I recently began having a debate with Tom2 on the "How does spacetime curvature become infinite?" thread. Since our debate is off-topic for that thread, I decided to continue the debate on this new thread.

I was previously explaining to Tom2 that relativity contradicts itself. The formulas used for time dilation and length contraction are simply patches to a hole that was created by the absolute model. In other words, the patch is proof that there's a hole, and the hole is proof that the absolute model is correct, and that relativity is wrong.

As proof of this, I am providing the mathematical explanation, given below, that length contraction and time dilation are used to attempt to make the principle of invariance of light correct (even though it isn't).

To illustrate my point, let's take two mirrors with light bouncing between them. As the two mirrors begin to move forward (so that the motion of the mirrors is parallel with the bouncing light), it appears that the light slows down. Relativity attempts to compensate for this "slowing" by compensating the effect with length contraction and time dilation. Below, I will explain this "slowing down" effect using the absolute model (assuming that the invariance of light is wrong), therefore proving that relativity is wrong, since the absolute and relative models both can't be correct.

First, assume you have two mirrors, and there is light bouncing back and forth between the mirrors. Now let's say that you start moving the mirrors forward, so that the motion of the mirrors is parallel with the motion of the light (the direction doesn't matter).

According to the ABSOLUTE model, the time it takes for the light to reach the mirror that is moving away from it is longer:

t1=d/(c-v)

where d is the distance between the mirrors and v is the speed of the moving mirrors.

But the time it takes for the light to reach the mirror that is moving towards it is shorter:

t2=d/(c+v)

The time it takes the light to reach a mirror and return would be:

t3=t1+t2
t3=(d/(c-v))+(d/(c+v))
t3=(d(c-v)+d(c+v))/(c+v)(c-v)
t3=(dc-dv+dc+dv)/(c^2-cv+cv-v^2)
t3=2dc/(c^2-v^2)

The average time of the one-way trip of the light would be:

t=t3/2
t=(2dc/(c^2-v^2))/2
t=dc/(c^2-v^2)

The average speed of the one-way trip of light would be:

v=d/t
v=d*(c^2-v^2)/dc
V=(c^2-v^2)/c REMEMBER THIS RESULT!!!!!

Now Einstein dictates that in this situation there is time dilation AND length contraction.

The time dilation is

T=T0/sqrt(1-(v^2/c^2)

we want to find T0:

T0=T*sqrt(1-(v^2/c^2))

The length contraction is:

L=L0*sqrt(1-(v^2/c^2))

we want L0:

L0=L/sqrt(1-(v^2/c^2))

Since v=d/t then:

v1=L0/TO
v1=L/sqrt(1-(v^2/c^2))*1/T*sqrt(1-(v^2/c^2))

Since we have that v obtained from the ABSOLUTE model above, let's remove L and T so that we only have the length contraction and time dilation factors:

a=1/sqrt(1-(v^2/c^2))*1/sqrt(1-(v^2/c^2))
a=1/(1-(v^2/c^2))

since 1-(v^2/c^2)=(c^2-v^2)/c^2 then

a=1/((c^2-v^2)/c^2)
a=c^2/(c^2-v^2)

Now let's see what we get when we multiply the velocity obtained from the absolute model with the effects of time dilation and length contraction:

v=V*a
v=((c^2-v^2)/c) * (c^2/(c^2-v^2))
v=c

In other words, time dilation and length contraction patch the results from the absolute model to make v=c. Therefore, Einstein's formulas for time dilation and length contraction are proof that the absolute model is right, and that relativity is wrong.

Tom

eeeh no

You contradict yourself. You must remember, it can only hold when the mirrors have a constant velocity!
I think you should first learn more about the exact condictions; formulate a more precise experiment; Show why relativity cannot be right; and tell us what is the alternative.

Honestly, I have seen none of the above!

Your high school math is to the theory as swords to a balrog.

Hi Tom,

"In other words, time dilation and length contraction patch the results from the absolute model to make v=c. Therefore, Einstein's formulas for time dilation and length contraction are proof that the absolute model is right, and that relativity is wrong."

Where does it prove that ? You have simply established a relation where you would let the speed of light vary (dependent on the direction of motion) and what relativity would predict. Your absolute model is what a Newtonian theory would predict. However, and this is exactly what relativity is all about: by assuming the extra condition "the speed of light is invariant for all observers" in addition to all Newtonian postulates, you get a model/description/theory that works better for extreme situations (high speeds, high energies).

What you have done is calculated a Newtonian result and compared it to a relativistic result: it is obvious that there are differences, but the extra assumptions in relativity are there to create the minor corrections required on Newtonian results. In this case, it is a multiplier factor (which is not unexpected since time dilation and length contraction formules involve a multiplication factor gamma). However, if you let v become much smaller than c (v << c) then your multiplier reduces to "a = 1", i.e. the relativistic and Newtonian result are the same (note: Newtonian mechanics are a limiting case, low speeds i.e. v << c, of relativity).

To conclude: your calculation is easily explained from both a Newtonian (which is your point of view) and a relativistic position.

And above all, the calculation does not tell us why we should prefer your absolute Newtonian world above the relativistic world (that seems to look a lot more like the real world).

Bye!

Crisp

Crisp,

To conclude: your calculation is easily explained from both a Newtonian (which is your point of view) and a relativistic position.

And above all, the calculation does not tell us why we should prefer your absolute Newtonian world above the relativistic world (that seems to look a lot more like the real world).

There is NO similarity between the Newtonian theory and relativity. They are opposites:

Newtonian theory (absolute model):

1) There is an absolute frame of reference.
2) The omnidirectional speed of light is only c in the absolute frame of reference.

Relativity:

1) There is no absolute frame of reference.
2) The omnidirectional speed of light is c in all frames of reference.

One model contradicts the other, so you can't derive one model from the other. Let me remind you again, I derived the formulas from the absolute model (assuming that the principle of invariance of light is wrong). If time dilation and length contraction patch the results from the absolute model so nicely, how can you argue that the absolute model is wrong. And if the absolute model is right, then relativity must be wrong. Or do you believe that they can both be correct??

As far as I see it, there are only two choices:

1) The principle of invariance of light is wrong

or

2) The principle of invariance of light is correct

Which one is it??

It appears that Einstein knew that 1 was right, so he used length contraction and time dilation to convert 1 into 2 in order to preserve his theory.

Truthfully, if length contraction and time dilation didn't perfectly patch the results from the absolute model, I would assume that relativity might be correct. But as you can see, this is not the case.

The fact is that time dilation and length contraction patch a hole. And the hole can ONLY be derived from one thing: THE ABSOLUTE MODEL. And the absolute model ASSUMES that the principle of invariance of light is WRONG.

If you believe that the hole can be derived from anything else besides the absolute model (and the assumption that the principle of invariance of light is wrong), please show me your formulas. And don't use the formulas for length contraction or time dilation to obtain the result, since we both know that it wouldn't qualify as proof. :)

Tom

Merlijn,

Show why relativity cannot be right;

I proved that relativity is wrong with my post. As I pointed out to Crisp, time dilation and length contraction PERFECTLY patch the results from the absolute model.

Let me remind you, I used the assumption that the principle of invariance of light is wrong in order to obtain the results for the absolute model. The ironic part is that relativity patches the results obtained from the absolute model. If the absolute model was wrong, there would be NOTHING to patch.

and tell us what is the alternative.

The alternative to what??? The fact that moving atomic clocks measure that time slows down???

If you look at the construction of atomic clocks, you will find that the caesium atoms in the clocks are stimulated and seperated using electromagnetic radiation. If the absolute model is correct, and the principle of invariance of light is wrong, then the speed of the electromagnetic radiation, relative to the clock, is influenced by the motion of the clock. The resulting change in the speed of the electromagnetic radiation in the clock, will influence the clock to give a false reading. As you can see, there is no need to use time dilation or length contraction to explain the "perceived" slowing down of time by the atomic clock.

One more thing : The math I used was intentionally simple so that everyone could understand. Even you.

Tom

So,

how exactly is it possible to ignore all the experimental evidence that realativity myst be true just because you personally dislike it?

Or mabey the evil scientists forged the results of the experiments so the world woulnd't find out their precious theory was wrong?

Tom,

It seems you've conveniently forgotten our past discussions on this topic.

Oh well...

Let's pick apart Tom's maths a little.
According to the ABSOLUTE model, the time it takes for the light to reach the mirror that is moving away from it is longer:

t1=d/(c-v)

where d is the distance between the mirrors and v is the speed of the moving mirrors.

But the time it takes for the light to reach the mirror that is moving towards it is shorter:

t2=d/(c+v)

The time it takes the light to reach a mirror and return would be:

t3=t1+t2
t3=(d/(c-v))+(d/(c+v))
t3=(d(c-v)+d(c+v))/(c+v)(c-v)
t3=(dc-dv+dc+dv)/(c^2-cv+cv-v^2)
t3=2dc/(c^2-v^2)

The average time of the one-way trip of the light would be:

t=t3/2
t=(2dc/(c^2-v^2))/2
t=dc/(c^2-v^2)

The average speed of the one-way trip of light would be:

v=d/t
v=d*(c^2-v^2)/dc
V=(c^2-v^2)/c REMEMBER THIS RESULT!!!!!
What does this mean? Remember that Tom claims to be postulating an absolute reference frame. Now V is supposed to be the speed of light as determined by somebody watching the mirrors and the light bouncing between them, with the whole apparatus moving. Notice that V depends on v (the speed of the mirrors). But why should the speed of light be affected by the movement of the mirrors? After all, unless it is being reflected it is moving in empty space. Shouldn't its speed be the usual value (=c)? In fact, Tom assumes that is its speed in the very first step of his calculation, which includes the constant c.

Tom appears to be assuming the speed of light is c in order to try to prove that its speed is in fact (c^2-v^2)/c.

Something is very wrong here.

How about an explanation, Tom?

Hi Tom,

"One model contradicts the other, so you can't derive one model from the other. Let me remind you again, I derived the formulas from the absolute model (assuming that the principle of invariance of light is wrong)."

Exactly my point: by assuming that the speed of light works in an additive way (c+V as you used), you leave out the invariance of the speed of light and you are basically reducing relativity to Newtonian mechanics.

Note that there is no mention of an absolute frame of reference in Newtonian mechanics (Newtonian mechanics is also a relative theory!!!).

I perhaps was wrong dismissing your theory as "pure classical Newtonian mechanics", but it resembles it quite a lot :).

