What is Paradox: Definition and 999 Discussions

A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.In logic, many paradoxes exist which are known to be invalid arguments, but which are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions which were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, cannot be easily resolved by making foundational changes in a logical system.Examples outside logic include the ship of Theseus from philosophy, a paradox which questions whether a ship repaired over time by replacing each and all of its wooden parts, one at a time, would remain the same ship. Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.In common usage, the word "paradox" often refers to statements that are ironic or unexpected, such as "the paradox that standing is more tiring than walking".

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  1. S

    B Energy conservation Paradox

    Hello, Stephen Hawking's book The Future of The Universe says that matter would have to exceed the minimum speed of 5 times the speed of light to exit a black hole. This means that the matter would have to be transferred to Energy using E=MC^2 but all energy is limited by the speed of light...
  2. P

    B Understanding the Twin Paradox: Simplifying with a Clear Experiment

    I have seen many attempts to rationalise the 'Twins Paradox', but none of the seem satisfactory. They usually use acceleration or asymmetric differences in inertial frame, or other aspects of special relativity that tend to obfuscate the problem/explanation. So proposing an experiment that...
  3. M

    I The inclined plane paradox...

    Hello and thank you for welcoming me to your forum! To get started, I would like to give you a little help: In the pattern experiment, when firing the cannon, if part of the momentum reaches the bird, and if another part of the momentum manages to stun the fish, what part of the momentum would...
  4. Hak

    I Paradox of the car and the driver in SR

    I would like to propose a relativistic problem that I cannot understand. A car of rest length L travels at close to the speed of light towards a garage, of length L, which also has an opening at the bottom. For a person next to the garage door, the car has a length less than L, due to the...
  5. jeff einstein

    B A contradiction of the equivalence principle?

    hi, I am a physics student in grade eleven. I do not have much knowledge of physics but I have a doubt: apart from the maths and the experiments, shouldn't larger masses be attracted to Earth's gravity rather than be attracted the same regardless of mass? if we had a scenario where we have...
  6. S

    B Another special relativity related "paradox"

    Full disclosure: I have asked this question on stackexchange too, but I think I didn't frame my question properly there, which probably led to misunderstandings and complicated answers. Plus some comments there led me to refine the question a bit so I hope it's in a good state now. I am new to...
  7. sergiokapone

    I Special Relativity Paradox "Terrorist and Spaceship"

    The ship left Earth at a speed of 0.5c . When the distance between the ship and Earth was 0.25 light year, a terrorist was caught on Earth who said that he had planted a bomb at the time of departure and activated it for 10 months. At that moment, a warning signal was sent from Earth. The...
  8. V

    B Triplets Paradox: Is There a Solution?

    One person (A) stays on Earth, while another (B) goes on a long journey and returns later. We can calculate the time interval for A and the proper time interval for B. Let's say we get Δt=100y and Δτ'=50y. We then consider a second traveler (C) going on a different journey, departing and...
  9. C

    A Runners in a race, probability paradox

    There are a number n of runners in a race. We know their expected times from start to finish μ(i) and the corresponding standard deviations σ(i). The probability of runner 0 to finish first is given by this integral: It's from here: https://www.untruth.org/~josh/math/normal-min.pdf The 0 is...
  10. SaintRodriguez

    I Time Paradox: A & B's Clocks Move Differently

    Two astronauts A and B are traveling at constant speed, one toward the other. From astronaut A's point of view, his partner B's clock is ticking at a slower rate than his. From astronaut B's point of view, it is his partner A's clock ticking at a slower rate. Does this set up a paradox? Because?
  11. B

    B The twin paradox and black holes

    Does the twin paradox hold around a black hole (or maybe less extreme gravitational fields)? In a gravitational fields like that of the Earth it seems to apply. If two particles fall together, with synchronized clocks, and one of them rests on a platform for a while, after which it accelerates...
  12. vibhuav

    I Twin Paradox: Aging Slower with Continuous Acceleration?

