# Why do mass, time and length change at a rate determined by Gamma?

1. Oct 7, 2011

### Dappy

In the commonly used light clock concept, where a photon bounces back and forth between 2 mirrors, it is easy to see how gamma works. Gamma is simply the factor of increase in the distance that the photon has to travel between mirrors. We can fully comprehend why time slows down at the rate that it doe's for the light clock.

Are there any known explanations as to why gamma can be used to determine the rate of change in time generally, mass and length in the direction of motion?

Real things happen in real ways. Simply knowing a rate of change is not enough. Surely the next questions should be "Why do things change at this rate"? And "What does this tell us about what is really going on at the most fundamental level of physical reality"?

2. Oct 7, 2011

### Matterwave

When Lorentz and Fitzgerald wrote down the Lorentz contraction, and when Lorentz created the Lorentz transformation, they asked themselves these same questions. Then a man named Einstein answered those questions. The known explanation is Special Relativity.

3. Oct 7, 2011

### elfmotat

Because of the priciple of relativity all clocks must slow in the same proportion, or else we'd be able to compare the time reading on one clock to that of another and be able calculate some velocity attributed to that time difference. Thus if you capculate the time dilation factor for a light clock, you have also done so for every other possible clock, including biological processes like how long you live, etc.

If you know how to work out the time dilation formula, figuring out length contration from there should benpretty straightforward. Figuring out the relativistic mass formula might be a bit trickier - most derivations I've seen involve analyzing collisions and conservation of momentum.

4. Oct 7, 2011

### Dappy

In the light clock example it is possible to imagine in a very physical way exactly why the clock experiences time dilation. It should be possible to imagine in a very physical way exactly how and why mass increases or length contracts. Simply knowing that the 3 formulas work is not enough.
Forgive me, but to my knowledge The Special Theory does not answer these questions. Concerning mass increases the nearest Einstein got to explaining what was going on, was to say that there seemed to be a spherical aspect to mass. Ambiguous to say the least.
I do not argue that these formulas work, but merely ask how they work.

5. Oct 7, 2011

### Naty1

That's among the best detail you'll get.

"Why" questions are almost impossible to answer in physics: Why does the electron have the mass we observe? Why do we observe four different "forces"? Why did the universe
originate in a big bang? Why is the speed of light the only constant??......

Maybe if you read about the history and insights of Lorentz and Fitzgerald you'll gain some
insights from what they were thinking:

http://en.wikipedia.org/wiki/Lorentz-FitzGerald_contraction#History

Notice: "conjecture" ..that is, an informed guess, rather than a logical sequence of thoughts emanating from first principles.

6. Oct 7, 2011

### Staff: Mentor

It does. In fact, those are not three separate formulas, but all come from one formula in SR.

The "very physical explanation" is Maxwells equations, which are invariant under the Lorentz transform. Given those you can see that between any pair of frames in which Maxwells equations hold time must dilate and length must contract.

Btw, the modern usage is that mass is invariant and does not change. The concept of relativistic mass is the same as total energy, just in different units.

7. Oct 7, 2011

### Dappy

Btw, the modern usage is that mass is invariant and does not change. The concept of relativistic mass is the same as total energy, just in different units.[/QUOTE]

Does this mean that the relativistic mass always remains the same as the rest mass?

Is this statement true?
The formula (m = m0 / √1-(v/c) squared) predicts that it would be impossible to speed anything with mass up to the speed c. The formula predicts that the mass of a body upon reaching the speed c would be infinite, this would take an infinite amount of energy to achieve. An impossible feat.

When we look at how a light clock experiences time dilation, we can see that the formula
√1-(v/c) squared, is nothing more than Pythagoras Theorem being applied to the distance ratio of 1 to (v/c), where 1 is the distance that the photon travels in relation to the distance of (v/c) travelled by the clock in its direction of motion.

There must be a simple explanation to explain what happens to mass and length.

8. Oct 7, 2011

### Staff: Mentor

No, it means that relativistic mass is a redundant and deprecated concept.

Yes, but since the point is that it takes an infinite amount of energy it is more clear to simply call the left hand side "total energy" rather than "relativistic mass". Then, it is clear that the energy becomes infinite as v->c. In typical units where c=1 there is no important distinction between the two.

Forget mass. Length contraction comes from the Lorentz transform, just like time dilation. They are two parts of the same thing, which is why it is not surprising that the same factor shows up in both. I already said this above, did you not see my answer?

9. Oct 7, 2011

### Dappy

I believe in the equivalence of mass and energy, and you put up a good argument. Einstein equated that from the fact that he took all these equations into consideration, that certain laws of conservation fall apart. From this aspect Einstein then went on to suggest mass and energy equivalence. Proof is probably the wrong word, and should be the lack of falsification. I am probably one of Einstein's greatest supporters, but it has been over a hundred years since we've heard all this, and there is so much more to come. For within the question of why doe's matter, length and time all follow principles that are so simple, there is a simple answer.

10. Oct 7, 2011

### Staff: Mentor

I think you are misunderstanding your textbook. Do you have a source or a quote that leads you to say this?

Yes, the Lorentz transform, or equivalently the Minkowski metric. SR answers this question clearly and simply, as you have been told repeatedly.