# E not equal to mc squared a possibility?

Discussion in 'Physics & Math' started by Lilalena, Oct 13, 2010.

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1. ### LilalenaRegistered Senior Member

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Has anyone ever come up with a new paradigm that disproved E=mc2? or at least shown that it is not as general as we think?

Thomas Kuhn said the latest paradigm always seems untouchable / indestructible. After a paradigm shift we fall into "puzzle solving" - working on little theories to help refine / further prop up the latest paradigm. Science has more "puzzle solvers" than
The amount of time a paradigm reigns is directly proportional to the amount of careers dependent on it being right. This can mean that we have more reason to uphold a paradigm than to move beyond it.

There seem to be empirical proofs that e=mc^2 but I'm just wondering if anyone can think of another way to look at things.

(Any responses, in laymen's terms please. Im not a mathematician).

Some info from Wikipedia:

Kuhn has made several important contributions to our understanding of the progress of knowledge:

* Science undergoes periodic "paradigm shifts" instead of progressing in a linear and continuous way
* These paradigm shifts open up new approaches to understanding that scientists would never have considered valid before
* Scientists can never divorce their subjective perspective from their work; thus, our comprehension of science can never rely on full "objectivity" - we must account for subjective perspectives as well

Last edited: Oct 13, 2010
2. ### rpennerFully WiredValued Senior Member

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Ah, but a naive reading of Kuhn is not the whole story.

In physical science, we also have the correspondence principle. Since we live in the same universe as our ancestors, if they had a theory that worked any new theory still has to work in the experimental cases where there old theory worked. Each new theory improves accuracy and/or extends the range of the previous theory.

Correspondence is about replacing a throw rug with a larger throw rug which covers at least the same area. Science is progressive and builds on the successes of the past.

Newton described momentum for a massive body as $\vec{p} = m \frac{d\vec{r}}{dt} = m \vec{v}$ which works well with small speeds. Special relativity needs to exactly reproduce the success of Newton for small velocities, and in special relativity, $\vec{p} = m \frac{d (\vec{r})}{d\tau}$ where $\tau$ is the "proper time" as seen by a co-moving clock. So the resulting formula exactly reproduces Newton's formula in the limit of small speeds: $\vec{p} = m \frac{d (\vec{r})}{d\tau} = \frac{m}{\sqrt{1 - \frac{1}{c^2}|\frac{d (\vec{r})}{dt}|^2}} \frac{d (\vec{r})}{dt} = \frac{m \vec{v}}{\sqrt{1 - \frac{|\vec{v}|^2}{c^2}}}$.

Another way to express the above expression, is $E^2 = m^2c^4 + |\vec{p}|^2c^2$ which works not only at reproducing the physics of Newtonian particles at small speed, but captures the Energy-momentum relationship of Maxwell's electromagnetism, and experimental matches results found by every experiment since the dawn of time.

3. ### RJBeeryNatural PhilosopherValued Senior Member

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I love this.
I relish thinking outside of the box, but only when observed data (or some other shortcoming of the existing predominant theory) suggests that I do so. Do you have such a reason for asking the question?

4. ### LilalenaRegistered Senior Member

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e is not equal to mc^2

But what if you wanted to create an opposing paradigm, just as an exercise?
Where would you start? Or what if you wanted to create a sort of "parallel" physics universe, what would be the main differences?

5. ### Green DestinyBannedBanned

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By new, no one cannot disprove what is already proven.

6. ### BWE1Rulers are for measuring.Registered Senior Member

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That misses Kuhn's larger point which is that Paradigms allow science to know what to study. It lets the specializations necessary for advanced science leave the basic arguments as solved, even if only specialists understand them, and work on esoteric areas suggested by the paradigm itself.

Also, at this point, the word paradigm is becoming so tangled due to the dramatically increasing consilience of science that it may not be useful in the same way now that it was then. E doesn't have to equal mc^2 for the modern paradigm anymore.

7. ### przyksquishyValued Senior Member

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E = mc[sup]2[/sup] is not a paradigm. The Special Theory of Relativity is what you might call a paradigm. E = mc[sup]2[/sup] is a prediction of that paradigm.

Depends on the "we". It's only valid for a massive particle at rest (provided we're talking about the invariant mass - see here). It doesn't apply to massless particles (eg. photons). This is well known among physicists, but apparently not so well known if "we" includes the general public, otherwise we'd hear "E = mc[sup]2[/sup], therefore the photon has mass!" a little less often.

