Resolving an apparent problem with the theory of Special Relativity

[CraigD]

In "Arguing Einstein" post#41, xersan described an interesting variation on the venerable "light clock" thought experiment often used to teach Special Relativity.

 

In summary, he showed that by simply tilting the light clock so it is not perpendicular to the direction of it's moving, it appears you can use SR to predict time dilation by any factor you wish, including the moving observer’s clock running faster! If true, this is clear evidence of a dreadful flaw in SR.

 

In this post, I'll attempt to show with a few simple diagrams and equations how to resolve this apparent problem, and how it sheds light on an important and often misunderstood implication of SR.

 

To improve readability, results for a specific case are included along side the equations, [enclosed in brackets]. To ease calculation, distance is in light-seconds and time in seconds. In this unit system, the speed of light, c = 1.

 

The light clock looks like this right triangle:

A-----S

| . ./.

| . / .

| ./. .

| / . .

R . . .

Where:

S is where the light pulse is emitted and detected

R is where the light pulse is reflected back toward S

A is a vertex of the right triangle formed by S, R, and A

D' = distance between A and S [3 ls]

W = distance between A and R [4 ls]

(By the Pythagorean identity) distance between R and S = (D'^2+W^2)^.5 [5 ls]

 

An observer at A, "Alice", sees a pulse of light leave S, reflect off R, and return to S in time T' =(2*(D'^2+W^2)^.5)/c [10 sec]

 

From the POV of a distant observer, "Bob", A, S, and R are moving east at velocity V [0.6 c].

Per SR, Bob sees the distance D between A and S to be shorter than Alice does,

D = D'*(1-(V/c)^2)^.5 [2.4 ls].

He sees the distance W to be the same. [4 ls]

 

Bob sees the pulse of light leave S and reach R in time T1, and return to S in time T2, for a total time T = T1+T2, which looks like this:

. . .S. E--------------S2

. . .|* | . . . . . * . .

. . .|* | . . . .*. . . .

. . .|.*| . . * . . . . .

. . .|.*| .*. . . . . . .

R . .B--R1

Where:

R1 is the position Bob sees R at at time T1 [2.4 ls]

S2 is the position Bob sees S at at time T1+T2 [7.5 ls]

E and B are the vertexes of the right triangles formed by S, R1, and B, and R1, S2, and E.

W = distance between S and B, or E and R1 [4]

V*T1-D = distance between B and R [0 – the “triangle” S,B,R1is actually a vertical line]

(W^2+(V*T1-D)^2)^.5 = distance between S and R [4]

V*T1-D + V*T2 +D = V*(T1+T2) = distance between E and S2

(W^2+(V*T2+D)^2)^.5 = distance between R1 and S2 [8.5]

 

So Bob sees the pulse reach R1 at

(solving T1 = ((W^2+(V*T1-D)^2)^.5)/c (using the quadratic formula))

T1= (-V*D +(V^2*D^2+(c^2-V^2)*(W^2+D^2))^.5 /(c^2-V^2) [4 sec],

and reach S2

(solving for T2= (W^2+(V*T1+D)^2)^.5)/c)

T2= (V*D +(V^2*D^2+(c^2-V^2)*(W^2+D^2))^.5 /(c^2-V^2) [8.5 sec],

for a total time of

T= T1+T2 = 2*(V^2*D^2+(c^2-V^2)*(W^2+D^2))^.5 /(c^2-V^2) [12.5 sec]

 

The ratio of the time T’ Alice measures and the time T Bob measures,

(simplifying T’/T = ((2*(D'^2+W^2)^.5)/c)/(2*(V^2*D^2+(c^2-V^2)*(W^2+D^2))^.5 /(c^2-V^2)))

is the familiar T’/T = (1-(V/c)^2)^.5 [.8]

 

:hihi: At this point, one has to ask “what’s going on?!” SR appears to be giving one value for time dilation, T1’/T1 [5/4 =1.25]

for half of the light clock’s cycle, then another, T2’/T2 [5/8.5 = ~0.5882],

that just happen to give the expected T’/T [.8]

When taken together. On the surface, this seems to make no sense.

 

To make sense of it, consider the difference between how “distant observer” Bob, and not-distant observer Alice “see” the position of the light pulse.

 

For Bob to be able to see it at all, there must be a bit more to the arrangement than we’ve described. Let’s imagine that a fine reflective dust is suspended along the path of the light pulse between S and R, reflecting enough light for him to see the pulse, but enough to weaken the pulse to much for Alice to detect it’s return to S. Bob is distant, which means the difference in distance the reflected light travels to reach him at various points along its path is so small it can be ignored, allowing us to make statements like “Bob sees the light pulse reach R after 4 seconds.”

 

For Alice, located exactly at S, things are very different. Reflected light from very near S reaches her in almost no time. Reflected light from very near R takes 5 seconds to reach her, barely before the returning pulse itself.

 

If you visualize the light clock + reflective dust arrangement, you’ll realize that from Alice’s perspective, it’s actually equivalent to an array of light clocks, varying in path length from almost nothing to the full 5 ls between S and R. Therefore, any “seeing” of the light pulse she does is really a measurement of a rount-trip pulse of a smaller, similar light clock. She can’t measure T1’, only many different T’s.

