# Counter-intuitive phenomena in math and physics

#### jedson303

##### New member

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#### Ackbach

##### Indicium Physicus
Staff member
Re: Cheap tricks

OK, Opaig. I see how that works. It does connect. Thanks.

I would have handled those two particular examples differently, the one from the other. That a negative times a negative equals a positive comes from what a negative is. The negative of a number is the thing you must add to the number in order to get zero. So the negative of $5$ is $-5$, because $-5+5=0$. So what is the negative of a negative number? It's the thing you must add to the negative number to get zero. What must I add to $-5$ in order to get zero? Answer: $5$. Therefore, $-(-5)=5$. So there is a logical explanation of this property in terms of more fundamental concepts.

However, that the speed of light is independent of the velocity of its source is one of the assumptions you must make in special relativity. So the "why" question is answered as, "It's an axiom or postulate, like the Euclidean idea that through any point not on a given straight line is only one line that does not intersect with the given line." You must assume the speed of light postulate. Now, if someone asks why you assume the speed of light postulate, I would reply that doing so yields predictions that are closer to the outcomes of experiments than other conflicting assumptions (such as Galilean relativity).

My two cents.

#### Opalg

##### MHB Oldtimer
Staff member
Re: Cheap tricks

However, that the speed of light is independent of the velocity of its source is one of the assumptions you must make in special relativity. So the "why" question is answered as, "It's an axiom or postulate, like the Euclidean idea that through any point not on a given straight line is only one line that does not intersect with the given line." You must assume the speed of light postulate. Now, if someone asks why you assume the speed of light postulate, I would reply that doing so yields predictions that are closer to the outcomes of experiments than other conflicting assumptions (such as Galilean relativity).
I am not a physicist, but I would put that a bit differently. Physics is different from mathematics in that it is founded on experiment. When the experiments of Michelson and Morley in the 1880s showed that there was no measurable effect on the speed of light by the velocity of its source, it must have seemed as mystifying to the scientific community as it did to the OP. It was only when Einstein put this peculiar phenomenon into a coherent theoretical framework that people were able to feel comfortable about it.

#### topsquark

##### Well-known member
MHB Math Helper
Re: Cheap tricks

I am not a physicist, but I would put that a bit differently. Physics is different from mathematics in that it is founded on experiment. When the experiments of Michelson and Morley in the 1880s showed that there was no measurable effect on the speed of light by the velocity of its source, it must have seemed as mystifying to the scientific community as it did to the OP. It was only when Einstein put this peculiar phenomenon into a coherent theoretical framework that people were able to feel comfortable about it.
A quick comment from the peanut gallery about Special Relativity. There was a severe problem when the Maxwell equations were written down: They do not obey Galilean relativity...that is velocities do not add. Lorentz took up the problem and stated that EM obeys a different set of transformations where again the velocities did not add.

Einstein's genius was to assume the Lorentz equations also held for Mechanics (and everything else!) Great work, but no one seems to remember Lorentz for his contribution.

-Dan

#### Opalg

##### MHB Oldtimer
Staff member
Re: Cheap tricks

A quick comment from the peanut gallery about Special Relativity. There was a severe problem when the Maxwell equations were written down: They do not obey Galilean relativity...that is velocities do not add. Lorentz took up the problem and stated that EM obeys a different set of transformations where again the velocities did not add.

Einstein's genius was to assume the Lorentz equations also held for Mechanics (and everything else!) Great work, but no one seems to remember Lorentz for his contribution.

-Dan
I am sure that Lorentz played a vital part in paving the way for Einstein, and I have even more admiration for the genius of James Clark Maxwell (Scotland's greatest-ever physicist, in my opinion) in daring to formulate equations that were inconsistent with the classical understanding of how velocities combine.

#### MarkFL

Staff member
Re: Cheap tricks

I see Maxwell as having made the first significant step in the unification of the forces of nature. I truly hope to see this project completed in my lifetime.

#### topsquark

##### Well-known member
MHB Math Helper
Re: Cheap tricks

I see Maxwell as having made the first significant step in the unification of the forces of nature. I truly hope to see this project completed in my lifetime.
Well we've got electo-weak theory (EM + weak nuclear force) reasonably pinned down now we've at least got a good idea about Strong-electroweak. Well, okay, there are several of these. But they all share many common traits at least.

So much for the GUT's. As far as getting gravity in there, again there are a number of theories that are in the running. And we still don't have a good theory of quantum gravity so we're kind of stymied when trying for a TOE. Gravity is going to take a while.

Although Doctor Michio Kaku and some others are acting like string theory is the answer. However they are still ignoring that we don't have any data to support it....

-Dan

#### topsquark

##### Well-known member
MHB Math Helper
Re: Cheap tricks

Ummmm... I just realized I managed to hi-jack the thread. Sorry about that!

-Dan