"If time dilation and length contraction patch the results from the absolute model so nicely, how can you argue that the absolute model is wrong. And if the absolute model is right, then relativity must be wrong."

As I tried to explain in my previous post, it is not suprising that time dilatation and length contraction "patch" your absolute results. That is a direct consequence of the invariance of the speed of light! This has been told to you before, but I'll repeat it once more: (-> means "leads to")

invariance of the speed of light
-> time dilatation and length contraction
-> Lorentz transformations

In the Lorentz transformations, there is a slight difference between the classical Newtonian transformations (called "Galilean transformations"). This difference is exactly a multiplicative factor GAMMA that occurs in the Lorentz transformations. Since (roughly speaking) the basic difference between Newtonian mechanics and Relativity is this GAMMA factor in the transformations, it is not suprising that your result (which is basically Newtonian mechanics with an absolute frame of reference) differs from the relativity result by a multiplicative factor, which you labeled "a" (the effects of time dilatation and length contraction).

You see this as a "patch", I see it as a direct result of the GAMMA factor in the Lorentz transformations. And moreover, as I already said, just because it looks like a "patch" doesn't mean that we should prefer one calculation over the other. You need to provide more evidence for your absolute model before making such a claim.

Bye!

Crisp

James R,

What does this mean? Remember that Tom claims to be postulating an absolute reference frame. Now V is supposed to be the speed of light as determined by somebody watching the mirrors and the light bouncing between them, with the whole apparatus moving. Notice that V depends on v (the speed of the mirrors). But why should the speed of light be affected by the movement of the mirrors? After all, unless it is being reflected it is moving in empty space. Shouldn't its speed be the usual value (=c)? In fact, Tom assumes that is its speed in the very first step of his calculation, which includes the constant c.

Tom appears to be assuming the speed of light is c in order to try to prove that its speed is in fact (c^2-v^2)/c.

Something is very wrong here.

How about an explanation, Tom?

The omnidirectional speed of light is only c in the absolute frame of reference.

As the mirrors move, the speed of light does not change in the absolute frame of reference: it remains c. However, the light appears to speed up and slow down relative to the observer traveling with the mirrors. As the light is traveling towards the mirror that is moving away from the light, the light appears to be moving slower than c (c-v) to the observer traveling with the clock. However, when the light is traveling towards the mirror that is moving towards the light, the light appears to be traveling faster than c (c+v) to the same observer.

When the observer measures the roundtrip speed of the light (to a mirror and back) the light appears to be traveling at the speed of (c^2-v^2)/c, while in reality, the one-way speed of the light remains c in the absolute frame of reference.

Tom

Crisp,

You see this as a "patch", I see it as a direct result of the GAMMA factor in the Lorentz transformations. And moreover, as I already said, just because it looks like a "patch" doesn't mean that we should prefer one calculation over the other. You need to provide more evidence for your absolute model before making such a claim.

Let's break this down to simple math:

v(relativity)=v(roundtrip from absolute model) * GAMMA

where v(relativity)=c


The fact is that :

GAMMA=v(relativity)/v(roundtrip from absloute model)

This means that the GAMMA factor is derived from the absolute model. It also means that the GAMMA factor is proof of the absolute model. As far as I know, there is no other way to derive the GAMMA factor than from the ABSOLUTE MODEL.

If I'm wrong, and the GAMMA factor can be derived without the use of the absolute model, please explain.

Tom

Tom,

When the observer measures the roundtrip speed of the light (to a mirror and back) the light appears to be traveling at the speed of (c^2-v^2)/c, while in reality, the one-way speed of the light remains c in the absolute frame of reference.
I see. So, you're working in the reference frame of somebody travelling with the mirrors. Ok...
Now Einstein dictates that in this situation there is time dilation AND length contraction.

The time dilation is

T=T0/sqrt(1-(v^2/c^2)

we want to find T0:

T0=T*sqrt(1-(v^2/c^2))

The length contraction is:

L=L0*sqrt(1-(v^2/c^2))

we want L0:

L0=L/sqrt(1-(v^2/c^2))

Since v=d/t then:

v1=L0/TO
v1=L/sqrt(1-(v^2/c^2))*1/T*sqrt(1-(v^2/c^2))

Sorry. I'm lost again. What exactly are T0, T, L0 and L in these equations? And what is v1?

T0 and L0 are the 'dimensions' of time and length when the frame is at rest
T and L are the dimensions when travelling near c
and I believe v1 is meant to be the velocity of the mirrors.
But I am not sure he means this.

I think the most probelematic part of the derivation is:
The average speed of the one-way trip of light would be:

v=d/t
v=d*(c^2-v^2)/dc
V=(c^2-v^2)/c REMEMBER THIS RESULT!!!!!

James R,

Now Einstein dictates that in this situation there is time dilation AND length contraction.

The time dilation is

T=T0/sqrt(1-(v^2/c^2)

we want to find T0:

T0=T*sqrt(1-(v^2/c^2))

The length contraction is:

L=L0*sqrt(1-(v^2/c^2))

we want L0:

L0=L/sqrt(1-(v^2/c^2))

Since v=d/t then:

v1=L0/TO
v1=L/sqrt(1-(v^2/c^2))*1/T*sqrt(1-(v^2/c^2))



Sorry. I'm lost again. What exactly are T0, T, L0 and L in these equations? And what is v1?

Let me simplify it:

Let's say sqrt(1-(v^2/c^2))=Gamma

Then time dilation is:

T=T0/Gamma

And length contraction is:

L=LO*Gamma

We have L and T from the absolute model (V=L/T). Therefore, we need to find L0 an T0:

T0=T*Gamma
L0=L/Gamma

We want to find the result of L0/T0:

L0/T0=(L/Gamma)/(T*Gamma)
L0/T0=(L/Gamma)*(1/(T*Gamma))
L0/T0=(L/T) * (1/Gamma^2)

We take L/T from the absolute model (V) which equals (c^2-v^2)/c:

L0/T0 = ((c^2-v^2)/c) * (1/Gamma^2)

Since (1/Gamma^2) = (c^2/(c^2-v^2)) :

L0/T0= ((c^2-v^2)/c) * (c^2/(c^2-v^2))

L0/T0=c


Tom

Tom,

You don't need to repeat your previous derivation. Just tell me what you understand L, L0, T and T0 to be, in your own words.

Hi Tom,

"If I'm wrong, and the GAMMA factor can be derived without the use of the absolute model, please explain."

I believe this was demonstrated already in our previous discussions on relativity. The formulas for time dilatation and length contraction have the GAMMA factor in them, and those are derived in Special Relativity without assuming the existance of an absolute frame of reference.

Bye!

Crisp

James,

You don't need to repeat your previous derivation. Just tell me what you understand L, L0, T and T0 to be, in your own words.

L an T would be distance and time without the effects of time dilation and length contraction, while L0 and T0 would be distance and time after the effects of time dilation. Tha actual values of L, L0, T, T0 are insignificant in the equations. The values that matter are L/T and L0/T0:

V1=L/T This I obtained from the absolute model.

V2=L0/T0 This, according to relativity, is equal to c

In other words, I obtained V1 from the absloute model and I had to multiply it by the length contraction and divide it by the time dilation to get the resulting speed that is dictated by relativity.

Tom

Crisp,

I believe this was demonstrated already in our previous discussions on relativity. The formulas for time dilatation and length contraction have the GAMMA factor in them, and those are derived in Special Relativity without assuming the existance of an absolute frame of reference.

I'm sorry because I either didn't read the post you are referring to, or I forgot it (or didn't understand it :)).

I'd appreciate if you, or James, can illustrate how the Gamma factor can be derived without using the absolute model.

Tom

Tom,

<i>L an T would be distance and time without the effects of time dilation and length contraction, while L0 and T0 would be distance and time after the effects of time dilation.</i>

So, who measures L and T, and who measures L0 and T0? Are these different quantities actually observed by any observer, or are they a mathematical game, in your opinion?

James,

So, who measures L and T, and who measures L0 and T0? Are these different quantities actually observed by any observer, or are they a mathematical game, in your opinion?

It all depends what the observer, who is measuring distance and time, assumes.

If the observer assumes that the average speed of the roundtrip of light is equal to (c^2-v^2)/c, as derived from the absolute model, then the observer will always measure distance to be L and time to be T in any frame of reference. And the values for L and T would remain constant regardless of speed.

However, if the observer assumes that the average speed of the roundtrip of light is always equal to c in all frames of reference(therefore, the one-way speed of light is equal to c in all frames of reference), as dictated by relativity, the observer will measure L0 as distance and T0 as time. L0 and T0 will change depending on speed.

Tom

I stayed away for as long as I could, but I am astounded that this has not been straightened out yet.


I was previously explaining to Tom2 that relativity contradicts itself. The formulas used for time dilation and length contraction are simply patches to a hole that was created by the absolute model.


And Tom2 was previously explaining to you that you are misrepresenting special relativity. Not only that, it seems that you misunderstand the "absolute model", because you presented the following website in support of it:

http://www.physics.wustl.edu/~visse...ight-clock.html

which is obviously in accordance with special relativity.

I'm sure you haven't looked at the relativity document I linked you to, and you probably won't in the future, but I'm going to post a link to it here just in case anyone else is interested in learning something today:

http://www.fourmilab.ch/etexts/einstein/specrel/www/


In other words, the patch is proof that there's a hole, and the hole is proof that the absolute model is correct, and that relativity is wrong.


As a side note, I should interject that this is the first of your many non-sequitirs. Aside from the fact that there is no hole in relativity, even if there were, that would not prove your theory, because there are multiple theories competing with relativity. As we shall see shortly, yours is not one of them, because "your theory" is really just special relativity.


First, assume you have two mirrors, and there is light bouncing back and forth between the mirrors. Now let's say that you start moving the mirrors forward, so that the motion of the mirrors is parallel with the motion of the light (the direction doesn't matter).

According to the ABSOLUTE model, the time it takes for the light to reach the mirror that is moving away from it is longer:

t1=d/(c-v)

where d is the distance between the mirrors and v is the speed of the moving mirrors.

But the time it takes for the light to reach the mirror that is moving towards it is shorter:

t2=d/(c+v)


This part is important:
You have assumed that the speed of the light pulse is the same in both directions, despite the fact that you claim you have not. Your derivation is EXACTLY in accordance with special relativity.

It should be no surprise, then, that you obtain the relativistic result.

In an absolute model, the person watching the moving mirrors would observe the exact same time for the round trip as would a person riding alongside the mirrors.

