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".
I understand Olbers' Paradox and its resolution, however such phrases as this - "If the universe extends infinitely, then eventually if we look out into the night sky, we should be able to see a star in any direction, even if the star is really far away" - which can be found...
I'm reading Chapter 5.3b in Wald's "General Relativity".
(i) On p105, it says that if the integral t=\int \frac{d \tau}{a(\tau)} converges, the Robertson Walker will be conformally related to a section of Minkowski spacetime above a t=constant hypersurface. This makes sense to me...it's kind...
Hi
Do any of you guys know what equations or formulas I should be using for questions like "If A is on Earth and B is an Astronaut traveling near the speed of light". Calculate the duration of B's journey to A and the duration of B's journey according to B.
I assume that B's time...
This question concerns a paradox I've come up with in GR. If somebody could tell me where it breaks down, I'd be much obliged. Thank you!
Assume there is spaceship A hovering above a black hole, and spaceship B further away from a black hole The black hole, A, and B are all lined up. (The...
I've been reading a little bit into mathematical paradoxes lately, and I'm not sure what to make of Bertrand's paradox (regarding the extraordinary set R). I understand the proof, but does this paradox extend to other areas of thought (on that note, this question might belong in the philosophy...
can anyone answer this one?
The baseball series has 4 teams in it and two are from los angeles. What are the chances of a Los Angeles team making it to the world series, at first I said simple. 50% but is this true? The dodgers are playing Philly, and in theory Philly has a 50% chance of...
Homework Statement
Explain why the noise power across a resistor in thermal equilibrium is limited in contradiction to the formula for the noise V_{RMS} = \sqrt{4RkT\Delta f}
which states that if we measure with infinite bandwidth we have infinitely large power
Homework Equations...
hi there
I am confused by the following setting on special relativity:
Suppose there are 4 people, say A, B, C and D, in the deepest vacuum - essentially no gravity or any force at all. Suppose further that all move in one-dimension with constant velocities - A moves towards west with 0.8c...
Differential geometry (which includes general relativity) often introduces the length differential, expressed as ds2=gabdxadxb, to introduce the covariant form of the metric tensor gab. However, this formulation scales ds2 incorrectly. The appearance of an index as a superscript, as in dxa...
Homework Statement
A 30 year old femal astronaut leaves her newborn child on Earth and goes on a round-trip voyage at a star that is 40 light-years away in a spaceship traveling at 0.90 c. What will be the ages of the astronaut and her son when she returns?
Homework Equations
t = to / {1...
I'm also working on this other question, which I think my instructor has a paradox in his algebra for lack of what to call it.
Can anyone suggest a logical way to answer this question?
Homework Statement
http://media.wiley.com/product_data/excerpt/19/04717580/0471758019.pdf
See problem #43 on...
We have two clocks, A and B. B is moving with constant velocity with respect to A. From the reference frame of A, B is running slow. From the reference frame of B, A is running slow. Why is this not a paradox?
Russels paradox says that the set of all sets not contained in themselves, i.e.
x=\{ y \ : \ y \not \in y \}
neither is or is not contained in itself. The set can be created based on an axiom saying that
"The set of objects with a property Q exists".
Let`s assume Q : "Is not contained within...
I read many threads in this forum (in QM section), and in many cases I witnessed the same logical flaw over and over again. People conclude that, for example, if world is deterministic, than there is no free will, because our consciousness is deterministic too. Why? Because our brain is nothing...
For a body of
m=1kg, v=0.1c, and rotating with r=1m, lorentz factor =1/0.99
the centripetal force is (c^2 *10^-2)/0.99 N
This force creates enough stress in the body to break it apart
This effect reduces at values of r comparable to c^2 which again is purely fictitious like the "superluminal...
1.
{This paradox denotes the fact that a satellite in a near circular orbit suffers an increase in velocity when subject to a drag force.}
The Specific energy of the satellite is K + U = E where K =v^2/2 is specific kinetic energy. U= -u/r is specific energy and E is specific total energy. If...
