Could Relativity Still Apply in a Universe Filled with Water?

[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 $$c = 2 \times 10^8 \frac{m}{s}$$.

 

[quantumdude]

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

 

[rushil]

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

 

[quantumdude]

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.

 

[Pengwuino]

http://www.nuc.umr.edu/reactor/reactor.html

That blue glow is Cerenkov radiation (second pic):)

 

[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.

 

[rushil]

OK! I forgot that!

But what about my original question? Please think about it!

 

[russ_watters]

Are there bubbles in this water...?

 

[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?

 

[rushil]

Bubbles that contain a mix of oxygen and nitrogen etc... ( the thing we call 'air') ---- this water is probably 'viscous free' so don't picture H_2 O when I say water!


I don't want to say it , but the Water I am talking about is something like aether or the moe recent quintessance - dark matter!

 

[JesseM]

But what about my original question? Please think about it!

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

 

[JesseM]

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 ??

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.

 

[rushil]

So Mr einstein ( the one who lives in water universe) 's derived formula wouldn't work? He would obviously use the observed speed of light in his universe --- 2 * 10^8 m/s !

 

[JesseM]

So Mr einstein ( the one who lives in water universe) 's derived formula wouldn't work? He would obviously use the observed speed of light in his universe --- 2 * 10^8 m/s !

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.

 

[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'!

 

[JesseM]

But there would be no way for him to know that higher value of 'c' without some 'alien' intervenison!?

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.

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'!

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.

 

[Janus]

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'!

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

 

[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.

 

[russ_watters]

Bubbles that contain a mix of oxygen and nitrogen etc... ( the thing we call 'air') ---- this water is probably 'viscous free' so don't picture H_2 O when I say water!

I don't want to say it , but the Water I am talking about is something like aether or the moe recent quintessance - dark matter!

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

 

[jtbell]

But there would be no way for him to know that higher value of 'c' without some 'alien' intervenison!?

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.

 

[Jimmy Snyder]

In my opinion, Professor Einstein would have been blown out of the water before he got started. The second postulate isn't true in any medium but a vacuum.

 

[JesseM]

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.

But the relativistic Doppler effect is usually derived from the Lorentz transform--are you saying the experimenter would just figure out the relationship between relative velocity and frequency shift empirically? Anyway, it's true that if your only method of measuring velocities is the Doppler effect, then you cannot measure velocities greater than the speed of light in the medium, but this seems like an arbitrary restriction. If an object passes one clock at t=1 second, and then passes another synchronized clock 2.5*10^8 meters away at t=2 second, then naturally I'm going to conclude that the object was moving at 2.5*10^8 meters/second, faster than the speed of light in the medium.

 

[bernhard.rothenstein]

As you can see from the paper I quote the Doppler effect can be derived without using the Lorentz transformations. You also can see a paper by Kalotas and Lee published in am.j.phys.

 

[JesseM]

As you can see from the paper I quote the Doppler effect can be derived without using the Lorentz transformations. You also can see a paper by Kalotas and Lee published in am.j.phys.

I guess you didn't get my PM, but none of the equations were visible in the papers you sent me...would you be willing to convert the equations into LaTex and post the derivation of the relativistic Doppler effect here?

edit: never mind, I just realized I could open the documents in microsoft word and then the equations became visible.

 

[rushil]

I'm sorry - I don't have acceess to the American Journal of Physics coz I am a high school student in India. Can someone Please send the abovesaid article to me . I'd love to see it!

 

[DrGreg]

If you carried out the Michelson-Morley experiment moving at high speed through water (or other medium of significant refractive index) wouldn't you be able to detect that the speed of light (relative to yourself, through the medium) varied in different directions?

I haven't time to do the calculation but it seems like you ought to.

By the way, I believe it was known in 1851, way before the formulation of Relativity, that the speed of light through water depends on the speed of the water. (See http://www.numericana.com/answer/relativity.htm#fizeau".)

 

[RandallB]

But what about my original question? Please think about it!

Yes think about it - let them call the water “aether”,
They have two scientists named Mike and More that produce a Mike-More experiment that shows that light does change speed depending on how fast you move though this aether. Not at all like our counterparts discovered.

Also, unlike us as their science would progress and see deeper into the microscopic they will at some point see that light is being absorbed and reemitted by tiny particles of their aether. Where we do not.

Maybe at some point they would interpret what they see as light going in straight lines as a version of light moving in tiny triangles such that it remains straight to them in the Macro-world but in the Micro-world it would actually travel greater distances requiring a higher speed like 3 x 10⁸.

