Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Postulate and special relativity

  1. Jan 11, 2008 #1
    Please tell me if it is correct to state that
    Everithing that is a result of the two postulate can be considered as a postulate. So we can postulate the existence of the length contraction in order to derive the Lorentz-Einstein transformations?
    Thanks
     
  2. jcsd
  3. Jan 11, 2008 #2

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    the lenght contraction arises due to Lorentnz-transformation, and Lorentz transformation comes from the two postulates of special relativity.
     
  4. Jan 11, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I'm not certain exactly what you are asking. Mathematically, a postulate is "given" and anything that "is a result" of one or more postulates is a "theorem", not a "postulate".
     
  5. Jan 11, 2008 #4
    special relativity terminology

    Thank you. So if I consider that the invariance of the space-time interval is an invariant then length contraction and time dilation which are a consequence of it are theorems. Can I say that if we derive the Lorentz-Einstein transformations using one of them, then the derivation is a result of a theorem?
     
  6. Jan 11, 2008 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, that would be theorem. Anything that is derived from some other fact is a theorem.

    (Frankly, I am not comfortable using mathematical or Logical terms in Physics. The "postulates" of relativity are themselves derived from experimental results. They are not "postulates" in the exact sense.)
     
  7. Jan 11, 2008 #6

    Shooting Star

    User Avatar
    Homework Helper

    I may be wrong, but to me it seemed like what you wanted to say was:

    if A and B are postulates, and A AND B together implies C, then can we treat C itself as a postulate? The answer is no, because C need not imply A and B individually. This is basic logic, nothing to do with Physics.
     
  8. Jan 15, 2008 #7
    In physics does not make sense to concern with postulates and theorems. There are experimental facts valid within certain conditions and consequences that makes the body of theory.
    The experimental facts may be invalid in other conditions.
    They are not postulates, first because they are not postulated, but observed.

    Also, the derivations of the experimental facts are not theorems, because they can contradict the original facts and be logically correct. Example: The Abraham-Lorentz force are not trully causal but can be derived from the coulomb force and the relativity which is itself causal.
     
  9. Jan 15, 2008 #8

    Shooting Star

    User Avatar
    Homework Helper

    > They are not postulates, first because they are not postulated, but observed.

    One of the very first "postulates" I came across in school was Avogadro's Postulate, stating that equal volumes of gases contain equal number of molecules.

    What had been "observed" at that time -- the molecules? They were not even universally believed in at that time.
     
  10. Jan 15, 2008 #9

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Very true. However, the next part of physics, after observing the experimental results, is to draw logical conclusions from those observations- that is the part of physics that uses mathematics. It is common to accept the experimental results as "postulates" in the mathematical sense in order to do that.

    Notice that "postulates" is in quotes. See my previous post.
     
  11. Jan 15, 2008 #10
    It's interesting to cite Hamilton. In the first of series of papers in which he begun to make the optical-mechanical analogy and defines his principal function, related to the action function, and the W function, related to the hamiltonian, he says that the evolution of science as the quest of understanding the nature begins with the observation of facts, a deductive process. As long as we can see related things we can use the inductive process to imagine a theory correlating the things and then make predictions and make new experiments to test the theory.

    We just expand our capacity to make previsions. We never understand anything and our theories are just methods to make previsions within certain scope. Mathematics is useful as long as it's the ideal tool to deal with patterns and we only try to correlate patterned observations. Those which don't seem to fit in the patterns we are used to or cannot be promptly reproduced are ignored. So a huge mass of observed things are ignored or not useful.
     
  12. Jan 15, 2008 #11
    Thanks to all. Would be correct to start teaching special relativity as:
    Accept the following facts
    1. The laws of physics are the same in all inertial reference frames
    2. The speed of light is the same in all inertial reference frames,
    in order to obtain results in accordance with special relativity theory
    without mentioning concepts like postulate or theorem?
     
  13. Jan 15, 2008 #12

    Shooting Star

    User Avatar
    Homework Helper

    Pauli added a third postulate: provided that the first two do not contradict each tother.
     
  14. Jan 16, 2008 #13
    Pauli quotation

    Do they?
     
  15. Jan 16, 2008 #14

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I agree. That would hardly be a "postulate" but a "proviso". Either they do or they don't.
     
  16. Jan 16, 2008 #15

    Shooting Star

    User Avatar
    Homework Helper

    As of today, the majority of scientists believe they do not. :smile:

    "Proviso" is a much better term. I don't remember who mentioned the word "postulate", but he was a big shot. Pauli had said something to the effect that behind the two postulates, there lies the "tacit assumption of the third postulate."
     
