRT

LAT-like physical spacetime model underlies SRT’s observed spacetime models

SRT & LAT Predict Same Results

In the Twin Paradox, no matter what frame is used as the starting frame, relative velocity predicts same NPTD as LAT’s absolute velocity

For a Wide Range of Phenomena, SRT and LAT predict same results

Tried To Define Experiment Where “LAT” Was Right vs SRT – Very Difficult- [An Exception Selleri’s Sagnac Experiment]

Same Results For Kinematics

For LAT/ESRT, the concept of absolute kinetic energy is used

In a collision, the total amount of absolute kinetic energy may differ from total amount of relative kinetic energy, but conservation laws make it so that the amount of available energy for particle creation is the same

Machian View

• LAT time dilation a function of difference in absolute kinetic energy

• Same phenomenon as GRT time dilation as a function of difference in grav. pot.

• Absolute kinetic energy is f(Absolute Motion wrt mass/energy configuration)

Modified SRT

Remove Last Three Paragraphs of Einstein’s 1905 SRT paper – most paradoxes/problems disappear as they are now outside the domain of SRT

2nd Postulate becomes: The speed of light is observed to be c by all inertial observers

Modified SRT

1st Postulate becomes: The mathematical form of the laws of physics for observations are invariant in all inertial systems

[Interestingly, for LAT/ESRT, the mathematical form remains the same, but the meaning changes]

Lorentz Geometry (LG)

LG can describe SRT view where each observer observes himself to be in the unique frame where all other frames seem to have slower clocks and shorter (in the direction of motion) meter sticks

Alternatively, LG can describe LAT view of there being a unique frame where all other frames actually have slower clocks, etc.

My Conclusion

(Modified) SRT & LAT-Like Theory Both Correct – But Cover Different Domains

LAT describes physical spacetime which is “obscured” – can’t even tell which is the unique frame

SRT describes how each observer observes spacetime & is derivable from LAT/ESRT

Prokhovnik, Builder, Frankl

Some “Otherwise” Respected Physicists Have Come To Similar Conclusions

Frankl starts with classical Doppler Effect as f(velocities wrt medium) and uses Relativity’s “Addition of (observed) Velocities” to derive relativistic Doppler Effect for 2D (Am. J. Phys, 52(4), April 1984)

How has the Debate Been Handled?

NPA is to SRT as physics comm. is to LAT (Not in Video Conferences, but in email discussions, etc.)

All anti-SRT attacks accepted, all defenses automatically rejected

Principle 9: There is not a shred of evidence even claimed to exist as confirmation of the reciprocity feature of SR – Really???????

E.G., Dividing By Zero

Work Formula NOT key to deriving SRT

Not dividing by zero since, in SRT, v can’t equal c

Even if v could equal c that does not automatically invalidate whole theory, but just for that special case

Something To Think About

At the very least, SRT So Often Gives The Right Answer It Must Point to Some Very Significant Property of Spacetime

Being Dismissive Blinds One to that Clue

Easier To Sell To Mainstream

References

• AN ASYMMETRIC MODEL OF SPACE-TIME BUILT ON LORENTZ GEOMETRY AND THE RESULTING EXTENSIONS OF SPECIAL RELATIVITY (Physics Essays Vol 7 #2 , 1994)

• A FULL UNDERSTANDING OF THE TWIN PARADOX REQUIRES AN EXTENSION OF SPECIAL RELATIVITY:  The Twin Paradox Analyzed Using Two Different Space-Time Models (Physics Essays Vol 8 #1 , 1995)

Special Relativity: “Inconsistent” Or Just “Incomplete” (A Reply To McCausland’s Reply) (Physics Essays Vol 11 #1 , 1998)

The Extension of Special Relativity: Algebraic Equivalence For Observations Plus A New Prediction" (Physics Essays Vol 12 #4 , 1999)

Correcting The Flaw In Special Relativity That Leads To The Twin Paradox – Reflections on a Debate With I. J. Good And I. McCausland (Physics Essays Vol 13 #4 , 2000)

• A Very Doable Experiment for NASA to Look Inside the Twin Paradox (Physics Essays Vol. 19 # 1, 2006)