 

What’s more, under SR, there’s no way to “trick” the system into not having this quality – no signaling with long sticks, faster-than-light communicators, etc. SR forbids any signal traveling faster than the speed of light.

 

In SR, this counterintuitive quality falls under the heading of simultaneity, and leads to many weird results.

[Perspicacious]

CraigD,

 

What result do you get when the light clock is placed horizontally (in the direction of motion)?

[Wizdumb]

The entire issue of time distortion is something highly questionable when considering the fact so much time distortion takes place within our minds. We really must be careful about determining whether the distortion is a product of our minds or an actual law of the physical world.

[CraigD]

... What result do you get when the light clock is placed horizontally (in the direction of motion)?

Calculating for the same case as above, but the 5 ls long clock oriented horizontaly,

V=.6, W=0, D’=5,

the equations give:

D=D’*(1-(V/c)^2)^.5 [4 ls],

T1= (-V*D +(V^2*D^2+(c^2-V^2)*(W^2+D^2))^.5 /(c^2-V^2) [2.5 sec],

and

T2= (V*D +(V^2*D^2+(c^2-V^2)*(W^2+D^2))^.5 /(c^2-V^2) [10 sec].

The total observed time T [12.5 sec],

And the resulting time dilation factor T’/T [10/12.5 =.8]

is, of course, unchanged – the whole point of xersian’s challenge to, and my explanation of, SR, is that the orientation of the clock should have no effect on time dilation.

[CraigD]

The entire issue of time distortion is something highly questionable when considering the fact so much time distortion takes place within our minds. We really must be careful about determining whether the distortion is a product of our minds or an actual law of the physical world.

I fear you may be confusing 2 separate qualities, “distorted perception of time” and “time dilation”.

 

The psychological perception of time is highly subjective. Our “internal clocks” often provide us with very inaccurate perceptions. This distortion, however, appears to be the result of the complicated, as yet poorly-understood phenomena of human thought, not any fundamental property of Physics. It can be, and commonly is, counteracted by the use of artificial devices, such as wrist watches.

 

”Time dilation” and “length (Lorentz-Fitzgerald) contraction” are very specific prediction of the theory or Relativity. Though SR’s interpretation raises vexing philosophical questions, its predictions are mundane facts, without which such everyday devices as GPS navigation systems would not function properly. It’s simply something that must be taken into account when considering the physics or engineering of very fast-moving things, or very precise measurements of time and distance, regardless of the nature of the minds that consider it. Fortunately, with the exception of super-accurate devices like GPS receivers, little in our experience can be adversely affected by such effects.

[xersan]

In "Arguing Einstein" post#41, xersan described an interesting variation on the venerable "light clock" thought experiment often used to teach Special Relativity.

 

In summary, he showed that by simply tilting the light clock so it is not perpendicular to the direction of it's moving, it appears you can use SR to predict time dilation by any factor you wish, including the moving observer’s clock running faster! If true, this is clear evidence of a dreadful flaw in SR.

 

 

 

You just perceived the event. According to my trials, independent brains (especially uninfected students <80 %> in universities) may understand this fiction transparently, simplicity.

 

This matter detains the minds for more one hundred years, because the fantastic conclusions (voyages in time) of the theory SR attend for their passion of mysticism. Human is in needs mystic subjects to pass over the vacuum of existence.

 

I had shown that also Lorentz’s transformations have < time contraction > at # 55 . Time dilation and time contraction never become for the same experiment simultaneously. Theory can not require scientific integrity. Theory of SR is not consistent by itself.

 

I had written a book about <Light Clock>. Somebody thınks that the light clock explains the time dilation clearly. But it is not true. Light Clock’s tempo is variable according to its direction and general motion of earth. Besides, there are the cases of the planes of mirrors are parallel or perpendicular according to motion’s direction:

 

Time deformations of light clock:

 

T’(parallel) = t / sqrt(1 – v2/c2) Attention please sqrt is required. (*)

 

T’(perpendicular) = t / (1 – v2/c2) NOT sqrt.

 

The essential formula of time dilation of SR derived from Lorentz’s transformations:

 

T’ = t.(1 – v/c) / sqrt(1 –v2/c2) (**)

Einstein had used (*) this formula at the end of his theory for time dilation instead of essential relation (**). But Lorentz's equations never give this relation. I discern a trick at this point.

 

The terms at numerator are primary degree. So the time deformations are related by direction. If the light is at opposite direction according to its source we must take (-) c (or v) . Inthis case it is obtained Time contraction; tempo of time become faster.

 

These all explanations has shown that, The theory of SR is wrong. I have other some arguments about the autopsy of the theory. But there is a key knowledge that it makes transparent the space-time exactly

[CraigD]

Time deformations of light clock:

 

T’(parallel) = t / sqrt(1 – v2/c2)…

T’(perpendicular) = t / (1 – v2/c2) …

I think I see how you reach this result.