Stationary observer:

Upward-moving light pulse has speed v+c. Pulse travels distance l1=d+vt1.
=>t1=l1/(c+v)=(d+vt1)/(c+v)

rearranging yields

t1=d/c (surprise, surprise)

Downward-moving light pulse has speed v-c. Pulse travels distance l2=d-vt2.
=>t2=l2/(v-c)=(d-vt2)/(v-c)

rearranging yields

t2=d/c.

This is exactly what would be observed by someone moving along with the mirrors, or anyone else, for that matter in the "absolute" model.

This is taught in any freshman physics textbook.

Tom

Tom2,


You have assumed that the speed of the light pulse is the same in both directions, despite the fact that you claim you have not. Your derivation is EXACTLY in accordance with special relativity.

WRONG. I claimed that the speed of light is only c in the absolute frame of reference. Relative to the moving mirrors, the speed of light is SLOWER or FASTER than c. Relativity dictates that the speed of light is c in ALL frames of reference. (c+v) and (c-v) clearly show that I DON't think that the speed of light is c relative to the mirrors.

Stationary observer:

Upward-moving light pulse has speed v+c. Pulse travels distance l1=d+vt1.
=>t1=l1/(c+v)=(d+vt1)/(c+v)

rearranging yields

t1=d/c (surprise, surprise)




What kind of phony math is that???

Either the speed is c and the distance is d+vt1, or the speed is c+v and the distance is d. Where the hell did you get the idea to increase the speed AND the distance at the same time. Any moron could see that it would balance out if you did it that way.

I know you didn't make this mistake accidently. I'm surprised that you would provide faulty math to try to prove your point.

Tom

for all v: t1=d/c

try (d+vt1)/(c+v) = d/c ?
you will get
(1+(vt1/d)) / (1+(v/c)) = 1
thus
1+ (vt1)/d = 1+ (v/c)
vt1/d = v/c
t1=d/c

blablablabla

quote:
--------------------------------------------------------------------------------
You have assumed that the speed of the light pulse is the same in both directions, despite the fact that you claim you have not. Your derivation is EXACTLY in accordance with special relativity.
--------------------------------------------------------------------------------



WRONG. I claimed that the speed of light is only c in the absolute frame of reference. Relative to the moving mirrors, the speed of light is SLOWER or FASTER than c. Relativity dictates that the speed of light is c in ALL frames of reference. (c+v) and (c-v) clearly show that I DON't think that the speed of light is c relative to the mirrors.


No, it doesn't. What it does clearly show is that you do not understand physics or mathematics. Furthermore, the bogus conclusion you draw from your "analysis" clearly shows that you don't understand logic, either.

Relativity
Assume that the speed of light is as Einstein says and look at it from the frame in which the mirrors are moving along the y-axis.

Event 1:
Pulse leaves lower mirror at y1=0, t1=0.

Event 2:
Pulse arrives at upper mirror, traveling at speed c. This event occurs at y2=d+vt2, because the upper mirror has moved a distance vt2. It is also the case that y2=ct2. Equating the two expressions for y2 yields:

d+vt2=ct2==>t2=d/(c-v)

Event 3:
Reflected pulse returns to lower mirror. It starts at y2 and travels in the -y direction for a time (t3-t2) at speed c. This yields:

y3-y2=-c(t3-t2)

It is also the case that y3-y2=-d+v(t3-t2), because the light traverses the distance d minus the distance that the lower mirror moves. Equating the two yields:

-d+v(t3-t2)=-c(t3-t2)
(c+v)(t3-t2)=d==>(t3-t2)=d/(c+v)

So yes, you did assume Einstein's speed of light postulate--Like it or not.


quote:
--------------------------------------------------------------------------------
Stationary observer:

Upward-moving light pulse has speed v+c. Pulse travels distance l1=d+vt1.
=>t1=l1/(c+v)=(d+vt1)/(c+v)

rearranging yields

t1=d/c (surprise, surprise)



--------------------------------------------------------------------------------



What kind of phony math is that???

Either the speed is c and the distance is d+vt1, or the speed is c+v and the distance is d. Where the hell did you get the idea to increase the speed AND the distance at the same time. Any moron could see that it would balance out if you did it that way.


Then why don't you get it?


I know you didn't make this mistake accidently. I'm surprised that you would provide faulty math to try to prove your point.


There's no mistake--that's the correct analysis.

I'm sorry that you have no understanding of Physics I or of Algebra I, but that's no reason to accuse me of trying to trick anyone.

Why don't you go get yourself an education? Maybe you can pull yourself out of Krackpot Korner one of these days. Until then, maybe you should think about not posting your "theories" in public. Not only do they damage the credibility of sciforums, but they also pose a risk to impressionable young people who come here to try to learn something.

Tom

Tom2,

Pulse arrives at upper mirror, traveling at speed c. This event occurs at y2=d+vt2, because the upper mirror has moved a distance vt2.

You're an idiot. Relativity dictates that it doesn't matter how fast the mirrors are moving, since the speed of light is c in ALL frames of reference. By incorporating vt2 in your formula, you are applying the absolute model. In the relative model, y2 always equals d regardless of the speed of the mirrors. That's why relativity is called relativity.

Tom

Just stopped by to see what was up at sciforums. Not much, apparently. Same old debates... LOL

Ok, with all due respect to all participants in this thread, I think you all have taken this discussion far beyond the elementary level at which it can be easily resolved. You don't need math for it; just some common sense.

The principal point in question is: why should the speed of light in a vacuum (between the mirrors) depend on the velocity of the mirrors through that vacuum? The two phenomena (light propagating through vacuum; mirrors propagating through vacuum) are completely independent from each other. If there is one and only one vacuum, then the speed of light in that vacuum is an absolute constant. This is the "absolute" reference frame Tom (Prosoothus) is talking about.

Any other reference frame is defined by dragging the coordinate system along with a matter/energy body propagating through the vacuum. If time and space are defined in absolute terms using the vacuum as the basis, then obviously they do not change no matter how you decide to translate your coordinate system (ignoring gravity for this discussion, since we are focusing on special relativity as opposed to GR.) For moving observers, the only thing that can change is their perceptions of time and distance. IOW, the time dilation and length contraction formulae are mathematical descriptions of the illusions suffered by moving observers.

These illusions are bred by the facts that
<ol>
<li>there is one and only one vacuum in which everything exists, and</li>
<li>that the speed of light in that vacuum is constant omnidirectionally</li>
</ol>

Based on these two assumptions (which are indeed not relativistic philosophically speaking in that they dictate existence of an absolute reference frame -- namely the vacuum) I've already derived the Lorentz transformations in the time dilation/length contraction form before on this forum, and Tom came quite a way to repeating my derivation.

Note that due to the assumption (2), this absolute-frame theory is not Newtonian. In a Newtonian universe, there would be no limit on speed of light; if a moving locomotive shone a light forward, then that light's velocity would truly, really be v+c in an absolute sense. The second assumption makes the model non-Newtonian and indeed makes it possible for a Relativistic (illusionist) theory to be valid.

Fact is, however, that there is no known way for us to detect the absolute reference frame of the vacuum, IOW we cannot determine whether an object is absolutely stationary or merely moving inertially. Thus, for all practical purposes SR works. However, from the perspective of interpretation and comprehension, SR's conceptualization of the illusory effects as in fact real is both deceptive and counterproductive as far as comprehensibility goes.

James, Crisp, Q, and Overdoze,

Assuming this experiment is done:

You have clock A and clock B. They are both next to each other on Earth (they are relatively stationairy). Their times are synchronized. Suddenly, clock B speeds away from clock A, and the Earth, at a speed of .90c. Clock B continues to travel at this speed for one year, and then turns around and travels back to clock A, at .90c, for another year. When clock B returns to clock A, clock B comes to rest (it falls into the same frame of reference as clock A and the Earth).

When the times of the two clocks are compared, what, according to relativity, will be found:

1) Clock A is slower than clock B
2) Clock B is slower than clock A
3) Clock A is synchronized with clock B

I don't need to know how much one clock is faster than the other, I just need to know which one is faster. Thanks.

Tom

overdoze:

Neat explanation. A thought though:

However, from the perspective of interpretation and comprehension, SR's conceptualization of the illusory effects as in fact real is both deceptive and counterproductive as far as comprehensibility goes.

I see it the other way around, that conceptualizing the relativistic effects as illusory is deceptive and counterproductive. The reason being that the effects are just as real as anything else we label as “real.” For example, in the twin paradox, which is explainable within the realm of SR, the reunited traveling twin (or atomic clock or whatever) is younger in a real, tangible way. When the reality of the effects is accepted, the absolute frame of reference becomes an artifact to explain why it isn’t detectable.

Having accepted the reality, one can move on to be productive in other areas such as cosmology. For example, at this site about models of the universe…

http://www.cosmologymodels.com/index2.html

…is this quote: “There is a problem with this [special relativity universe] model. Consider a galaxy rushing away from us at a constant velocity of very nearly the speed of light. Light that it emitted when the universe was half as old as it is now would just be getting to us now and we could not have a lookback time … greater than half the age of the universe. We find we are able to see much further back in time than this.”

Because the author ignores or otherwise doesn’t accept the reality of SR effects, he sees a problem where there isn't one. Galaxies rushing away from us at relativistic velocities would really, tangibly be hardly aging relative to us, so, despite the travel time of the light, we could observe them at any age, even prior to the formation of the galaxy, all the way back to the first observable moments after the big bang (the cosmic microwave background radiation).

Originally posted by Prosoothus
You have clock A and clock B. They are both next to each other on Earth (they are relatively stationairy). Their times are synchronized. Suddenly, clock B speeds away from clock A, and ... then turns around and travels back to clock A ... When the times of the two clocks are compared, what, according to relativity, will be found:

1) Clock A is slower than clock B
2) Clock B is slower than clock A
3) Clock A is synchronized with clock B


The answer is 2). This is due to the fact that clock B is the one that made the round-trip. If instead A sped up so as to catch up with B, then 1) would be true. It is also possible for B to decelerate and A to accelerate and catch up to it in such a way that 3) would hold. Depends on who is doing the most accelerating.

Originally posted by zanket
The reason being that the effects are just as real as anything else we label as “real.” For example, in the twin paradox, which is explainable within the realm of SR, the reunited traveling twin (or atomic clock or whatever) is younger in a real, tangible way.