    I understand that the travelling twin (T, say) is subjected to acceleration and deceleration while the stay-at-home twin (S) is in inertial frame all the time. It is this asymmetry which results in the travelling twin aging less than the other, when they two meet up. Since acceleration is the...
  13. J

    I Solving Paradox: Man Running with Pole Reaches Door Before Button is Pressed

    I think I broke special relativity…not really but I am clearly over looking something. Imagin a man carrying a pole (like a pole vaulter) running at speed v. The length of the pole = L, so in the frame of the person watching this man run, the length of the pole is observed as L/γ. There is a...
  14. EclogiteFacies

    I Andromeda Paradox - confused

    Hi all, I'm a bit nervous about the implications of relativity, not the block universe stuff I can work with that.. What worries me regards planes of simultaneity, when I'm walking away from you my plane of simultaneity will contain you from your past, so the you in my reference frame...
  15. S

    I Please help with another twin paradox situation (sorry)

    In the image below from the website http://www.mysearch.org.uk/website1/html/250.Twins.html , they try to explain why the two situations are not symmetric, but I don't understand their approach. Even if the website is not giving a sufficient explanation, I would still like to know why the two...
  16. ynojunin

    B My paraphrased explanation of the Twin Paradox

    So I've been trying really hard to understand the theory of relativity at its most basic level lately, and recently I dove down the rabbit hole of the Twin Paradox. This has led me through a series of youtube videos, each one claiming to present a different solution, explain why the other...
  17. amorphos_b

    Gun with a tachyon bullet paradox

    Gun with a tachyon bullet paradox if you had a device akin to some kind of ‘gun’, which created tachyons and the fired them, perhaps in a beam or some kind of ‘packet’, when they go faster than the speed of light would go back in time. Lets say the ‘bullet’ or beam, went out into the universe...
  18. topsquark

    I Twin Paradox: Calculating Stan's Time Elapsed According to Moe

    I know, I know, yet another Twin Paradox thread. (My apologies if this is already on the Forum somewhere. I found a similar discussion but with no answer to my question. I'd appreciate a link if someone has already given an answer to it.) I'm trying to construct the time elapsed for Stan...
  19. T

    I Probability paradox: P(X=x)=1/n >1

    I have a random variable X in range(0,n) where n<1, with a uniform distribution Then the probability of sample space S=n x P(X=x) x<=n which must be 1 Manipulating the equation P(X=x)=1/n >1 Then this violates the fundamental law of probability which says that any probability must be at most 1...
  20. AndrzejB

    Special relativity paradox

    Alice measures the spin, also Bob measures. If we assume that the signals (from Alice to Bob) were sent, they had to be with the speed e.g. 10 c But in another frame of reference Bob first measures, next Alice. Measurement of Alice was cause and was sent back in time, or measurement of Bob was...
  21. O

    B Understanding twin paradox without math

    Using a simple time clock in the horizontal position you can see the solution to the twin paradox. In this graph the Time clock tics once every half year on earth. 5 years pass on Earth 4 years pass on the spaceship. You don't have to worry about mysterious simultaneity or time jumps...
  22. Sagittarius A-Star

    I Twin Paradox with accelerated Motion

    Alice rests at ##X=L+1## in the inertial frame (T, X). Bob is at rest in the Rindler frame (t, x) at ##x=1## and has the proper acceleration ##\alpha=1##. In the rest frame of Alice, Bob moves from event ##E_1=(-T_2, L+1)## over the distance of ##L## in negative X-direction to event ##(0, 1)##...
  23. alan123hk

    B Understanding Lewin's Circuit Paradox: Explained Simply and Clearly

    I just saw the following clip on youtube It seems that many people are still interested in this topic. Here is the simple clear explanation I came up with, is there any error please ? This means that voltmeter 2 is not measuring the potential difference produced by the charge...
  24. M

