# Relativity - a new viewpoint

1. Dec 13, 2005

### rushil

Relativity - a new viewpoint!!

This question came to my mind after I discussed my previous questions on Photons with my Physics teacher. I have posted them on this forum and am awaiting a reply. I urge you to see them before reading this. It may establish the context fully and also answer my doubts.

Suppose we lived in a "Water - Universe " that is in such a universe which was completely filled with water to infinity(in all dimensions). Now suppose a Mr. Einstein was born here and he tried to formulate his equations based on Michelson- Morley experiment in such a universe. Now of course, since the residents of such a world don't know a thing called free space and just water-filled space(which is effectively their free space) , so they would calculate the speed of light(even Maxwell and all other workers) as the $$2 \times 10^8$$ m\s (approx) (let's not bring in vacuum and in water to keep it clear) So , now if Lorentz and Einstein tried to formulate their relativity eqns (not knowing about "vacuum" as we know it) , will the transformations like
$$l = \frac{l_0}{ \sqrt{ 1- \frac{v^2}{c^2} } }$$ have $$c$$ as $$2 \times 10^8$$ m\s?????

Thus unless some alien species ( who by some act of God or through another species and so on...(infinite regression) got to know) tells them that they live in "Water Universe" , they would continue to work through their equations using $$c = 2 \times 10^8 \frac{m}{s}$$.

2. Dec 13, 2005

### Tom Mattson

Staff Emeritus
They may not have come up with relativity at all, because they could in principle observe bodies moving faster than light.

3. Dec 13, 2005

### rushil

Well, let's keep out speculative stuff for now! Let's stick to stuff thats usually proved and observed in our real world till date! Anyways, I'm not aware of the theory of warp drives etc!!! :tongue:

4. Dec 13, 2005

### Tom Mattson

Staff Emeritus
When light is travels through a medium, it is in fact possible for other bodies to move faster than the speed of light in that medium. It's not speculative, it's called the Cerenkov effect. Detectors in particle accelerators are engineered based on it.

5. Dec 13, 2005

### Pengwuino

6. Dec 13, 2005

### JesseM

Also, if they set c=2*10^8 m/s, they would notice that natural clocks (such as decaying particles) do not have their "ticks" extended by exactly $$1/\sqrt{1 - v^2/c^2}$$, as relativity demands. In fact, by measuring how time actually does dilate, they could in principle figure out the "true" speed of light, if they assume that relativity is correct (ie if they assume that light travels at a constant speed in all frames and that the laws of physics should work the same in all frames).

This also means that if they assumed c=2*10^8 meters/second and used that in the Lorentz transform, then they would be able to see that the laws of physics don't work the same in different reference frames defined by this transformation--there would be only one frame where natural clocks would tick at the same rate as coordinate time, for example.

7. Dec 13, 2005

### rushil

OK! I forgot that!!!

8. Dec 13, 2005

### Staff: Mentor

Are there bubbles in this water...?

9. Dec 13, 2005

### rushil

But if they calculated their sppeds of lights and lorentz transformations etc. around c = 2 * 10^8 m/s , wouldn't all the ticks and measurements turn out to be correct to the formula they derive using just c = 2* 10^8 m/s ?? Please remember, the people in this Water Universe do not know a thing known as 'vaccuum' (as we know it!) .... their vacuum = water .... so they think speed of light = 2 *10^8 m/s .... they do not know anything about 3 *10^8 m/s !!! Know what ---- is such a situation even possible???

10. Dec 13, 2005

### rushil

Bubbles that contain a mix of oxygen and nitrogen etc... ( the thing we call 'air') ---- this water is probably 'viscous free' so dont picture H_2 O when I say water!!!!

I dont want to say it , but the Water I am talking about is something like aether or the moe recent quintessance - dark matter!! :tongue2:

11. Dec 13, 2005

### JesseM

What part of your original post are you referring to as your "original question"?

12. Dec 13, 2005

### JesseM

No, because clocks tick at the same rate in water as they do in the vacuum. The time dilation formula with c=3*10^8 meters per second still applies to a clock sitting in water, the speed that clocks tick doesn't change to reflect the slower speed of light through water.

13. Dec 13, 2005

### rushil

So Mr einstein ( the one who lives in water universe) 's derived formula wouldnt work??? He would obviously use the observed speed of light in his universe --- 2 * 10^8 m/s !!

14. Dec 13, 2005

### JesseM

Right, the formulas wouldn't work--like I said earlier, the formulas would give the wrong value for time dilation, and it wouldn't be true that the laws of physics would work the same way in different coordinate systems given by the Lorentz transform if you used the wrong value of c in the transform. However, by noticing the actual time dilation, a clever physicist might deduce that the "c" that should be used in the formulas should be higher than the observed velocity of light.

15. Dec 13, 2005

### rushil

But there would be no way for him to know that higher value of 'c' without some 'alien' intervenison!??? Also, his universe would work fine with his laws and formulae using c = 2 * 10^8 m/s if he neglected that 'time dilation anomaly'!! :surprised

16. Dec 13, 2005

### JesseM

No, that's what I'm saying--he could deduce the correct value of c by observing the amount of time dilation experienced by a clock in motion relative to him. For example, say I observe the ticks of a clock moving at 1.8*10^8 meters/sec relative to me are extended by a factor of 1.25. Then I can solve the equation $$1.25 = 1/\sqrt{1 - (1.8*10^8 m/s)^2 / c^2 }$$ for c, giving me c=3*10^8 m/s.
The problems would be bigger than that--in general, the laws of physics should not obey the same equations in different coordinate systems given by the Lorentz transform with the wrong value of c.

17. Dec 13, 2005

### Janus

Staff Emeritus
Actually, he would have to neglect a whole lot more than that.

18. Dec 14, 2005

### bernhard.rothenstein

Consider the observer confined in the not friendly medium transparent medium, equipped with the same measuring and experimental devices as his twin on the shore. He will start by measuring the two-way velocity of light in water C. Considering that the transparent medium is isotropic and homogeneous he decides that the one way velocities of light c=C(0)/n are equal to C. From that point he could follow a strategy proposed by Asher Peres (Am.J.Phys. 55(6) 1987). performing a radar echo experiment that enables him to measure the velocity V of a mirror moving relative to him. He could extend the results to a Doppler Effect experiment that leads directly to the addition law of relativistic velocities. Extending the problem to two space dimensions he derives the aberration of light effect and finally the Lorentz-Einstein transformations for the space-time coordinates of the same event.
Synchronizing his clocks with C he has no devices for measuring speeds >C.

19. Dec 14, 2005

### Staff: Mentor

You could just ask: what if there was an aether?

20. Dec 14, 2005

### Staff: Mentor

He can build a high-energy particle accelerator (an underwater Fermilab or CERN? the mind boggles! ) and observe that his particle beams have a limiting speed of $3 \times 10^8$ m/s.