An insight like that would open up a whole new version of physics to them! Well beyond what they had thought based solely on the aether.

Does this help tie their water world to ours for you?

 

[lightgrav]

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.

The microwave field propagation in the electrodynamic accelerators is also 2e8 m/s, and the limiting speed of their charged particles will be essentially 2e8 m/s since they radiate energy so effectively as they approach this.
Perhaps the electrostatic device of their jan derCraft could get electrons over 2e8 m/s , but that would depend on the the E-field strength possible in water (which I happen to NOT know), and they would quickly slow to C.

Without unstable particles that will travel far at constant speed near C,
they won't be able to check their time-dilation expectations.

Once in a while, they'll see an "ultra-high Energy cosmic ray" with way more energy than their accelerators can produce in a single particle.

But their Max Well will have already taken the sqrt (epsilon_o)(mu_o) and gotten 2e8 m/s , and Anystein will have imagined examining a light wave that he's riding on, coming up with LoryEnt's conditions a different way.

What will get them off-track will be the mass-Energy relation. I've got to think about that one a while myself.

 

[michael879]

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.

The formulas would all work fine theoretically. They would only fall apart experimentally. Until someone actually went fast enough to observe a time dilation, everything would appear to work.

 

[michael879]

In my opinion, Professor Einstein would have been blown out of the water before he got started. The second postulate isn't true in any medium but a vacuum.

the second postulate is true in any medium, the speed of light is always the same, in any reference frame, in any medium

 

[JesseM]

The formulas would all work fine theoretically. They would only fall apart experimentally. Until someone actually went fast enough to observe a time dilation, everything would appear to work.

There'd be plenty of other experiments that would show the formulas don't work though, like observing the decay times of particles that are moving at high velocities, or trying to measure the speed of light in different directions as in the Michelson-Morley experiment, or measuring how much energy is created when various particles are annihilated, or trying to build a system of GPS clocks that takes into account relativity.

 

[michael879]

There'd be plenty of other experiments that would show the formulas don't work though, like observing the decay times of particles that are moving at high velocities, or trying to measure the speed of light in different directions as in the Michelson-Morley experiment, or measuring how much energy is created when various particles are annihilated, or trying to build a system of GPS clocks that takes into account relativity.

yea sry, I just meant the mathematically it would all work, until it made false predictions about nature

 

[rushil]

Yes think about it - let them call the water “aether”,
They have two scientists named Mike and More that produce a Mike-More experiment that shows that light does change speed depending on how fast you move though this aether. Not at all like our counterparts discovered.
Also, unlike us as their science would progress and see deeper into the microscopic they will at some point see that light is being absorbed and reemitted by tiny particles of their aether. Where we do not.
Maybe at some point they would interpret what they see as light going in straight lines as a version of light moving in tiny triangles such that it remains straight to them in the Macro-world but in the Micro-world it would actually travel greater distances requiring a higher speed like 3 x 10⁸.
An insight like that would open up a whole new version of physics to them! Well beyond what they had thought based solely on the aether.
Does this help tie their water world to ours for you?

Randal has epitomised what I have to say... maybe stuff starts going 'wrong' ( as we would consider it) if the people in this universe applied the formulae using the speed of light they measured. I just want to clarify one thing ( while the great discussion continues! ) - we all agree that if Mr Einstein derived his equations using the speed of light he measured in THIS medium, his formulas would not work and would not conform to the results observed! ? - thereby HE IS NOT FAMOUS!

 

[Jimmy Snyder]

the second postulate is true in any medium, the speed of light is always the same, in any reference frame, in any medium

Here is the second postulate, lifted directly from this translation: http://www.fourmilab.ch/etexts/einstein/specrel/www/

that light is always propagated in empty space with a definite velocity c

In other words, you are claiming more than Professor Einstein did. Yet it is well known that measurements of the speed of light in water does depend on the motion of the water relative to the emitter. I quote http://uk.geocities.com/kevinharkess/pdf/appendix_b.pdf

He (Fizeau) discovered that changes in the speed of light are proportional to the water's flow rate.

 

[bernhard.rothenstein]

I think that as long as water is still anm observer equipped with a light source could perform the radar echo experiment, the radar detection and the Doppler effect experiment considering that the light signals propagate with speed c/n. If water moves we should ask a "time out" for thinking and defining the experiment observers are going to perform.