An axiom, postulate or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning.As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (A and B) implies A), while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic).
When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In most cases, a non-logical axiom is simply a formal logical expression used in deduction to build a mathematical theory, and might or might not be self-evident in nature (e.g., parallel postulate in Euclidean geometry). To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms), and there may be multiple ways to axiomatize a given mathematical domain.
Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics.
The LT can be derived from the first postulate of SR, assuming linearity an that velocity composition is commutative, and that GT can be excluded: ##t' \neq t##.
Definition of the constant velocity ##v##:
##x' = 0 \Rightarrow x-vt=0\ \ \ \ \ \ ##(1)
With assumed linearity follows for the...
I was reading about thermodynamics postulates when i came over the differnetial fundamental equation:
I understand that the second element is just pressure and last element is chemical energy, but he problem is i don't understand what is the use of entropy and how does it contribute to a...
Has there been so far any prediction validated in experimental outcomes that these theories make as a result of the modification of the Schrodinger equation?
Would the second postulate (The speed of light in free space has the same value c in all inertial reference frames.)be also true if it was in some medium instead of in free space? I know the value won't be c anymore but I want to know whether the speed of light in that medium would be the same...
What is the physical and mathmatical meaning, of the metaphorical action of 'looking out of the window' or 'not looking out of the window', of a ship, a starship, a train, an elevator or any other vehicle, in postulates such Galilean postulate and SR 1st postulate and in GR weak and strong...
So I was watching one of Susskind's lecture on Youtube* and about the 37:00 mark he has this equation relating the frequency of a matter wave to its wavelength:
$$\nu = \frac{h}{2m\lambda^2}.$$
This is arrived at by assuming that matter has a wavelike nature and that the energy and momentum...
I'm trying my hand at deriving Lorentz transformations using 3 postulates - it's a linear transformation, the frames are equivalent, so they see the same speed of each other's origins and that the speed of light is the same. Let's say frame ##S## is moving at velocity ##v## in the...
A postulate is a statement that is taken to be true, to serve as a premise or starting point for further theories.
(e.g. Bohr's postulates)
Hypothesis is a theory which can after testing be accepted or rejected. But a postulate is something that is assumed to be true without proof.
Among other...
This is a basic assumption that's made during the derivation of results of special theory of relativity is that space is homogeneous i.e. space intervals shouldn't be given preference based on our choice of origin. However I want to understand more about this assumption and its importance...
Hi guys,
A real easy one. Are the following postulates completely true about general relativity as they are pretty amazing to me.
1) Black holes are a solution to his field equations for GR (or are predicted by the theory)
2) His field equations also suggested the universe was expanding
3)...
Why can't we prove euclids fifth postulate
What's wrong in this proof:
why can't we prove that there is only one line which passes through a single point which is parallel to a line.
If we can prove that two lines are parallel by proving that the alternate angles of a transverse passing...
For example, Brian Greene says in The Elegant Universe regarding special relativity and train moving with constant velocity relative to platform: By the principle of relativity or first postulate, "there is no way for an observer on this train to detect any influence of the train's motion. But...
Homework Statement
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List two postulates of special relativity and then in your own words explain how these two statements are synthesized in Einstein's theory.
Homework Equations
1. The laws of physics are the same in all inertial reference frames.
2. Light propagates through a vacuum...
My text of physics, Gettys's, proves that the magnetic field on the axis of a solenoid, in whose loops, of linear density ##n## (i.e. there are ##n## loops per length unit), a current of intensity ##I## flows, has the same direction as the loops' moment of magnetic dipole and magnitude ##\mu_0...
For quite a long time now I'm having some trouble to bridge the gap between two different approaches to Special Relativity.
The first approach is the traditional one. It is the approach that Einstein presented in his paper and that is taught in most of the basic textbooks. In this approach...
So I'm taking a course in QM right now and would like some clarifications on the postulates of QM, mainly I'm looking for physical intuition and may be for someone to clear some misconceptions if I have any, so without further ado let's begin:
first I'd like to state the postulates as I'm...
Does the constancy of the speed of light for all observers naturally emerge from the Minkowski spacetime metric?
Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric?
Suppose we begin with Minkowski spacetime and the Minkoswki metric...
I know STR is based on two postulates viz.
1.All laws of physics are equally valid in all inertial frames of reference i.e There is no such experiment one can perform to know whether he is moving or not if he is in an inertial frame of reference.
2.The speed of light is constant(3*10^8 m/s...
In Herbert Callen's text 'Thermodynamics and an introduction to thermostatistics' 2nd edition, he introduces four postulates of thermodynamics in the first chapter. The third postulate incorporates an 'additivity property' which is stated as 'The entropy of a composite system is additive over...
Is it possible that there is a set of postulates (or statements) whose logical implications imply the quantum nature of our Universe, the postulates of quantum mechanics?
Could there be more than one set?
Thanks for any help!
In this above image you can see that, The Galilean transformation for t=t' was rejected by Einstein and then again in Einstein 2nd postulates it was written"Velocity of Light is independent on inertial frame i.e it could be the same from all inertial frame"
So how can something is rejected and...
I think postulates of Relativity is related to Inertial frames. As according to postulates "1)The laws of physics, including electromagnetism, are the same in all inertial frames. 2)Every observer measures the same value c for the speed of light (in vacuum) in all inertial frames. "
But in the...
I am trying to find the basic list of postulates that lay the foundation for QM, but i see a different list of postulates in different textbooks and different places.
In MIT lectures, Prof Allan Adams gives 3 basic postulates: 1. State of a system given by Wave function. 2. Mod squared psi gives...