Some time ago someone introduced me to the following scenario.
Imagine you ship loads of oil rig pipes into space, and you assemble them to a length of many kilometers, and you start that long pipe spinning on its long axis. You add vibration damping, to get rid of any transverse, longitudinal...
Hi guys, I have a question regarding the Gibbs paradox. Let's say we take a container A of helium gas and place it next to another container B also containing helium gas at the same temperature and pressure. When we remove the partition (wall) between them, what happens?
If we use classical...
Modified Car and ditch paradox!
Suppose there is a car moving on a road in relativistic speed. The road has a ditch (hole) which is litter bigger than the car when both are at rest.
Modification: Assume that the car will fall on the ditch if all of its tyres are in the air at the same...
How exactly to calculate the age difference in "Twin paradox"
In so much of the text I have seen the "twin paradox" is resolved by simply showing how the condition is asymmetrical, they make no calculation on how this asymmetry results in age difference. I have seen some claiming that its...
Lets look at two mind experiments.
Experiment 1.
We generate pair of entangle photons in opposite polarization states.
At Alice's wing we have polarizer with polarization axis oriented vertically and detector that registers "clicks".
At Bob's wing we have the same setup - polarizer with...
There is a rod treating as rigid body, the rod which mass is m and lenghth is R rotate about one end of itself with the angular acceleration \alpha . Apply a tangential external force f on another end to make the rod rotate. Now divide the rod into elements of mass. For each mass element dm with...
Einstein, champion of the incompleteness of quantum mechanics, wrote a letter to Schrodinger describing a situation where gunpowder is in a half-exploded half-stable state. This was a reductio ad absurdum argument for the incompleteness of QM, since, according to Einstein, "in reality there is...
What is the resolution of the black hole information paradox?
According to quantum theory, information — whether it describes the velocity of a particle or the precise manner in which ink marks or pixels are arranged on a document — cannot disappear from the universe. But the physicists Kip...
A/to special relativity if one is moving faster, he sees that the clocks w.r.t which he is having relative motion are ticking faster.It increases my curiosity to know what would an observer w.r.t whom the person is having relative motion see, if he observes the
watch of the traveller.Will he...
You all have heard of the paradox whereas when you travel to the past and kill your grandfather you should not have existed in the presence whatsoever because you have killed your origins. So far so good...but I thought of another case, which I believe is more interesting since so far the...
I already posted about this under a different thread (Time dilation for clock thrown up and caught back) but, after reading some of the replies, figured that that was not the right way of attacking my real problem, which is figuring out what happens to time during a Big Crunch. So I will restate...
Bell's spaceship paradox --- reversed
The "[URL was discussed already https://www.physicsforums.com/showthread.php?t=236681", but I would like to add a twist. I take for granted, that the thread breaks, as described by Bell himself.
Suppose the experiment starts out with a bit of slack on...
Curry's paradox can be used to (dis)prove the riemann hypothesis and string theory, and even prove the (non)existence of God... no, actually, Curry's paradox IS God. :biggrin:
Just kidding... I am now (speaking somewhat hyperbolically) freaked out. Does Curry's paradox go like this (try "1 =...
Take two uncharged particles (e.g., neutrons) at rest with respect to one another in empty space. Now apply 1 Joule of energy to accelerating them apart. They will eventually come again to rest with 1 Joule of gravitational potential and accelerate back together due to gravity. Their kinetic...
Can someone explain how Hardy's Paradox is resolved? As well, what could someone infer from this regarding both Copenhagen Interpretation and Bohm's theory?
I have thought of an interesting property of time travel based on Novikov's self-consistency principle. I'm sure it's not wholly original, but if someone has heard of it before, I'd really like to know the name given to it so I can research it:
If you find yourself next to a future version of...
I heard some scientists say special relativity may not be relative to your frame of reference, but rather possibly distant galaxies or great sources of gravity?