    I Lorentz Contraction & Twin Paradox

    The twin paradox is connected to the special relativity but I wonder simply if one might construct the paradox (or something very similar) based on the Lorentz’ (and FitzGerald) work alone? Several ingredients in the paradox, time dilation and Lorentz contraction, are often mentioned with...
  25. Ahmed1029

    I Resolving the Twin Paradox: Non-Straight Paths and Proper Time in Space-Time

    Is the twin paradox settled by saying that any non-straight path between two events (points) in space-time has less proper time that a straight path between the two events? So the twin in the frame which has a longer trajectory between the two pints(curved) will have less elapsed time?
  26. Kairos

    I Twin Paradox with radioactive twins

    Replace the twins in the twin experiment by identical radioactive samples containing the same starting number ## N_0 ## of atoms. One (A) stays on Earth while the other (B) makes a round trip at high speed. When back the traveling sample is more radioactive because its half-life ## \Delta t1/2...
  27. Lluis Olle

    I Twin paradox for (accelerated) dummies?

    Applying the Lorentz transformation to velocity and acceleration, we can easily obtain that Aγ3 = α, where A is the acceleration measured by the stationary observer and α is the proper acceleration of the relative moving object. From this point, the equations for a constant accelerated motion...
  28. BadgerBadger92

    B Grandfather Paradox & Self Consistency Principle: Are They Different?

    https://www.popularmechanics.com/science/a41106690/grandfather-paradox-time-travel/ I’ve been studying the self consistency principle, being the idea in time travel that history (the past) must be conserved. When I read about the grandfather paradox it sounded like the same thing. Are these two...
  29. Lluis Olle

    I Some thoughts about Bell's string paradox alternatives

    Thinking about Bell's string paradox , I understand that if both spaceships maintain the same and constant proper acceleration, the string breaks because of the non-simultaneity of the acceleration effects at both ends of the string. But I want to introduce and consider a slight and subtle...
  30. P

    B Einstein's Twin Paradox: Confusing Solution?

    In Einstein's twin paradox,the solution comes like this: The twin on the spaceship de-accelerates his spaceship first and then accelerates in the reverse direction.This means his reference frame is not inertial hence he doesn't measure greater time interval as the other twin does...
  31. Bolzmann_brain

    I The Bolzmann brain paradox

    Assuming that all of my brain states are equally likely to be BBs, and that BBs may exist somewhere outside the event horizon and I won't know about this аnd also the fact that I am either BB or OO, by memorizing 70,000 digits in this way, it is expected that I have increased my chance that I...
  32. H

    A Is there a lost information paradox for quantum physics?

    Hi Pfs, When Stephen Hawking proposed the idea of black hole information it appeared that information could be lost. it was a problem in GR which is a dererminitic theory. Knowing initial data and Hamiltonian tells you what was and will be. It is not the case in quantum physics. things evolve...
  33. H

    B Twin Paradox (3 objects version)

    Consider 3 objects, A, B, and C, in relative motion along the x direction. EVENT 1 B passes A while moving at a constant v = 3/5c relative to A. Both clocks set to t = 0. EVENT 2 C passes B when B’s clock reads t = 5 while C is moving at a constant v = 3/5c towards (and relative) to A. C’s...
  34. G

    I Paradox: How can we look back at the Big Bang?

    The Webb telescope images show galaxies that are so far away that it takes ages for their light to reach us, so long that we can see galaxies as they were soon after the big bang. How amazing - but hold on. If we came from the big bang, and nothing travels faster than light, how come we are here...
  35. M

    Exploring the Paradox of Life in an Entropic Universe

    Not sure to ask here or in Physics/Cosmology. How could life have begun much less evolve (or even planets form) if according to the 2nd Law of Thermodynamics entropy always increases with time?
  36. E

    B How does the EPR paradox work?