  17. Jan 16, 2008 #16

    Shooting Star

    User Avatar
    Homework Helper

    First of all, the link cannot be followed, but there's a way to fix it, which I don't know. Perhaps a mentor will help.

    Secondly, why is this link given in this thread, and that too quoting HallsofIvy? Please start a new thread.
     
  18. Jan 17, 2008 #17

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I disagree with the attitude towards postulates in physics that some posters have expressed in this thread. Every theory of physics needs a set of unambiguous statements that defines the theory, just as "group theory" (mathematics) needs the definition of a group. Those statements are the theory's postulates. I don't care if we call them "postulates" or "definitions" or something else, but it's ridiculous to say that we shouldn't concern ourselves with these things. No matter what we call them, they are the starting point of the theory, and everything that the theory says can be derived from them. So of course it's important to make sure that they really are unambiguous and consistent.

    Einstein's postulates were most certainly not experimental facts. Yes, they had some experimental support, but it's not like someone had proved that they were true. They are assumptions that attempt to define the theory. From a mathematical point of view, they do a terrible job, because they contain hidden assumptions and use terms that need to be rigorously defined to make sense (in particular "inertial frame").

    Because of that, there may be a way to interpret them as contradictory statements. I don't know if there is, but I do know that there's also a way to interpret them as statements that certainly aren't. Those statements (together) are equivalent to this one:

    "Space and time can be represented mathematically by Minkowski space"

    This is the only "postulate" (or whatever you prefer to call it) that's needed. It's the statment that defines what special relativity is.

    Now, about the "proviso" that the postulates must not contradict each other... I have spent some time thinking about what the hidden assumptions are and how to define an inertial frame without explicitly mentioning the Minkowski metric, and I believe that the definition of an inertial frame must look something like this:

    "A inertial frame is a member of the only subgroup of the group of all global coordinate systems on the set of space-time events M, that map straight lines to straight lines and is consistent with Einstein's postulates"

    I guess if we try to represent M with something other than [itex]\mathbb{R}^4[/itex], this group might not exist or not be unique. So the "proviso" can be thought of as a guideline to follow when we attempt to make the postulates rigorous. However, it's so absurdly obvious that it makes no sense to even mention it.
     
  19. Jan 17, 2008 #18

    Fredrik

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I would call them postulates and use them to derive theorems. But I would also explain the problems, and show how to turn them into unambigous mathematical statements. If you are unable to do that, there's another perfectly valid approach, which is probably more appropriate for less advanced students anyway:

    1. Show them Einstein's postulates. Explain how the first one was motivated by Newtonian mechanics and the second by the Michelson-Morley experiment and Maxwell's equations. Also admit that they aren't very good from a mathematical point of view.

    2. Use them to "derive" the Lorentz transformation non-rigorously. Skip every step that is difficult, if you can motivate it by saying that "it seems reasonable to guess that this is correct". (In particular, you don't try to prove that homogeneous Lorentz transformations must be linear. Just guess that they are).

    3. When you finally arrive at the Minkowski metric, you explain that now we are able to guess that the entire content of the theory can be stated like this: "Space and time can be represented mathematically by Minkowski space".

    4. Explain that it's completely irrelevant that we used sloppy proofs to get to this point, because we were just trying to find a good way to define the theory properly. Now that we have a definition, i.e. now that we actually have a theory (which we didn't before), it's up to the experimentalists to determine how well it approximates nature.
     
    Last edited: Jan 17, 2008
  20. Jan 17, 2008 #19
    My position is that if you think you can do physics by postulating and deriving logical conclusions as theorems and make this a theory you have never done physics.
    There are so much possibilities that are cut by the experimental facts you cannot create nothing just by bare logic. Einstein already known what he was trying to do. The postulates are just a synthetic expression of a lot of things he learned.
    It's interesting to point that the great majority of Einstein's though experiments leaded him to wrong conclusions. The ones those became famous due to its correctness were based on experimental facts.
    One could say that in mathematics you have postulates and try to find the consequences and in physics you have the consequences and try to find the postulates. But the reality is that even in mathematics the majority of theorems had begun with the both the postulates and the conclusions lefting the work of create the connections. If you don't know this you have never done mathematics too.
     
  21. Jan 17, 2008 #20

    Shooting Star

    User Avatar
    Homework Helper

    I think the postulates of Physics can be treated exactly like the axioms of Mathematics, with the terms to be used defined as clearly as possible, until the predictions run into trouble. Then new ones have to be made. The making of a postulate takes a long, long time and several years of experiments or thinking.

    (Sorry, don't have time now. Will discuss later.)

    I would have loved to see you saying that to Pauli's face. He used shred up other physicists for things like this. Mincemeat man, mincemeat. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Postulate and special relativity
Loading...