I heard they sent a jet around the world with an atomic clock, and also decaying sub atomic particles down a tube, to test special...
Hi, all,
Let's say we deploy some random points on a line of finite length according to a poisson distribution of density \lambda. Can I say that these points are also "uniformly" distributed on the same line?
thks
I am new to the forums so hello everyone.
I have spent time trying to understand the twin paradox, and I have only partially grasped it.
What I specifically don't grasp is...what really happens when the traveler changes inertial frames from leaving Earth to heading towards Earth? I know...
Please see if you can resolve the following relativistic paradox for me.
Capacitor is being charged at rest and accelerated to relativistic velocity.
If we turn capacitor plates perpendicular to the direction of motion, width of dielectric contracts and amount of energy, stored in the...
Einstein once upon a time said that the faster you go the slower time goes.
Speed is Distance/Time.
If Time goes slower as a cause of speed, then the Time variable would be smaller and thus the speed greater. This would cause an infinite acceleration as more speed would cause the time to...
Homework Statement
The Pole and Barn Paradox
Suppose a very fast runner (v=0.600c) holding a long horizontal pole runs through a barn that is open at both ends. The length of the pole (in its rest frame) is 6.00m, and the length of the barn (in its rest frame) is 5.00m. In the barn's...
Well first hello, I'm not really into physics, learning computer science at uni atm. However wanted to get something off my mind.
Was browsing wikipedia a while ago and came across Hilbert's Paradox, the idea that a hotel with infinite rooms that are all full can still accept new guests by...
I've been doing quite a bit of reading on the Klein Paradox, though I have to admit a lot of the math goes over my head. So I was hoping you guys at PF could clarify a few things and help me check my conceptual understanding so far.
I found this post...
Can somehow confirm that my understanding of the EPR Paradox is correct. Here goes...
Essentially you can entangle two photons, and send them in opposite directions. If we detect one of the photons, we can find out its properties, and since the properties of the two photons are linked, also...
I need someone to resolve this paradox for me.
Before I start, here are the basic ideas:
Okay, so every moving particle has a DeBroglie wavelength: E=hc/\lambda.
This also means that each particle has a frequency: E=hf
So it also has a period: E=h/\tau
So any given mass has a DeBroglie...
Gas Flow into Vacuum Paradox ??
Hi,
I've just been reading up on 1-D isentropic, compressible flow through a nozzle (constant cross-sectional area) and have hit a bit of a conceptual road block which I was hoping someone would help resolve.
I'm interested in the mass flow rate of the gas...
Hello,
I was reading about Faradays rotating disk paradox wherein when both the copper disk and magnet are rotated together an eddy current is induced along the radius of the copper disk. My question is if a maganitized steel disk (with one side being the N pole and the other side...
Hi,
I am little bit lost in what is so called EPR paradox (see also http://en.wikipedia.org/wiki/EPR_paradox). It takes into account two particles A and B that have some "same" characteristics (states) and by messuring some of this characteristics of particle A implies that the same...
In the twin paradox, the twin that experiences the most acceleration does not age as much. If I synchronize two digital watches, then put one in a centrifuge for a long time, one watch will experience much more acceleration than the other. If they remain synchronized, why is the acceleration...
Hello All,
I have been challenged by a friend to look into Gravitational waves and some questions he has about them -- but I have always been a slow starter. Took physics with SR in college, got my BSEE, happily can build analog circuitry of all kinds -- but found that certain questions about...
The hydrogen atom 1s wave function is a maximum at r = 0. But the 1s radial probability density, peaks at r = Bohr radius and is zero at r = 0. can someone explain this paradox?
Hi all, I'm new here, I was on another forum asking this question but there was a lack of a response, so I hope you guys can help me out!
Ok, so after a few weeks of grappling with the twin paradox, I finally accept that the twin that travels on the rocket and back is the one that ages less...