Er, evidence?

Nobody lost their job when classical physics and Galilean relativity were overturned. I've never heard of any instance of career dependence on a particular paradigm in physics. If anything, relieving researchers of that particular worry is one of the main arguments given in favour of awarding tenure.

Even physicists' reputations aren't really threatened if paradigms are overturned. For older paradigms such as quantum theory and relativity, the people who established them are dead. Even barring that, well established paradigms in science have, pretty much by definition, survived extensive scrutiny and testing. Even if they turn out to be wrong, the fact they've endured so long puts a lower bound on their usefulness. There's a popular essay by Isaac Asimov that explains this point quite well.

In any case, history has given people such an incentive to overturn paradigms that it seems to have become self-justifying. It was brave of Galileo to suggest ideas that conflicted with the paradigm of his day. That isn't true any more. Nowadays, being seen as a "free thinker" has become fashionable. It's an image people actively pursue for its own sake. Figures like Galileo, Einstein, and Darwin are famous for the revolutions they started, and now everyone wants to mimic that success (in a way, this is screamingly ironic when you think about it). In Einstein's case in particular, many more people know his theory was revolutionary than are actually familiar with the theory. Popular physics is full of this sort of attitude: lots of talk about how weird and revolutionary theories are, with only a few words thrown in about what the theories are actually about.

You also see it in society in general. Just look at the way politicians - who, remember, are aiming to appeal to as much of the voting public as possible - present their campaigns: it's all about how they're going to bring about change. Also look at the language and vocabulary we've developed. Imagine some idea that's generally well accepted - how many ways could you think of casting that in a positive light? Our own linguistic conventions are biased against that: "orthodox", "conventional", "mainstream", "traditional", "established", etc. all carry negative connotations implying blind faith, even though that isn't a necessary part of their definitions. "Well established" is better, but it only works by specifically suggesting the idea is justified in being "established". I suppose "time tested" is also positive, but looks rather odd used in reference to ideas or theories.

Last edited: Oct 14, 2010
8. ### rpennerFully WiredValued Senior Member

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Thanks -- I accidentally overwrote the window where I was writing my reply on this theme.

9. ### RJBeeryNatural PhilosopherValued Senior Member

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Ultrafuture, maybe you're just wondering what life would be like under different circumstances (i.e. different physical constants)?

You might find Smolin's fecund universes interesting. From what I've read, though, even the most subtle change in our fundamental physical constants destroys any viability in that Universe for Life as we know it to develop.

10. ### AlphaNumericFully ionizedModerator

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There are derivations of $E^{2} = m^{2} + p^{2}$ which are logically sound provided their assumptions are true, ie that's what Einstein did. This means that provided the assumptions are true then $E^{2} = m^{2} + p^{2}$ is true and that if $E^{2} = m^{2} + p^{2}$ is not true then neither can all the assumptions be true.

So the question becomes whether or now anyone can demonstrate the assumptions (the speed of light in a vacuum is seen to be the same by all inertial observes and that all inertial frames give equivalent physics) to be true. They cannot be proven true, they can only be tested both directly and indirectly (ie testing $E^{2} = m^{2} + p^{2}$ is an indirect test of them).

For a century now we've been testing $E^{2} = m^{2} + p^{2}$ in many different ways, as it forms the core of both general relativity and quantum field theory, ie our models of the very big and the very small both use it so if its wrong it'll mean they are wrong somewhere. Thus far $E^{2} = m^{2} + p^{2}$ has passed every test to the limits of our ability to test it. This doesn't mean it is correct but that its certainly a very good approximation to how the universe really is.

Sure, someone might come along and propose a new relationship but given we know that $E^{2} = m^{2} + p^{2}$ is very accurate for a great many things it means that whatever the new relationship would be it would have to be almost identical to $E^{2} = m^{2} + p^{2}$ when you consider the experiments we've tested $E^{2} = m^{2} + p^{2}$ in.

For instance, Newtonian mechanics is very good at modelling how a ball moves through the air or a car accelerates and brakes. It is not very good at modelling the dynamics of superfast particles, you have to use special relativity. However when you use special relativity to model how a car accelerates and brakes you find you get pretty much exactly the same answer as Newtonian mechanics, which must happen since we know Newtonian mechanics is very close to right for that thing. In the same way whatever replaces special relativity will say much the same as special relativity in anything but the most extremely of circumstances because special relativity is known to be very accurate in every circumstance we've ever tested it.

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