Ok, consider rates of metabolism in a reptilian. You can chill it so that its metabolism goes really slow and its perception of the passage of time slows down accordingly. Or you can warm it up so its metabolism goes faster. Fact is that the reptilian's life span is going to depend on how fast its metabolism goes, so you can control its lifespan by controlling its temperature. You can even freeze it solid and thaw it back a million years later -- so you can expand its lifespan dramatically.

However, if we took the analogy to relativity toward its typical extreme, we would have to claim that by cooling down the reptilian we are actually slowing down the flow of time in its reference frame. You might find that acceptable, but I find that ludicrous. All we did was slow down the rate of reactions -- and by slowing down this rate, we've slowed down the reptilian's measurements of time. So even though the universe continues to evolve at the same rate as ever, the reptilian's structure is evolving slower than normal due to the "suspension" we introduced through lower temperature.

It's the same thing with moving objects. In moving objects, quantum interactions limited to light-speed take longer to occur between any two objects separated by a given distance than if these objects were absolutely at rest. This is easy to show just by considering a fixed distance between the objects, and calculating the roundtrip time between them using the speed of light as the speed of force carriers. Thus, in moving objects everything must happen slower -- but more so along direction of motion than orthogonal to it. This assymetry gives rise to "length contraction" in addition to overall "time dilation".


When the reality of the effects is accepted, the absolute frame of reference becomes an artifact to explain why it isn’t detectable.


Nobody disputes the reality of the effects. The point is interpretation. Classical relativity requires us to accept the mind-bending concept of each distinct reference frame having its own time and space manifold. This, despite the fact that all these distinct reference frames must coexist within the same universe. Classical relativity allows for retrograde time travel (at least mathematically) -- but when time is considered as a universal process of change and given that only measurements of it can slow down relative to absolute rest, then it becomes glaringly obvious that time travel is impossible. You might be able to see how this easily eliminates all of the paradoxes with time travel in one fell swoop. Time really ceases to be a dimension or a coordinate; it merely becomes a measurement of reaction rate relative to the absolute.


Galaxies rushing away from us at relativistic velocities would really, tangibly be hardly aging relative to us, so, despite the travel time of the light, we could observe them at any age, even prior to the formation of the galaxy, all the way back to the first observable moments after the big bang (the cosmic microwave background radiation)

That is actually incorrect. The "rushing" is due to expansion of spacetime between galaxies, and not to the galaxies' actual velocities through spacetime relative to each other. For any two galaxies to actually be moving relative to each other at relativistic speeds would be astonishingly unlikely, considering that galaxies tend to form from rarefied matter initially spread evenly through the universe, hence upon collapse averaging all the velocities of individual particles to something close to absolute rest. Only later intergalactic gravitational interactions can set galaxies in motion relative to each other, and such interactions hardly result in relativistic speeds.

When the times of the two clocks are compared, what, according to relativity, will be found

When clock B arrives back on Earth, both clocks at rest relative to each other will be ticking at the same rate however, clock B will have ticked slower during its journey therefore, clock B will show less time had passed relative to clock A.

Hi Overdoze,

I find it strange that as a relativist, you seem to opt for an absolute frame of reference. However, all ingredients for complete relativity (no absolute FOR) are in your post:

"In moving objects, quantum interactions limited to light-speed take longer to occur between any two objects separated by a given distance than if these objects were absolutely at rest. - ... - . Thus, in moving objects everything must happen slower"

On the other hand:

"but when time is considered as a universal process of change and given that only measurements of it can slow down relative to absolute rest."

On one side, I think you are saying that time dilatation for an observer is an illusion (time goes slower relative to some absolute timescale), while on the other hand you agree that all quantum processes occur slower because of the finite interaction speed.

Two remarks/questions:

1) How do you account for additional terms in the Lorentz transformations that are not related to length contraction or time dilatation ? These terms additionally "slow" time, and are unrelated to finite interaction speed.

2) If all quantum processes occur slower, then wouldn't also the perception of this "absolute time" you propose slow down for the time-dilatated observer ?

As you probably have guessed, I am not in favour of an absolute frame of reference (or absolute timescale if you like). You seem to have thought things over quite a bit, and I really am interested on what your answers on the above questions will be :).


Tom,

The question you proposed is basically the twin paradox. There are several possible answers (depending on whether you use special or general relativity). Concerning special relativity, the moving clock (B) would be running behind clock A (left on earth). However, if I remember correctly, if you take General Relativity into account, the answer is different. Unfortunately I haven't been initiated in GR, so I guess we'll have to wait for someone knowing the theory to resolve that issue :).


Bye!

Crisp

overdoze:

Ok, consider rates of metabolism in a reptilian. ...

That’s an interesting analogy but too apples-to-oranges. Whereas the chilled reptile’s structure would evolve slower than normal in its reference frame, a fast-moving reptile’s structure would evolve normally in its frame, just slower relative to us. A watch either reptile wears could evidence that.

In moving objects, quantum interactions limited to light-speed take longer to occur between any two objects separated by a given distance than if these objects were absolutely at rest. This is easy to show just by considering a fixed distance between the objects, and calculating the roundtrip time between them using the speed of light as the speed of force carriers. Thus, in moving objects everything must happen slower ...

The slowdown caused by the time required for light or a force to travel between objects moving apart is a Doppler effect and was well understood when relativity came along. Time distortion is observable regardless of the changing distance between objects. For example, a diagram in one of my books shows one ship circling another. The caption is “The top vessel in this diagram moves in a circle of very large radius around the bottom vessel. Since the two ships are always the same distance from each other, we observe no Doppler effect, but we still see relativistic time distortion.” Also “... while Doppler shifts are the result of changes in spatial separation, the relativistic effect is an actual reduction in the rate of time.” Keep in mind that when objects are moving towards each other, the Doppler effect is a quickening rather than a slowdown.

Classical relativity requires us to accept the mind-bending concept of each distinct reference frame having its own time and space manifold. This, despite the fact that all these distinct reference frames must coexist within the same universe.

So bend your mind already! :p

Classical relativity allows for retrograde time travel (at least mathematically) -- but when time is considered as a universal process of change and given that only measurements of it can slow down relative to absolute rest, then it becomes glaringly obvious that time travel is impossible.

Perhaps, or you could say that time can actually slow down relative to you, yet it remains glaringly obvious that backwards time travel is impossible.

The "rushing" is due to expansion of spacetime between galaxies, and not to the galaxies' actual velocities through spacetime relative to each other.

Many references say that, but when you examine their reasoning it’s based on speculation.

For any two galaxies to actually be moving relative to each other at relativistic speeds would be astonishingly unlikely, considering that galaxies tend to form from rarefied matter initially spread evenly through the universe, hence upon collapse averaging all the velocities of individual particles to something close to absolute rest. Only later intergalactic gravitational interactions can set galaxies in motion relative to each other, and such interactions hardly result in relativistic speeds.

I disagree about the odds on both counts. A rough calculation tells me that cosmic expansion in a region of space the size of our galaxy is only 2 km/s. On a galactic or even a supercluster scale, then, gravity far overwhelms the expansion to allow the galaxies to form from rarefied matter initially spread evenly throughout the universe. Nature could have initially set all matter in relatively expanding motion (where every piece of matter is moving relative to the other pieces at velocities ranging from 0 to a limit of c, the faster the remoter) and let gravity coalesce matter as it may, which would be only within pockets of space small enough to allow the gravity to overwhelm the expansion.

Nobody disputes the reality of the effects. The point is interpretation.

Yep, and it’s always debatable. Regarding cosmological time distortion, I prefer this interpretation from one of my books: “What is the age of the universe now? You can’t really answer that question. ... You can’t assign an age to the whole universe if its parts are in motion relative to each other. Each part has its own proper age. Note that this is not because it takes time for the light to get from the distant parts to you. It is because the ever remoter parts are in ever more rapid motion relative to you.”

Q, Crisp, and Overdoze,

Quote frome Overdoze:

The answer is 2). This is due to the fact that clock B is the one that made the round-trip. If instead A sped up so as to catch up with B, then 1) would be true. It is also possible for B to decelerate and A to accelerate and catch up to it in such a way that 3) would hold. Depends on who is doing the most accelerating.

Quote from Q:

When clock B arrives back on Earth, both clocks at rest relative to each other will be ticking at the same rate however, clock B will have ticked slower during its journey therefore, clock B will show less time had passed relative to clock A.

Quote from Crisp,

Concerning special relativity, the moving clock (B) would be running behind clock A (left on earth). However, if I remember correctly, if you take General Relativity into account, the answer is different.

I don't understand??:bugeye:

According to clock B's frame of reference, the Earth and clock A sped away at .90c from clock B, while clock B remained stationairy. Why is it that clock B is slower than clock A, and not vice versa?? Doesn't relativity dictate that both of the frames of reference (clock A's and clock B's) are equally valid???

The reason I brought up this "experiment", was that if it's true what the three of you said, then clock B was ticking slower than clock A because it was travelling faster than clock A in the absolute frame of reference. This would mean that the absolute motion (which overdoze argues can't be determined) of a clock can be derived from the "perceived" time dilation it is experiencing, compared to the time of the stationairy clock.

Example: If you have two clocks (A and B), and clock B begins to travel at .90c, the difference between the time dilations of the two clocks would be the time dilation factor dictated by relativity ONLY if the clock A was at absolute rest. However, if the time dilation between the two clocks is smaller than the time dilation dictated by relativity, that would mean that clock A is not stationairy in the absolute frame of reference, but that it is moving in the opposite direction of clock B in the absolute frame of reference.

Tom

Originally posted by Crisp
On one side, I think you are saying that time dilatation for an observer is an illusion (time goes slower relative to some absolute timescale), while on the other hand you agree that all quantum processes occur slower because of the finite interaction speed.


Yes, I see how I might have confused you. :)

Perhaps this might help. I consider two aspects of reality: the actual reality, and measurements of it. This applies to time just as well as to anything else. Thus, there is the actual flow of time, and then there are measurements of it made by observers.

If an observer's measurement of time is distorted so as to make time flow slower for the observer, then the observer will in fact experience a slower reaction rate. This effect is both illusion and reality, in that it is real for the observer (everything happens slower) but at the same time it is illusory (since time never in fact slowed down; light is still propagating at the same rate even in the observer's frame of reference -- it's only the bidirectional, roundtrip, propagation interval between any two relatively fixed points that increases for the moving observer.)


1) How do you account for additional terms in the Lorentz transformations that are not related to length contraction or time dilatation ? These terms additionally "slow" time, and are unrelated to finite interaction speed.


