Postulate and special relativity

[bernhard.rothenstein]

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

 

[malawi_glenn]

the length contraction arises due to Lorentnz-transformation, and Lorentz transformation comes from the two postulates of special relativity.

 

[HallsofIvy]

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

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".

 

[bernhard.rothenstein]

special relativity terminology

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".

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?

 

[HallsofIvy]

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.)

 

[Shooting Star]

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

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.

 

[danime]

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.

 

[Shooting Star]

> 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.

 

[HallsofIvy]

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.

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.

 

[danime]

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.

 

[bernhard.rothenstein]

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?

 

[Shooting Star]

Pauli added a third postulate: provided that the first two do not contradict each tother.

 

[bernhard.rothenstein]

Pauli quotation

Pauli added a third postulate: provided that the first two do not contradict each tother.

Do they?

 

[HallsofIvy]

Pauli added a third postulate: provided that the first two do not contradict each tother.

Do they?

I agree. That would hardly be a "postulate" but a "proviso". Either they do or they don't.

 

[Shooting Star]

Do they?

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

I agree. That would hardly be a "postulate" but a "proviso". Either they do or they don't.

"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."

 

[Shooting Star]

isten up everybody this is unbelivable antimatter origins in space has been discovered
http://news.yahoo.com/s/space/200801...ntimatterfound

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.

 

[Fredrik]

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 statement 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 \mathbb{R}^4, 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.

 

[Fredrik]

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?

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.

 

[danime]

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.

 

[Shooting Star]

I would call them postulates and use them to derive theorems.

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.)

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.

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.

 

[danime]

It's not a matter of agreeing or disagreeing. It's a matter of doing real work and seeing that to create an entire theory you can use already existent theorems or make yours as demanded, some are even physics theorems. But they are just small steps, like a post-it to prevent you of making errors.
Even theorems that are rather abstracts and are real theories like Noether theorem are based on observations or long lasted general assumptions based on observations. It's common to redefine some quantity when some theorem fails too. :)

 

[Fredrik]

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.

This is a bit incoherent, so I'm not sure what your point is. Maybe you were just trying to say what Shooting star said here:

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.

What you're describing here is the process of finding a useful theory. I was talking about the fact that you can't claim to have a theory until you actually have a set of statements that defines it.

My post was in response to the claim that terms such as "postulates" have no place in physics, and in SR in particular. My point was that they do because SR wouldn't be a theory without a rigorous foundation.

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.

I wouldn't have minded saying it to his face, because I know I'm right. I doubt it would have been much of a discussion though.

 

[danime]

What you're describing here is the process of finding a useful theory. I was talking about the fact that you can't claim to have a theory until you actually have a set of statements that defines it.

My post was in response to the claim that terms such as "postulates" have no place in physics, and in SR in particular. My point was that they do because SR wouldn't be a theory without a rigorous foundation.

I think I really missed what you were saying. In principle you are right, though sometimes you cannot define a theory, but just have useful tools that make the body of the theory, once everybody knows what is the theory but cannot put it to the paper as postulates. Very simple theories as SR can be reduced to a few postulates and theorems, but try to make it with condensed matter or hydrodynamics. Even SR is contradictory when it is used as a basis to electrodynamics.

Don't underestimate the capacity of Pauli to destroy your arguments. People like Bohr, Heisenberg, Einstein, Kramers, Feynman, to cite a few have done this and became disarmed in their arguments by Pauli. Pauli was something like an oracle where people shoot their theories to see if it survives. Most of the time the response was a crude "It's foolish".

 

[yuiop]

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?

Interestingly the first postulate was formulated by Galileo in 1639 (over 200 years earlier than Einstein). This postulate could have been rephrased (IMHO) as "It is impossible to carry out any physical measurement that would distinguish one inertial frame from another." In Galileo's time they did not have the technology to measure the speed of light and they were uncertain if the speed of light was finite or infinite. If they had conjectured that the speed of light was finite then they could conceivably have come up with the special theory of relativity using these two postulates:

1. It is impossible to carry out any physical measurement that would distinguish one inertial frame from another.
2. The speed of light is finite.

Having worked out that for the speed of light to be finite, that objects with relative motion would have to length contract, time would dilate and that there is no universal concept of simultaneous time they probably would have decided it was all too bizarre and concluded that the speed of light must be infinite.

 

[Fredrik]

That version of #2 isn't sufficient. You have to postulate that it's the same in all inertial frames, not just finite. (The speed of...anything really, is also finite, but you can't build a theory of relativity around the speed of a flying duck).

Also, that version of #1 has it's difficulties. My computer is stationary in a certain group of inertial frames, and moving in another set of inertial frames. I can obviously do an experiment to determine if my computer is moving or not.

 

[yuiop]

That version of #2 isn't sufficient. You have to postulate that it's the same in all inertial frames, not just finite. (The speed of...anything really, is also finite, but you can't build a theory of relativity around the speed of a flying duck).

Also, that version of #1 has it's difficulties. My computer is stationary in a certain group of inertial frames, and moving in another set of inertial frames. I can obviously do an experiment to determine if my computer is moving or not.

If your pc is stationary with respect to you, an observer moving relative to you could claim he is stationary and both you and your pc are moving relative to him. Neither of you could prove you were in a preferred inertial reference frame.

Perhaps I should try and rephrase the two postulates again to try and exclude ducks (although Galileo did use butterflies and fish in his example).

1) Any measurement of the laws of physics in an inertial reference frame cannot determine the absolute motion of the reference frame.
2) The speed of light is governed by the laws of physics and is finite.

The point I was trying to make is that once you decide the speed of light is determined by the laws of physics (or is a law of physics) and if that speed is finite, it then follows that the speed of lght must be constant to all observers or postulate #1 would be violated.

The first postulate as originally stated by Einstein really went without saying as it it was pretty much an accepted principle of physics ever since Galileo proposed it over 260 years earlier and never shown to be wrong.

 

[Fredrik]

But the laws of physics could say that the speed of light must be 299792458 m/s relative to the light source. Your new #2 only works if we interpret it as implicitly implying that the speed of light is independent of the speed of the light source, and then we might as well say that explicitly. (I wouldn't have interpreted your #2 that way if I didn't already know SR and what you are trying to accomplish).