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.

 

[RandallB]

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!

I don't understand your point, are you saying Einstein only appears to be famous in our world? - just because of something in your fictional water world.
If your talking about someone 'equivalent’ to him in the water world do us a favor and avoid confusion by assign a new name for that person in that “frame” of world.
Lets call that person Ms Eins as a woman would do better in water any way.
I see no reason that Eins would not become famous with her theory of relativity, even if it is based on “slow light”. It would still be an major concept improvement of the old classical 17th century ideas of “Newt” (that name goes well with water).

At least until they discover in a laboratory they can create a volume without any water in it, by removing their aether and replaced with a void. Something will have to happen because problems will show up in the theory. In addition to updating the great but flawed version of relativity by Ms Eins, they will need to come to grips with the concept of a “void” being more fundamental then the aether they have been familiar with – not just that light can travel faster than they thought! Clearing up problems that would have to become obvious as science progressed into the particle physics.

 

[yogi]

The relativistic transforms derived by Einstein follow from the first postulate - that experiments made in every inertial frame will lead to the same result - In Galilean relativity the same assumption is incorporated as to mechanical measurments... what Einstein did was extend the notion to experiments that would reveal the velocity of light. You will not get conforming results when attempting to measure the velocity of light in water with respect to which you are moving just as you will not get correct results when attempting to measure the velocity of sound relative to air when you are moving with respect to the air. The so called
aether has the unique property that velocity with respect thereto is meaningless (according to Einstein). This is not the case wrt other mediums.

 

[RandallB]

Exactly; where Einstein would be creating postulates on knowing the speed of light as 3.0E+8 and that it didn’t change. Ms Eins in rushil’s water "or thick ether" world light would have a local light speed of 2.0E+8 and would it be faster or slower depending on the speed of the source. She wouldn’t be able to create a complete relativity theory until the idea of a true vacuum was understood.

Also note that the theories of “Newt” couldn’t match up well with Newton and prior very well. Until the could see and understand that energy could be lost into creating disturbances the media that is carrying the light at an artificially slow speed they wouldn’t be able to define the conservation of energy as not even the parabolas of Galileo’s cannon balls would work correctly nor could planetary orbits be maintained within this “aether”. The whole history and laws of science in such a world would be greatly different; it may be a difficult just to get the idea of a vacuum.

 

[rushil]

Aqausians - living in Aqausia - the water filled universe ( please use this name from now!) do not know about 'vacuum' as we call it! Their 'vacuum' is effectively a space filled with Just Aqua - the name for aether in Aqausia!

Besides, hoe would they prove for the first time that THERE IS A SPEED LIMIT in Aqausia given that Aquasians can never reach speeds as high as 2*10^8 m/s ( we know this because our correctly derived relations predict that too much energy is required to reach such high speeds!) , and light travels at 2* 10^8 m/s?!

 

[Ich]

As I understood, the "water" should be without resistance and play the role of an aether.
Then you would find that the speed of light is not a constant, therefore no need to derive SR. This would change when you observe particles faster than light, but with a constant maximum velocity. Still, SR would lose most of its attraction because there is a preferred frame and you could not unite electrodynamics with Newtonian mechanics.
In the real world, SR is found to be appropriate because it reflects most elegantly the perfect symmetry between inertial frames.

 

[RandallB]

Aqausians - living in Aqausia - the water filled universe ( please use this name from now!) do not know about 'vacuum' as we call it! Their 'vacuum' is effectively a space filled with Just Aqua - the name for aether in Aqausia!
Besides, hoe would they prove for the first time that THERE IS A SPEED LIMIT in Aqausia given that Aquasians can never reach speeds as high as 2*10^8 m/s ( we know this because our correctly derived relations predict that too much energy is required to reach such high speeds!) , and light travels at 2* 10^8 m/s?!

But remember the simple physics of a billiard ball bounce off a billiard ball conservation of vis-viva, all these depend on the interaction of the force of EM. And EM uses virtual photons to manage those interactions - thus the Aquasians have Aqausia withdrawing energy from any movement as the Aqausia itself is disturbed and parts moved by transmitting that light. Thus until they can "see" Aqausia as being something that takes-up energy with movement as it interacts with everything, they will not be able to understand the simplest of physics. Example only in areas without Aqausia will be able to maintain energy conserving orbits. Understanding these kind of issues would need to be resolved (by somehow discovering vacuum not Aqausia exists where orbits do) long before their science would be ready to address things like finding the correct speed of light.