If you consider the Lorentz transformations in the time dilation/length contraction form, then there are no additional terms to account for. If you recall, I've already derived these transformations on this forum before. See here:

http://www.sciforums.com/showthread.php?s=&threadid=7801&perpage=20&pagenumber=8#post124437

On the other hand, if you're talking about the general form of the transformations that includes the initial separation between events and allows to actually calculate the time of observing a remote event for a given inertial observer, then the additional terms merely have to do with this initial separation between the observer and the event.


2) If all quantum processes occur slower, then wouldn't also the perception of this "absolute time" you propose slow down for the time-dilatated observer ?


This would be a qualified yes. In fact, not all quantum processes occur slower. Conspicuously, light itself is not affected. Rather, it is all the processes that depend on exchange of information (e.g. through virtual force carriers) that must slow down. This is only due to the extended time interval over which these exchanges can occur, due to the system's motion relative to the medium through which light propagates (the vacuum.) Note that in mentioning "slowing down" and "extended time intervals", I am inherently using the notion of absolute time. Thus no manner of motion could ever affect this absolute, universal time flow; all you can ever accomplish is to slow down reactions in a system by setting it in motion with respect to the absolute reference frame.

Originally posted by zanket
That’s an interesting analogy but too apples-to-oranges. Whereas the chilled reptile’s structure would evolve slower than normal in its reference frame, a fast-moving reptile’s structure would evolve normally in its frame, just slower relative to us. A watch either reptile wears could evidence that.


Apples and oranges are still fruits. And I'm comparing fruits to fruits. The point was that just as frost has a retarding effect on the chemical reaction rates in a lizard, so does motion relative to absolute rest have a retarding effect on the quantum reaction rates of any massive object.


The slowdown caused by the time required for light or a force to travel between objects moving apart is a Doppler effect and was well understood when relativity came along.


You misunderstood me. I was not talking about objects moving apart. Rather, I'm talking about objects moving together, maintaining constant distance between each other.


Many references say that, but when you examine their reasoning it’s based on speculation. [with respect to spacetime expansion - overdoze]


It's the only reasonable conclusion. The alternative is that we are at the center of the universe, and the rest of the universe is flying away from us. If you take such a primitive, anisotropic, geocentric view, then I can see your point. However, if you assume that our region of space is not special in any way, then the same picture of cosmic expansion away from the observer must be in evidence no matter where in space the observer is located. Given that matter's speed of propagation through space is limited to below c, the only way this could work is if the space itself expanded rather than galaxies flying away from each other through rigid space (otherwise, galaxies farther and farther away from us would eventually have to fly through space at speeds faster than c.)


A rough calculation tells me that cosmic expansion in a region of space the size of our galaxy is only 2 km/s. On a galactic or even a supercluster scale, then, gravity far overwhelms the expansion to allow the galaxies to form from rarefied matter initially spread evenly throughout the universe.


I don't pretend to know which calculation you are referring to, but let's just work with your figure. Our galaxy is roughly 100,000 light years across. The distance between two typical galaxies in a cluster is perhaps 1,000,000 light years. At this scale, the expansion would result in 20 km/s. If you take something 15,000,000,000 light years away, it would be traveling away from the observer at 300,000 km/s (lightspeed.) Anything farther than 15 billion light years would actually recede faster than speed of light, which means we will never ever be able to see it. This would be the horizon of the observable universe (for the given expansion rate) -- where "observable" means observable in principle, even in the remotest future. Granted, the figures above are all ballpark estimates, but hopefully you get the idea.


“What is the age of the universe now? You can’t really answer that question. ... You can’t assign an age to the whole universe if its parts are in motion relative to each other. Each part has its own proper age. Note that this is not because it takes time for the light to get from the distant parts to you. It is because the ever remoter parts are in ever more rapid motion relative to you.”


There is a good point here, but I don't think it's entirely correct. Given an assumption that space expands everywhere uniformly, you can start with the observed local densities of matter and work backwards, considering interactions between the inflationary force, momentum, and gravity, and working with the best estimates of the past history of the inflationary force obtained from averaging observations of distant cosmological objects. You would be able to calculate roughly the point back in time when all currently observable matter was crammed together in densities and temperatures approaching infinity. The time interval between then and now would then be roughly the age of the universe.

Originally posted by Prosoothus
Doesn't relativity dictate that both of the frames of reference (clock A's and clock B's) are equally valid???


But they are not equal. Special relativity only discusses inertial reference frames. In your example, clock B is accelerating while clock A is not. This makes all the difference.


The reason I brought up this "experiment", was that if it's true what the three of you said, then clock B was ticking slower than clock A because it was travelling faster than clock A in the absolute frame of reference.


Not exactly. Clock B was traveling faster with respect to the absolute frame of reference on average during its entire trajectory. This means, for example, that it might have been moving slower when it was moving away from A, but moving super-fast when it was returning to A. Or maybe it was moving super-fast when it was moving away from A and slow when it was returning to A. Or any other possibility in between. The reason it works out the same in either case, is due to the symmetry introduced by B's looping trajectory.

Overdoze,

But they are not equal. Special relativity only discusses inertial reference frames. In your example, clock B is accelerating while clock A is not. This makes all the difference.

How do you know that B was accelerating from A??? Why are you so sure that A wasn't accelerating from B???How are you determining which clock is stationairy, and which one is accelerating??

One more thing: For the sake of simplicity, assume that there is no accelleration. Assume that clock B's speed increases from 0 to .90c instantaneously.

Tom

Originally posted by Prosoothus
How do you know that B was accelerating from A???


Because B will feel the artificial gravity, and A will not.


One more thing: For the sake of simplicity, assume that there is no accelleration. Assume that clock B's speed increases from 0 to .90c instantaneously.


The time course of acceleration doesn't matter. See the second part of my reply above. That explains the true relevance behind acceleration.

Clock B will experience acceleration on the outbound trip as well as the return trip. According to GR, objects will experience time dilation effects within a gravity well, relative to another observer.

gLT/c^2

g = acceleration due to gravity
L = distance between observers
T = length of time of gravitational effects
c = well, you know this one.

Overdoze,

Because B will feel the artificial gravity, and A will not.

True, but how will B know if it is accelerating or decellerating?

Tom

Originally posted by Prosoothus
but how will B know if it is accelerating or decellerating?


That's irrelevant, as previously explained, due to the symmetry of B's trajectory. IOW, at some point in its trajectory it may be accelerating; if so, it will have to be decelerating at some other point so as to return to A. (Note: here I'm using "accelerating" in the sense of a positive change in speed, rather than the more proper mathematical sense of changing velocity.)

Overdoze,

Do you agree that the time dilation a clock experiences is based on it's speed relative to the absolute frame of reference?

If so, wouldn't you be able to take two clocks travelling at different speeds, and determine their absolute speeds by using their time dilations and their relative speeds to one another??

Tom

Prosoothus

If so, wouldn't you be able to take two clocks travelling at different speeds, and determine their absolute speeds by using their time dilations and their relative speeds to one another??

You are soooo close to proving to yourself there is no absolute frame of reference. ;)

Originally posted by Prosoothus
Do you agree that the time dilation a clock experiences is based on it's speed relative to the absolute frame of reference?


That's correct, with the qualification that we're talking about the so-called proper time of the clock (as opposed to its time as observed by some other inertial observer.)


If so, wouldn't you be able to take two clocks travelling at different speeds, and determine their absolute speeds by using their time dilations and their relative speeds to one another??


No, because their observations of each other would be mutually symmetrical. This is a property of the Lorentz transformations. That is, if an object X is Lorentz-transformed with respect to you as the observer, then you will appear identically Lorentz-transformed to object X with X as the observer.

Overdoze,

Let me try to prove my point:

Experiment 2:

You have three clocks on Earth. One is stationairy, while the other two (A and B) travel away from Earth at .45c in opposite directions (A and B are travelling at .90c away from each other). After a long trip, they turn around and come back to Earth. When the observer on Earth reads them, what will the result be:

1) Clock A is slower than clock B
2) Clock B is slower than clock A
3) Clocks A and B are still synchronized.

Tom

The answer is 3) -- assuming both clocks turn back after the same time interval as individually measured by each of them. Again, symmetry comes into play.

Overdoze,

I see your point. Your claiming that the time dilation averages out due to the roundtrip of the clock(s). I assume that if it was a one-way trip, the absolute motions can be derived from the clocks readings.

Tom

Originally posted by Prosoothus
Your claiming that the time dilation averages out due to the roundtrip of the clock(s). I assume that if it was a one-way trip, the absolute motions can be derived from the clocks readings.


Except the irony is, there is no way for the clocks to see each other's reading without a roundtrip being involved. If the clocks themselves don't turn around and meet up, then the signals they send to each other will serve as their proxies to complete the "roundtrip". In either case, information is making roundtrips, and it's at this more abstract and universal level that most relativists think. IOW, the statement about speed of light ends up being translated into a statement about information propagation and everything else gets recast accordingly in terms of information transfers.

overdoze:

However, if you assume that our region of space is not special in any way, then the same picture of cosmic expansion away from the observer must be in evidence no matter where in space the observer is located. Given that matter's speed of propagation through space is limited to below c, the only way this could work is if the space itself expanded rather than galaxies flying away from each other through rigid space (otherwise, galaxies farther and farther away from us would eventually have to fly through space at speeds faster than c.)

They wouldn’t have to exceed c. If it can be accepted that the universe is infinite in extent, it is only a step further to see that the universe might be infinite in a (special) relativistic way, where the furthest galaxy is moving at .9(infinite number of 9’s)c. Just like no galaxy need be the last galaxy in an infinite universe, no galaxy need exceed c--an approachable not attainable limit just like infinity--in a relativistic universe. Such a universe adheres to the cosmological principle and seems simpler and more consistent to me than the models cosmologists propose today. It also more closely matches what we observe (namely a flat universe).

Remember that when you add velocities in relativity, you get less than their sum. In a relativistic universe, if the galaxies were equally spaced and every galaxy was receding from its closest neighbor at v, the furthest galaxies from you would not exceed c relative to you. Every galaxy would observe the universe as fairly uniform in structure at each successive radius in every direction, just like we do.

Anything farther than 15 billion light years would actually recede faster than speed of light, which means we will never ever be able to see it. This would be the horizon of the observable universe (for the given expansion rate) -- where "observable" means observable in principle, even in the remotest future.

That is actually what cosmologists propose. But it need not be that way. It could be that 15 billion light years away the galaxies are receding at .9(millions of 9’s)c and 30 billion light years they are receding at .9(billions of 9’s)c. And so on and true for every observer in the universe. This would make the entire universe--even if infinite in extent—theoretically observable at ages ranging from the first observable moments (background radiation) to the present, which is you.