In the book, 'Scale Relativity and Fractal Space-Time: A New Approach to Unifying Relativity and Quantum Mechanics', the author, Laurent Nottale, makes a few interesting comments in the introduction of his book which seems a bit unclear to me.
In the general introduction of the book, Nottale...
There are certain conclusions that can be explained by quantum physics about the photoelectric effect:
1) photoelectrons only emitted if frequency>threshold frequency and hence energy of photon> work function
2)Increasing intensity increases no. of photons (and thus photoelectrons provided f>f0...
The speed of light is constant in all inertial frames of reference
Imagine a thought experiment, an observer at rest sending a light pulse towards a spaceship, he measures the speed of light to be 3x10^8 m/s, now assume that the spaceship also travels at the speed of light and an astronaut in...
Show that the operators x^2 p_x^2+p_x^2 x^2 and 〖 (xp_x+p_x x)〗^2/2 differ only by terms of order ℏ^2.
The attempt at a solution is attached (Postulates.pdf)
Homework Statement
Consider relationship for a thermodynamic system:
S=A[UVN]^d , where A is a constant and d a real number.
I need to explain why d=1/3 is the only allowed value consistent with the postulates of thermodynamics.
The Attempt at a Solution
I'm having a hard time...
I find the fundamental postulates of QM very ad-hoc and strange.
Compare them to the fundamental postulates of special relativity, special relativity naturally arises out of classical electromagnetism and the equivalence of all inertial frames, while QM seems to come out of nowhere.
Is it ok to formulate the postulates of SR like so:
1) If two reference frames are in a constant rectilinear motion relative to one another, then the laws of physics take the same form in both of them.
2) If two reference frames are in a constant rectilinear motion relative to one another...
Hello
Some authors claim that Einstein's second postulate (constant speed of light) simply emerges from the first one (or more precisely, its converse contradicts the first postulate).
Serway Modern Physics:
Now, is that true? And if yes, what's so special about light than other object (ex...
I've been reading up on gauge theory and it isn't easy. Can someone give me an easy summary of its fundamental scope and postulates without too much math. It seems really important insofar as it defines itself as something of a "parent" theory to most of the leading cosmological models of the...
can someone please explain "Postulates of Classical Statistical Mechanics" , "priori probability" , "equilibrium" ..i m a post graduatation student .and in physics these chapters are seem very difficult i need some step by step explanation ..
If we know the exact radius of a circle, then we can't have an exact circumference, and if we know the exact circumference, then we can't know the exact radius.
If these postulates are true, then I realize that this idea is not original but probably known since B.C.
I've spent a good part of the day looking for a post by one of the members which appeared 3 or 4 years ago and which was linked to every so often by other members. The list had about 10 items in it, one of which was the triangle inequality theorem. IIRC the poster said that he/ she referred...
According to the first postulate of Special Relativity, all the laws of physics are symmetrical in all inertial frames. So that also means that Maxwell's equations are true in any such frame (experimentally verified). Now we can easily uncouple the four first-order differential equations in free...
I like the way quantum mechanics can be expressed as a set of five or six axioms, like in Daniel T. Gillespie's A Quantum Mechanics Primer or David McMahon's Quantum Mechanics Demystified.
Is there a similar set of axioms for quantum field theory?
Homework Statement
Consider the fundamental equation S = AUnVmNr where A is a positive constant. Evaluate the permissible values of the three constants n, m, and r if the fundamental equation is to satisfy the thermodynamic postulates and if, in addition, we wish to have P increase with U/V...
Peano's Postulates 1889 – In Original Italian
Nel 1889 pubblica Arithmetices Principia nova methodo exposita opera, tutta in latino, famosa in tutto il mondo: la teoria dei numeri naturali si sviluppa a partire da cinque semplici proprietà (gli assiomi di Peano):
I. Uno è un numero...
I read that the form of a galilean transformation on the point (t,x) is the following:
constant velocity transform by velocity v: (t,x) ---> (t,x+vt)
translation transform by (t0,x0): (t,x)--->(t+t0,x+x0)
rotation transformation by rotation matrix R: (t,x)--->(t,Rx)
and that it is based...
Hey i was just wondering where Einstein got the idea for his postulates of the speed of light being the same in all reference frames and that there is no preferred frame.
These are really postulates of physics in general, but is aimed mostly toward the dynamics of space and time and of motion, specifically to that which is necessary to derive Special Relativity. This is not a theory, but a collection of postulates which serve as the foundation of many such...
As we know very famous equation E= mc2
While deriving this equation there are two postulates
Postulate I:
The laws of physics are the same in same in all inertial frames.
Postulate II:
The speed of light (in a vacuum) has the same constant value c in all inertial frames.
If we...
Out of curiosity, I was recently reading through Euclid's Elements online (http://aleph0.clarku.edu/~djoyce/java/elements/elements.html" )
My question is, is this the general opinion of all mathematicians? Also, has anyone tried to fix this problem, and how many more postulates would they...
I have now understood special Relativity and now going to study quantum mechanics. But I am having hard time to understand the proofs of different phenomenas like barrier tunneling. I am also not understanding the wave function and the de-Broglie waves.
So please anyone here could list me what...
I am interested to see a clear enumeration of the postulates of this interpretation. There seem to be something fuzzy about how MWI describes what we call "reality". It might be a problem with the theory or, more probable, a misunderstanding of my part.
Here is a list I found on Google...
Imagine a thought experiment: A is conducting a classical mechanics experiment (e.g. bouncing a ball on the table) and B is moving relative to A at speed so great that the table of A is contracted to the size of an atom. According to the postulates of special relativity, the physics of A and B...