 

[DrGreg]

Besides, how would they prove for the first time that THERE IS A SPEED LIMIT in Aquasia given that Aquasians can never reach speeds as high as 2*10⁸ m/s?

Not true -- it's entirely possible for particles to travel faster than the speed of light-through-aqua (as has been pointed out earlier in this thread). Look up http://en.wikipedia.org/wiki/Cherenkov_effect" .

 

[Janus]

Aqausians - living in Aqausia - the water filled universe ( please use this name from now!) do not know about 'vacuum' as we call it! Their 'vacuum' is effectively a space filled with Just Aqua - the name for aether in Aqausia!

Before we can answer your questions, we must nail down the the properties of this Aqua and the laws of nature in Aquasia.

Is Aqua viscous? Does it share all characteristics with water? (if you seal a container, and then move that container does the Aqua inside move with the container or not?
Or does Aqua takes the place of the classical aether? (IOW, is Aquasia not even in a Relativistic Universe?

Or is Aqua the equivalent of a vacuum in a Relativistic universe, one in which the speed of light in a vacuum is 2e8 m/s ?

Or is Aqua some mixture of all the above? Light travels through it as it was water, but it is non-viscous and can not be contained in a vessel like the aether, yet the universe of Aquasia is relativistic and shares all the other laws of our universe?

 

[yogi]

Yes janus - I agree that a little learning is a dangerous thing - the problem is that the best of us only has a little learning - so we try to perceive truth with only half sufficient knowledge. We take as "right" the ideas of Einstein - yet for the most part they were untested until much later in his life - as Einstein himself professed: "we can only dimly perceive the intelligence manifested in nature" So re the present interrogatory, can we say that the speed of light is a property of the universe? - the space/time frame that defines its speed - the issue to me is the nature of what we regard as space - we know it has characteristics - capacitance, inductance, energy ...yet it is massless and totally undetectable by any means yet devised . Could we even construct a universe where space is filled with a perfect frictionless fluid having the density of water - I doubt it, Such a medium would not support transverse waves - whereas a medium under tension would - but neither water nor any other fluid is capable of supporting shear

If we are going to understand the universe, we must first understand space - for that is the stuff of which it is made

 

[rushil]

I have a question regarding the Michaq-moraq experiment conducted in Aquasia!
Wouldn't it, if carried out in exactly the same way as on Earth, still yield wrong results if the theory used simple Galilean transformations as on Earth? I think it would... However, here comes the catch. On earth, Einstein concluded that the speed of light is constant on the basis of this experiment. But since the Aquasians DO observe object sat speeds greater than 2 * 10^8 m/s, and they also observe that the speed of light depends on the motion of teh body in Aquasia, what conclusions do they draw from the Mich- More experiment?
The Theory of galilean transforms in Aquasia has just c_w instead of c in vacuum! So the displacement in fringes would still NOT conform to thery...however, it would NOT lead Aquasians to conclude anything about a speed limit in Aqausia? Or would it?

What would be the significane of Mich-more experiment in Aqausia!

( I have two more posts - please read! )

 

[rushil]

As far as I thing, Aqua in Aquasia is just the aether!

Nothing more , nothing less! Its undetectable but we assume, for now , that it exists! I think doing this is not too much of a 'wrong' given that Modern theoretical physics on Earth has envisioned stranger things!

I hope all of us keep in mind that Aqua in Aquasia = something like aether that was thought about some years ago, when we discuss things!

Definition of aqua - inviscous, undetectable, invisible, liquid filling space till infinity...

 

[rushil]

I try to derive that speed of light in Aquasia is NOT independent of motion of emitting body... please see if it is correct.

K is an observer on Earth seeing the boxed universe 'Aqausia' . K' is an observer in Aqausia ( stationary) , Let M be a moving object in Aqausai, with speed v. K' can look only inside Aqausia. C_w is speed of light in aquasia = 2* 10^8. C is true speed of light = 3 * 10^8. Now the speed of light emitted by M in frame of K is (v + c_w )/( 1 + vc_w / c^2 )

Speed of K wrt K' = 0. therefore, speed of light emitted by M in K' frame is same as in K frame ... ( note K' does not know the correct equations and is not doind ANY calculations. All calculations are being done by K)

Thus, even in Aqausia, the speed of light ( as observed - not calculated) DOES depend on speed of motion of emitting body!

 

[rushil]

Hey guys,,, why has the discussion stopped! Are these ideas going somewhere? Is this idea worth further study!? Please speak!

 

[Crazy8s]

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.

This is because light is not a particle, and the Cernekov effect is a particle.