You would be able to calculate roughly the point back in time when all currently observable matter was crammed together in densities and temperatures approaching infinity. The time interval between then and now would then be roughly the age of the universe.

There’s no incompatibility with big bang theory. The age of the universe is calculated by us, we who are the oldest beings in it as we observe it. Most everything else, because it is receding from us, is aging slower to be younger. Everything could still have been simultaneously born. In the twin paradox, the twins can agree both that the traveling twin is years younger and that they were born on the same day.

Regarding the twin paradox:

Many books will tell you that the traveling twin is younger because he accelerated and leave it at that. Or they might elaborate to say that the traveling twin feels the equivalent of a gravitational field during acceleration and gravity slows clocks. Or they might erroneously say that all the time distortion occurred during the traveling twin’s acceleration. There is an intuitive way to view the paradox, no tensor calculus required. Here is the step-by-step:

Treat each twin as moving, relative to the other twin taken as stationary. Ask yourself, what is each twin moving relative to? The stay-at-home twin is moving relative only to the traveling twin. The traveling twin, on the other hand, is moving relative to both the stay-at-home twin and the space between the twins.

Both twins are accelerating, relative to each other. That only the traveling twin feels the acceleration is important only to discern who is moving relative to the space between the twins. He who feels the acceleration, accelerates relative to all of space along his axis of motion, this axis including his twin. He who doesn’t, accelerates relative only to his twin.

Special relativity tells us that moving objects contract along their axis of motion. That applies to the twins. The stay-at-home twin observes that the traveling twin is contracted along his axis of motion. The traveling twin, by virtue of moving relative to all of space along his axis of motion, observes this entire axis including the stay-at-home twin contracted.

Ask yourself, what proper distance is each twin traversing? (“Proper” means “as measured by an observer in his own reference frame.”) If the stay-at-home twin observes that the traveling twin made a 1-unit round trip, the traveling twin observes himself traversing less than that distance, because proper distance is contracted along his axis of motion, and the twins' trips are otherwise symmetrical. The traveling twin moves through a contracted version of the stay-at-home twin’s space. That is how the twins' trips are asymmetrical. Both twins have accurate clocks that measure the elapsed proper time away from each other. The traveling twin’s clock shows less elapsed proper time upon reuniting, for the simple reason that the traveling twin traverses less distance than the stay-at-home twin. The clock is like an odometer.

I agree with you, yet consider Relitivity (E=mc2) being applied to light its-self. Then what happens.

Uh-oh, I feel a "does light have mass" thread coming up :)

Originally posted by Prosoothus
Relativity dictates that it doesn't matter how fast the mirrors are moving, since the speed of light is c in ALL frames of reference.


Yes, that’s right. The difference between us is that I know how to correctly implement that into a mathematical analysis, whereas you do not.


By incorporating vt2 in your formula, you are applying the absolute model. In the relative model, y2 always equals d regardless of the speed of the mirrors.


I don’t know whether to laugh or scream.

Your statement above is incorrect. The speed of light postulate does not say that the distance traveled by a light pulse is the same in all frames of reference! It says that the speed (gasp!) of the light pulse is the same for all frames of reference (duh!).

If our observer is watching the mirrors move past him at speed ‘v’, and he determines that the mirrors are separated by a distance ‘d’, then there is no way he could possibly determine that the light traveled a distance ‘d’, because the top mirror moves from its original position while the pulse is in transit. More precisely, the top mirror moves a distance vt2, and so the light pulse must move that additional distance to catch it.

Your mistake is that you made an assumption that is not implied by relativity, namely invariance of the spatial interval traversed by the light pulse. This is such an elementary point that I am really quite shocked that you haven’t gotten it by now. It seems clear that relativity is a subject that you not only do not know, but also do not want to learn. That really is too bad for you, because you’re going to continue to look like a jackass every time you misrepresent it—especially because I linked you to Einstein’s paper 2 or 3 times already. You really have no excuse.



That's why relativity is called relativity.


I don’t need you to tell me what relativity is. I could teach you a great deal about this subject, but you are so dead-set against learning anything that disagrees with your preconceived notions that you won’t have it. I recently read through the “Unrelative Relativity I and II” threads. Your attitude towards education is very childish, as it seems to be “Don’t confuse me with the facts, because I’ve already made up my mind.”

If you could just get beyond this ridiculous “relativity is illogical” mantra that you keep repeating, you would start making some progress in your understanding.


You're an idiot.


And you would be funny, if you weren’t such a sad case. You seem to really enjoy your total ignorance of math, physics and logic. That is the only reasonable explanation of why you consistently and categorically reject one valid post after another by people who are only trying to correct your misunderstanding. At least you appear to be listening to overdoze--there may be hope for you yet.

Try to at least learn Algebra I and Physics I. Your Reign of Error has gone on for far too long.

Tom

Originally posted by overdoze
Ok, with all due respect to all participants in this thread, I think you all have taken this discussion far beyond the elementary level at which it can be easily resolved. You don't need math for it; just some common sense.


I disagree with that. The mathematics must be looked at, because Prosoothus is trying to compare special relativity to Galilean relativity. Also, he got both of them wrong, which further warrants a closer look at the math, because his argument flows from his mis-derivation.


The principal point in question is: why should the speed of light in a vacuum (between the mirrors) depend on the velocity of the mirrors through that vacuum?


No, the principal point in question is: "Is relativity internally consistent or not?"

Again, you need the mathematics to settle it.


The two phenomena (light propagating through vacuum; mirrors propagating through vacuum) are completely independent from each other. If there is one and only one vacuum, then the speed of light in that vacuum is an absolute constant. This is the "absolute" reference frame Tom (Prosoothus) is talking about.


I'm not sure that that is correct. Prosoothus made it clear that he espouses Galilean relativity. The frame of absolute rest in that scheme is the frame in which Maxwell's equations take on their textbook form. Is that necessarily the "vacuum frame"? If so, it is not obvious to me.


For moving observers, the only thing that can change is their perceptions of time and distance. IOW, the time dilation and length contraction formulae are mathematical descriptions of the illusions suffered by moving observers.


I definitely don't agree with this. The predictions of the Lorentz transformation are not predictions on what an observer sees, they are predictions of what actually happens in that observer's frame.

A simple example will serve to prove the point. Two events occur simultaneously in frame S. Event 1 is a red flash 3E8m to the right of the origin, and Event 2 is a blue flash 6E8m to the left. Light from Event 1 reaches the origin in 1s, and light from Event 2 reaches the origin in 2s. Thus, the observer sees the events 1s apart, when they are actually simultaneous in his frame.

Tom

Tom2:

I definitely don't agree with this. The predictions of the Lorentz transformation are not predictions on what an observer sees, they are predictions of what actually happens in that observer's frame.

Along those lines, do you see anything wrong in the following story?:

If I am passing by the Earth towards the Andromeda galaxy--some 3 million light years away as measured from the Earth--at a velocity < c relative to the galaxy that will get me there in 1 proper year, my proper distance to the galaxy must be < 1 light year. If I then decelerate in 10 proper years to a full stop relative to the Earth and galaxy by the halfway point between them, my proper distance to the galaxy increases from < 1 light year to 1.5 million light years during the deceleration. Although the galaxy is measurably receding from me at far > c, I continue to receive light from the galaxy, although the light is extremely redshifted.

Uh-oh, I feel a "does light have mass" thread coming up

I don't recall having had a discussion about that :D

prosoothus, overdoze etc. don't you get a headache of this stuff? this seems to be the never ending story on this board
I still think, to say it oversimplistic and short, that relativity discussions is a problem of interpretation of experiments. It's also a discussion about philosophy. I think all relativists are positivists to the bone.

Tom2,

If our observer is watching the mirrors move past him at speed ‘v’, and he determines that the mirrors are separated by a distance ‘d’, then there is no way he could possibly determine that the light traveled a distance ‘d’, because the top mirror moves from its original position while the pulse is in transit. More precisely, the top mirror moves a distance vt2, and so the light pulse must move that additional distance to catch it.

You are comparing the movement of the mirrors to a stationairy observer. Unfortunately, the stationairy observer you are referring to is the absolute frame of reference. Just because you are calling the "absolute frame of reference" an observer, doesn't make your equations relativistic.

You know it's funny, when you first came to sciforums you where actually a person that someone could talk to. Unfortunately, over time, you became a stuck-snob that specializes in personal attacks instead of logical arguments. No, I don't have a PHD in theoretical physics, but I didn't think it was required on sciforums.

I consider it real funny how you claim that my equations and logic are wrong, even though these are the very same equations that overdoze has shown me a few months earlier. Yet I see no personal attacks on overdoze.

I hate to disappoint you, but relativity is not brain surgery. The reason I find relativity so hard to understand is because it's illogical. Sure, relativity can give a nice and cute result when dealing with the round-trip of light. But relativity breaks down when you attempt to apply it to a one-way trip of light.

Finally, let me say that if your convinced that I can't or won't learn, then just disregard my posts. I will disregard your posts, and we will both be happy. After all, I'm sure that you won't lose your job if you can't teach me relativity. :)

Tom

c'est moi,

Welcome back!!! Where have you been???

prosoothus, overdoze etc. don't you get a headache of this stuff? this seems to be the never ending story on this board

Well, I started this thread to continue a discussion I was having with Tom2 (a new poster) an another thread. I also wanted to bring the fact into the open that time dilation and/or length contraction compensate for the variance created by the absolute model. Overdoze was the first to explain this to me, but since his explaination has in the middle of a large thread, I felt it necessary to start a new thread that was exclusively dedicated to the topic.

Tom

Prosoothus

The reason I find relativity so hard to understand is because it's illogical.

Illogical, no. Counter-intuitive, yes. But the fact that you think it's hard to understand is no reason to believe it's wrong.

Sure, relativity can give a nice and cute result when dealing with the round-trip of light. But relativity breaks down when you attempt to apply it to a one-way trip of light.

No, because if it breaks down on a one-way trip, it would always break down. That's not the case.

Finally, let me say that if your convinced that I can't or won't learn, then just disregard my posts.

Where is the fun in that ? ;)

Q,

No, because if it breaks down on a one-way trip, it would always break down. That's not the case.

Let me be more specific:

Let's say you are in a frame of reference moving at .90c. If you shine a light in your frame of reference towards a mirror so that the light reflects and comes back to you, you will find that you only need one time dilation and length contraction to convert the speed of light from c in your frame of reference to c in another frame of reference.