    Hi, I've heard about the EPR paradox as follows: Leave two entangled particles A and B carried by scientists A' and B', with a pair of incompatible properties (eg spin up/down and left/right) in possible Green/Yellow and Blue/Red states. If one measures Yellow state (eg, particle B in spin up...
  37. C

    I Mechanical energy paradox

    Hello everyone! I've been studying work and energy, and one problem I have is understanding conservation of mechanical energy. If on a rollercoaster you have two points A and B you expect the mechanical energy at A to be equal to the mechanical energy at point B, makes sense to me; but I started...
  38. Gamma Anon

    I Is the Killer Crate Paradox Resolved?

    Hi Physics Forums, I've devised a thought experiment called the "Killer Crate Paradox" to put a spotlight on an issue I'm having, with regards to understanding length contraction, specifically in instances where multiple objects are observable and they have different velocities and directions...
  39. G

    A A double slit thought experiment leading to a paradox

    Consider a Double Slits experiment in which the light source is monochromatic and each slit very narrow. There will be many fringes visible on either side of the axis. 1) If the light source is pulsed with very short, randomly spaced, pulses it will produce spectrally broadened radiation and...
  40. R

    I Help me resolve this apparent paradox

    This is the third time I try posting, and the first time after having written an Introduction. I hope it will work this time. Imagine we have a cuboid of mass ##M## and height ##2 r## that slides without friction on a horizontal surface. It is accelerated by a line or rod that is connected to...
  41. Grinkle

    B Why is the BH Information Paradox Called a Paradox?

    We don't have a quantum theory of gravity. To my B level thinking, losing information at the EH of a black hole is just one of multiple known places where QM meets relativity and it becomes clear that our understanding is incomplete. I don't see it as any different than making the same...
  42. W

    B Monty Hall Paradox: Why Does It Matter What Host Knows?

    Suppose you are participating in a game show, and at one point three doors are presented. It's announced that one of them has a car prize behind it and the other two have a goat, and for you to choose one of the doors. After choosing the host opens one of the other doors and reveals a goat, and...
  43. F

    I A paradox for two moving protons?

    Before introducing Special Relativity, a textbook highlights the inconsistency of Maxwell's Electrodynamics and Newtonian Mechanics through the standard discussion about the velocity of light in different frames of reference. A further inconsistency discussed. In some inertial frame of...
  44. Oldman too

    I A new approach to the information Paradox

    Summary: New black hole simulations that incorporate quantum gravity indicate that when a black hole dies, it produces a gravitational shock wave that radiates information, a finding that could solve the information paradox. Hello, Please excuse the rather "conversational" approach I'm using...
  45. wnvl2

    I Relativity paradox: rocket landing in a cylinder

    A rocket has length L with a separate head on top. The rocket lands in a cilinder on Earth with height L with speed v. From the point of view of the rocket, the cylinder undergoes a Lorentz contraction. The rocket will therefore collide with the bottom of the cilinder and damage it. From the...
  46. J

    I Does it make sense to speak about the Grandfather paradox in QM?

    Since QM is not deterministic, the future state B is not determined by the previous state A (at time A, B was only a possibility, not a certainty). Then, when we are at time B, and assuming we could move back in time (of course, we cannot do that, but let us make a Gedankenexperiment), it just...
  47. Lars Krogh-Stea

    B Hilbert's paradox of the Grand Hotel - An easier solution?

    I know the paradox is about a hypotethical hotel with hypotethical guests, how else could new people arrive, when everyone (infinite) is already inside;) But maybe the ones outside are aliens, I don't know.. My real point though, is that there's no need for the intricate shuffeling of guests...
  48. PeterDonis

    I Kinematic Decomposition for "Rod and Hole" Relativity Paradox

    In a recent thread, I said that if there was interest, I would post in a separate thread the calculations for the kinematic decomposition of the congruence of worldlines describing the rod in the "rod and hole" relativity paradox discussed in that thread. Since there was interest, I am posting...
  49. B

    B Loschmidt's paradox and free gas expansion

    Following up on a previous discussion: https://www.physicsforums.com/threads/conservation-of-momentum-in-a-closed-system.1009693/post-6570341 An uncontained system of particles interacting only by elastic collision is the same as a gas undergoing free expansion. If, for simplicity, the...
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