In other words, the Gamma factor (time dilation and length contraction) is required to convert the roundtrip of light from c in one frame of reference to c in another frame of reference in order to preserve the principle of invariance of light.

However, if you don't have a roundtrip of light, but have a one way trip of light in your frame of reference, a single Gamma factor is insuficient for the conversion. If you have your flashlight pointing in multiple directions in your moving frame of reference, you will need to apply a different Gamma factor for every beam of light in order for the conversion to be correct.

I expressed this problem to James in a previous thread, and the only way he found to convert the one-way beams of light shining in multiple directions in a moving frame of reference to another frame of reference, while preserving the principle of invariance of light, was to apply MULTIPLE time dilations to each beam of light in the SAME frame of reference. Unfortunately, as you know, you can't have multiple time dilations in the same frame of reference.

So, as you can see, relativity was meant to compensate for the round-trip of light in a moving frame of reference. It was never meant to compensate for the one-way trip of light in the same frame.

Tom

"Illogical, no. Counter-intuitive, yes."

It is not counter-intuitive. You sit in the train, the other starts moving, but you don't know, it feels like you start moving. Is that counter-intuitive? It's just wrong: do you agree with me that the human body and its senses is not much of a champion compared to other animals? If you'd have better developed senses, you would perfectly know if you were moving or not, regardless of the other train moving. You might for example feel that the wheels below you aren't turning, etc.

Do you agree with me that space has a structure? If your senses would be even more developed, maybe you'd feel the structure around you, just like you can feel a soundwave of a bass resonating in your body. The theory of relativity is an attempt of filling the gap of our shortcomings as observers. That's why many people tend to resist to it. It yields correct results but it's not the whole truth. Philosophically it is incorrect.

"But the fact that you think it's hard to understand is no reason to believe it's wrong. "

it's not hard to understand

Originally posted by Prosoothus:
You are comparing the movement of the mirrors to a stationairy observer. Unfortunately, the stationairy observer you are referring to is the absolute frame of reference. Just because you are calling the "absolute frame of reference" an observer, doesn't make your equations relativistic.


My equations are relativistic because I assume that the speed of light is the same in both directions. I have pointed this out over and over again, and you are still ignoring it.

You claim to adopt the Newtonian/Galilean scheme, and you also claim that you can derive time dilation from it. That is simply not the case, as I have shown. When one further considers that time and space are completely decoupled in the time transformation (IOW, t’=t), your analysis is again overturned.


You know it's funny, when you first came to sciforums you where actually a person that someone could talk to.


And I still am.


Unfortunately, over time, you became a stuck-snob that specializes in personal attacks instead of logical arguments.


Look in the mirror, bub.

I always respond with logical arguments, or at least a reference that contains the argument I wish to present. Over time, I would get responses from you such as “that’s stupid” or “If you don’t see what I’m talking about then I feel sorry for you.” Finally, in this thread you set out to prove that relativity is self-contradictory. I correctly refuted you. Rather than address it, you accused me of dishonesty and called me an idiot.

You set the tone for this, not me. But I am willing to start from square-one if you are.


No, I don't have a PHD in theoretical physics, but I didn't think it was required on sciforums.


No one expects you to have a PhD—just a willingness to learn. That means, among other things, reading up on the subjects you wish to critique. It also means that you have to get out of the habit of saying that something is “stupid” or “illogical” for no other reason than that you find it personally distasteful.


I consider it real funny how you claim that my equations and logic are wrong,


Claim? No, Tom, I have demonstrated that your analysis is wrong. I don’t claim things like that, I show them.


even though these are the very same equations that overdoze has shown me a few months earlier. Yet I see no personal attacks on overdoze.


1. I have not seen overdoze’s presentation.
2. It’s not that the equations are wrong, it’s that they don’t say what you want them to say.


I hate to disappoint you, but relativity is not brain surgery.


I am not disappointed, because I don’t think it’s that tough either.


The reason I find relativity so hard to understand is because it's illogical.


First, you have yet to show that relativity is “illogical”. Second, you have yet to see that it is not relativity, but only your misunderstanding of it that is “illogical”.

Without question, SR is counter-intuitive, but that doesn’t mean that it is self-contradictory. Common sense is not an acceptable guide in science, because it is a notoriously unreliable one.


Sure, relativity can give a nice and cute result when dealing with the round-trip of light. But relativity breaks down when you attempt to apply it to a one-way trip of light.


When you say “breaks down”, that means to me one of two things:

One, there is something wrong mathematically (divergence, multiple-valued function, etc). In that sense, SR does not break down at all except in one circumstance: a massive particle traveling at the speed of light. From this we draw the inference that such a situation is impossible, according to SR. However, there is no self-contradiction here. I contradiction ensues when an argument contains two premises that cannot both be true. Given that, SR has no logical contradiction, because both postulates are independent of each other.

Two, “breaks down” can also mean that some experiment has been done that runs contrary to the predictions of SR, and I know that this has not been done.

So, if you care to support your statement above, I will show you why it is wrong.

That said, there is a sticking point with relativity and the one-way speed of light. No experiment has been done to verify that the speed of light is independent of the speed of the source, so this postulate remains unconfirmed—but that does not mean that SR is self-contradictory. The problem is this: there is another theory of relativity which has a frame of absolute rest, and which predicts the same results for the two-way speed of light that SR does, but does not postulate that the speed of light is independent of the speed of the source. However, this theory is not the Newtonian/Galilean one that you claim to agree with.

Galilean relativity goes like this:
Premise 1: There is a frame of absolute rest (the “aether”).
Premise 2: The laws of mechanics are the same in every inertial frame.
Conclusion: The Galilean Transformation

The trouble with this scheme is that it leaves electrodynamics out in the cold. The EM wave equation is not Galilean-covariant. That this scheme is wrong is verified every time you are driving in your car and listening to the radio, because if you are moving relative to the source (radio transmitter), then Galileo says that for you that transmitted wave is no longer a traveling wave, so it should never come to your antenna in the way that it does. Thus, Newton/Galileo is demonstrably incorrect.

Lorentz supplied the additional premise of length contraction, and with it he developed a valid scheme that agrees with SR in the over-and-back measurements of the speed of light. However, Lorentz’ theory was discarded because it is far less economical and it seems to be less plausible—two totally subjective judgments, to be sure.

The one-way measurement of the speed of light in two different frames will determine whether Einstein or Lorentz is correct. However, you should be aware that time dilation and length contraction are unavoidable aspects of either scheme.

I have studied these theories for a long time. One of the great things about a forum like this is that you can take advantage of the experience and knowledge of people who actually do research in the field—but you have to listen and think.


Finally, let me say that if your convinced that I can't or won't learn, then just disregard my posts. I will disregard your posts, and we will both be happy.


That isn’t going to happen. Yes, I think you refuse to learn this stuff. I think it is clear from, among other things, the fact that you are still saying that relativity introduces length contraction and time dilation to compensate for the speed of light postulate. A serious reading of any derivation of relativity will reveal that this is simply not the case, and I have linked you to just such a derivation.

I can only conclude one thing: that you never bothered to look at it.

However, I think that you can learn relativity (if not, I would not have bothered to present the link). But even if you never do change your stance on learning relativity, I am still going to respond to your posts. I meant it when I said that your posts are potentially harmful stumbling blocks to people who sincerely want to learn from this forum. That’s why I think your posts should be refuted, and that you should re-consider them in the light of what is being said to you here—not only by me, but also by James R, (Q), thed, etc… You have received some terrific feedback in this forum, and you have yet to really capitalize on it to advance your understanding—but it’s never too late to start.

Tom

Originally posted by zanket:
Along those lines, do you see anything wrong in the following story?:

If I am passing by the Earth towards the Andromeda galaxy--some 3 million light years away as measured from the Earth--at a velocity < c relative to the galaxy that will get me there in 1 proper year, my proper distance to the galaxy must be < 1 light year.


Well, the proper distance to the galaxy is 3 million ly no matter how fast you are moving—that is how it is defined. I’m not too sure if the rest of your case depends on that, though, so it may not matter.


If I then decelerate in 10 proper years to a full stop relative to the Earth and galaxy by the halfway point between them, my proper distance to the galaxy increases from < 1 light year to 1.5 million light years during the deceleration.


Funny you should mention that—I am just now preparing to sit down and get serious about the following document, entitled “Marzkhe-Wheeler Coordinates for Accelarated Observers in Special Relativity.”
http://xxx.lanl.gov/PS_cache/gr-qc/pdf/0006/0006095.pdf

Until I get though it, I’m not too sure how to handle the problem, so it seems you’ve caught me with my pants down. It’s a tough problem, to say the least.


Although the galaxy is measurably receding from me at far > c, I continue to receive light from the galaxy, although the light is extremely redshifted.


Are you saying that the galaxy is moving away from your origin at a rate that is greater than 3E8 m/s as measured by you? Or are you saying that the rate of recession is >c in the same sense that superluminal jets move apart at a rate that is >c?

Tom

Hi Tom2,

"Galilean relativity goes like this:
Premise 1: There is a frame of absolute rest (the “aether”).
Premise 2: The laws of mechanics are the same in every inertial frame.
Conclusion: The Galilean Transformation"

Could you cite a reference on this please ? I remember my textbooks on Galilean transformations never mentioned anything about an absolute frame of reference. In fact, I remember vividly that even Newtonian mechanics is a relative theory, in the sense that there is no prefered frame of reference (that must be why they call the transformation principle the "Galilean principle of relativity" ;)).

Bye!

Crisp

Originally posted by Crisp
Could you cite a reference on this please ? I remember my textbooks on Galilean transformations never mentioned anything about an absolute frame of reference. In fact, I remember vividly that even Newtonian mechanics is a relative theory, in the sense that there is no prefered frame of reference (that must be why they call the transformation principle the "Galilean principle of relativity" ;)).


You know what? I left out a step.

If one considers only mechanics, then you are exactly right--there is no need for a frame of absolute rest. However, the form of the EM wave equation is not preserved under the GT. What's more, no transformation of the field itself can be done to recover the form (as it can with quantum mechanics).

If you want to get E+M under the umbrella of Galileo/Newton, you have to enlarge the logical system to include a frame of absolute rest. That frame is the frame in which Maxwell's equations take their textbook form.

I should have made that clearer before presenting my breakdown of Newton/Galileo.

Good catch, Crisp.

Tom

zanket,

You said:

<i>The traveling twin, on the other hand, is moving relative to both the stay-at-home twin and the space between the twins.</i>

This sounds suspiciously like an ether theory to me.

Space is not a substance. It is a coordinate system. There is no absolute space that you can measure motion relative to.

Tom2,

You set the tone for this, not me. But I am willing to start from square-one if you are.

Well, regardless of who started, I will refrain myself from making any more personal attacks.

The one-way measurement of the speed of light in two different frames will determine whether Einstein or Lorentz is correct. However, you should be aware that time dilation and length contraction are unavoidable aspects of either scheme.

I'm interested in the answers you have for the following thought experiment. I apologize to James and Crisp since we already had a long debate about this very same experiment.

Experiment:

Let's say that you are flying through space in your spaceship at .90c with two flashlights in your hand. You have a clock in your spaceship, and you are flying towards a stationairy clock.

The moment you fly over the stationairy clock, you turn your clock and the stationairy clock on. Also at the same time, you turn on both of your flashlights: you point one flashlight forward (in the direction of your motion) and you point the other flashlight backwards.

You continue travelling at .90c while pointing your flashlights in opposite directions for 1 second of the stationairy clock.

After 1 second of the stationairy clock, the backwards beam of light is 300,000 km away from the stationairy clock, and the forward beam of light is 300,000 km away from the stationairy clock in the staionairy clock's frame of reference.

Since your spaceship is now 270,000 km away from the stationairy clock in the stationairy clock's frame of reference, the backwards beam of light is 570,000 km away and the forward beam of light is 30,000 km away from your spaceship relative to the stationairy clock's frame of reference. To summarize:

In the stationairy clock's frame of reference:

L1=570,000 km
L2=30,000 km
t=1 second

Now since you are travelling at .90c, relativity dictates that you are experiencing time dilation and length contraction relative to the stationairy frame of reference.

Question: Apply the time dilation and length contraction resulting from your motion to the values given above so that the speed of BOTH of the beams of light in your frame of reference are equal to c.

Overdoze: I'm interested in your result, as well.

Tom

Although I can accept ... No, not take issue with, your use of the
expression 'stationary clock'; but when you use the expression 'the
stationairy frame of reference' I've got to ask: What are you talking
about?

A 'primary' frame of reference? ... Okaaay.
A 'stationary' frame of reference? ... Nokay.

Take care.

Chagur,

Although I can accept ... No, not take issue with, your use of the expression 'stationary clock'; but when you use the expression 'the stationairy frame of reference' I've got to ask: What are you talking about?

Sorry for the confusion.

When I said "stationairy clock" I meant a clock that is "relatively" motionless, such as a clock on Earth.

When I said "stationairy frame of reference", I meant the frame of reference of the "stationairy clock".

I hope this clears things up. :)

Tom

I suspected as much, but there was the possibility that I had
missed something while reading through the thread; therefore
the post.

Take care.

cest moi

If you'd have better developed senses, you would perfectly know if you were moving or not, regardless of the other train moving. You might for example feel that the wheels below you aren't turning

The analogy of the trains, or buses, or cars, or whatever, is commonly used to explain certain aspects of reference frames in a simplified way. It is commonly used because we cannot experience velocities in space. If we could, those analogies would become redundant. It is true that in each example acceleration would be noticed however, once we are moving at a constant velocity, the analogy of not knowing who is moving becomes relevant.

btw - I don't care how "sensitive" ones senses become, it is highly unlikely one could ever "feel" wheels turning. If one were in a sitting position, would the senses in ones backside be required acuteness to determine wheel rotation ? :D

Originally posted by Prosoothus
Question: Apply the time dilation and length contraction resulting from your motion to the values given above so that the speed of BOTH of the beams of light in your frame of reference are equal to c.

Overdoze: I'm interested in your result, as well.


Awww, shucks. Nice to know someone around here still cares what I think. :)

Sorry I haven't been a more prolific/frequent poster lately. Simply too many things to juggle... Anyway, my analysis is simple. In your particular problem, Lorentz transformations don't even come into play. You can treat it using Newtonian relativity, which has been mentioned by others here.

Point is, you don't know which frame is "stationary" vs. "moving". For the "stationary" frame, the moving frame is moving. For the "moving" frame, the "stationary" frame is moving while the "moving" frame thinks that it stands still.

Anyway, as judged by the "moving" frame, its lightfronts are moving out at the same speed both forward and backward. The "stationary" frame is flying backward at 0.9c, so of course it will be closer to the backward lightfront than the forward lightfront.

As judged by the "stationary" frame, its lightfronts are moving out at the same speed both forward and backward. The "moving" frame is flying forward at 0.9c, so of course it will be closer to the forward lightfront than the backward lightfront.

Neither of the observers is absolutely right since neither knows absolutely whether he is stationary or not; the only think they know is that they're both at rest. Both observers are right within their own reference frames, as all of their observations and conclusions are internally and mutually consistent. In fact, either observer can easily calculate how the world looks from the point of view of the other observer, and it would be an equally valid and consistent description of the world. Think of it as two distinct perspectives from two distinct observation platforms painting their correct but different views of the same universe.

Originally posted by zanket
If it can be accepted that the universe is infinite in extent, it is only a step further to see that the universe might be infinite in a (special) relativistic way, where the furthest galaxy is moving at .9(infinite number of 9’s)c. ... Such a universe adheres to the cosmological principle and seems simpler and more consistent to me than the models cosmologists propose today.


This has a bunch of problems.

First of all, it gives the universe a center and further according to your picture puts us square at this center. Why should the universe be so anisotropic? Why should we happen to occupy such a privileged location; what are the odds of that happening in an infinite universe?

Second, you would have to explain how such a bizarre distribution of galactic velocities would come about naturally.

Third, this does not explain the cosmic background radiation. Under your model, the CBR would span the entire spectrum (being merely combined emissions from the infinite universe) rather than being concentrated in a narrow microwave band. Under the inflationary model, the CBR is not only explained but its precise wavelength and intensity as a function of the universe's age is predicted.

Fourth, this does not explain the power spectrum of cosmic matter density. The inflationary model matches this spectrum quite well based on postulated magnification of quantum fluctuations and plasma sound waves during the inflation era. As far as I can tell, there is no explanation of the observed cosmic matter distribution under your model.

Fifth, distant galaxies might have problems maintaining normal orbital dynamics due to their relativistically amplified momenta.

Sixth, you'd have trouble explaining the inflationary effect that has been reported lately to actually be accelerating the expansion of the universe (meaning that according to latest data the universe is not flat but in fact open.)

Finally, if you run such a universe back in time to its inception, you should see that it no longer collapses neatly into a point. Because galaxies 15 billion years away move away from the center at virtually the same speed as galaxies 150 billion years away, that would mean that 15 billion years ago the universe consisted of the Big Bang nucleus surrounded by an infinite expanse of matter speeding away from it at near lightspeed. You get a non-instantaneous, ongoing Big Bang. No such thing is observed, so it must have stopped. How, why, why now?

Tom2:

Thanks for responding and for the link to the interesting doc.

Well, the proper distance to the galaxy is 3 million ly no matter how fast you are moving—that is how it is defined. I’m not too sure if the rest of your case depends on that, though, so it may not matter.

I mean that the distance from the Earth to the galaxy, as measured by us on the Earth, is 3 million light years. But I, in the ship, at the moment I pass by the Earth, measure my ETA to the galaxy at 1 proper year. So doesn’t that guarantee that my proper distance to the galaxy is < 1 light year? Because if my proper distance was >= 1 light year then I’d have to be moving relative to the Earth and the galaxy at > c to reach the galaxy in 1 proper year.

Until I get though it, I’m not too sure how to handle the problem, so it seems you’ve caught me with my pants down. It’s a tough problem, to say the least.

While I’m flattered given your level of physics, mustn’t it be true that my proper distance to the galaxy increases from < 1 light year to 1.5 million light years during the deceleration? As above, it seems my proper distance before deceleration must be < 1 light year. And after deceleration, when the Earth-me-galaxy system is at rest with respect to each other, with me in the middle, it seems my proper distance must be half of the distance that the Earth measures to the galaxy. Since I measure my proper distance before and after deceleration, it seems acceleration doesn’t muddy the equation, allowing me to simply use special relativity for the before measurement, and just divide by 2 for the after measurement. Can you give some indication as to why it’s not that simple?

Are you saying that the galaxy is moving away from your origin at a rate that is greater than 3E8 m/s as measured by you? Or are you saying that the rate of recession is >c in the same sense that superluminal jets move apart at a rate that is >c?

Assuming by “origin” you mean where I’m at when I measure, the former but let me clarify. Some of my books are clear to make a distinction between what you measure locally and what you measure from afar. They point out that you can, for example, measure objects approaching you at >= c due to the time it takes their image to get to you (a “signal transmission delay time effect”). They say the solution is to imagine that you have a team of observers who are all at rest with respect to you (you are all “flying” in formation). The assistant observer who is local to the object measures the relative velocity and sends you the information. Upon receipt of the information you would find that the galaxy was moving relative to you at < c as expected. The galaxy only appears to move relative to you at >= c.

So I could restate like this: “Although the galaxy is measurably receding from me at far > c, as measured by me from afar, all my assistant observers, who are at rest with respect to me but local to the galaxy, measure their velocity relative to the galaxy at < c, and, this being my true velocity relative to the galaxy, I continue to receive light from the galaxy, although the light is extremely redshifted.”

I’m only guessing the galaxy’s light would be redshifted as I observe it, simply because it seems too odd to accept otherwise given that, although my assistant observers tell me that I continue to close the gap between myself and the galaxy during my deceleration, I nevertheless measure the galaxy shooting away from me at far > c. If I could see the galaxy (if its light remains in the visible range), I should see it move from taking half my field of vision, to telescopic distance.

James R:

This sounds suspiciously like an ether theory to me.<br>Space is not a substance. It is a coordinate system. There is no absolute space that you can measure motion relative to.

No absolute space is required for my statement “The traveling twin, on the other hand, is moving relative to both the stay-at-home twin and the space between the twins” to be true.

Imagine that the stay-at-home twin is on the Earth, and the Earth has an incredibly tall tower on it, such as the 37,000 km behemoth in Arthur C. Clarke’s book 3001. If the traveling twin moves parallel to this tower, he measures its height contracted. Imagine the tower has altitude markers affixed at every 1 km as measured from the ground. The traveling twin measures < 1 km between the markers. Remove the tower and leave the markers separated by space. He still measures them &