 

From post#1, we have: T = 2*(V^2*D^2+(c^2-V^2)*(W^2+D^2))^.5 /(c^2-V^2)

 

A W and D for the “parallel” case, W=1, D=0, and using the usual distance units where c=1

gives: T = 2 /(1-(V/c)^2)^.5,

which agrees with your t / sqrt(1 – v2/c2) .

 

A W and D for the “perpendicular” case, W=0, D=1, gives:

T = 2 /(1-(V/c)^2),

Which agrees with you t / (1 – v2/c2) .

 

:eek_big: Again, we have a result that seems to say the orientation of the light clock has an effect on time dilation, which neither makes sense, nor agrees with experimental evidence. The reason for the result, however, is not an inconsistency in Special Relativity, but a mistake in the calculations. I’ve highlighted the mistakes above in red.

 

From the diagram, the parameter we should be selecting is not the distance D seen by distant observer Bob, but the distance D’ seen by Alice, at S. The distance D that Bob sees is shorter than the distance D’ that Alice sees by the familiar

D = D’*(1-(V/c)^2)^.5.

 

Redoing the 2nd calculation without confusing D’ and D, we get:

 

A W and D’ for the “perpendicular” case, W=0, D’=1, gives:

T = 2*(V^2*D’^2*(1-(V/c)^2)+(c^2-V^2)* D’^2*(1-(V/c)^2))^.5 /(c^2-V^2)

= 2 /(1-(V/c)^2),

which agrees with the “parallel” case, as expected.

 

In summary, your result,

T’(perpendicular) = t / (1 – v2/c2),

is due to the failure to distinguish between the distance D’ that Alice sees, and D that Bob sees.

 

:) There are many problems with Relativity. It is at heart a classical theory, difficult to reconcile with another cornerstone of the current scientific consensus view of reality, Quantum Physics. The contradictory results of calculating the geometry of light clocks examined above don’t reveal a problem with Relativity, however, but an error in the calculations, as I’ve shown.

 

An autopsy of the Theory of Relativity is premature – nothing in this or ”Arguing Einstein” thread show it to be dead, or even seriously ill.

[xersan]

ONE STEP BEYOND (7)

 

I will work to explain that Lorentz’s transformations have not the scientific integrity.

 

In the well-known experiment of SR it is taken aim to obtain the same value of < c > in the train and on the perron. We will use this experiment also. If you wish you may take the world instead of the train. We measure the velocity of light on the world by the units kilometer and second. And its value is 300 000 km/s.

 

The train travels by the speed of < v >.

 

Lorentz’s equations transform the values of units. For example; if v = 60 % c

 

L’ = L.sqrt (1 –v2/c2) = 0.80 L

 

t’ = t (1 – v/c) / sqrt(1 – v2/c2) = 0.5 t

 

It means : One unit of meter in the train is 0.80 meter according to observer on the perron. And we must call the units according to its place (reference or relative system):

 

The unit of length in train = trainmeter ( = 0.80 railmeter ; for v = 0.60 c )

The unit of time in train = trainsecond (= 0.5 railsecond; for v = 0.60 c)

 

The unit of length on perron = railmeter ( = 1.25 trainmeter; for v = 0.60 c)

The unit of time on perron = railsecond ( = 2 trainsecond ; for v = 0.60 c)

 

Now we use Lorentz equations for t = 5 railsecond

 

x = c. t = 300 000 . 5 = 1 500 000 railkm ( c = 300 000 railkm/railsecond)

 

x’ = (x – vt) / sqrt (1 – v2/c2) = 600 000 / 0.80 = 750 000 trainkm

t’ = (t – vx/c2) / sqrt (1 – v2/c2) = 2 / 0.80 = 2.5 trainsecond

 

And our aim has obtained: c = x’ / t’ = 750 000 / 2.5 = 300 000 trainkm/trainsecond

 

It means we can assure the fixed value of the light’s speed by the units in relative system. We can calculate it by the units in reference system:

 

300 000 trainkm / trainsecond = 240 000 / 2 = 120 000 railkm / railsecond

 

What is this ? This is an evidence of the end of the theory SR. Because The units must be same to obtain the same fixed value of light’s velocity. This like that: If You give to your child every week 50 USD. After today you will may give him 50 japanese-yen according to Einstein.

[xersan]

An autopsy of the Theory of Relativity is premature – nothing in this or ”Arguing Einstein” thread show it to be dead, or even seriously ill.

 

The human is not ready yet. Fantastic conclusions of SR are perceived by the brains at the meaning philosophic necessity. The clear arguments (as twin paradox) have no chance for their thinking scientific. You may see from reaction and defending in this forum.

 

The arguments are usually about a point of theory. Of course they must have integrity to consider. And it is required a new paradigm for light kinematics to convince and to finish disorder.

 

I have the new paradigm for light kinematics. It makes transparent the theory and its defects. But new paradigm has no excitement and doesn’t give philosophic addition. I prefer to tell its mistakes.

[Qfwfq]

We really must be careful about determining whether the distortion is a product of our minds or an actual law of the physical world.

It's a coordinate transformation. I keep repeating this. (It's a coordinate transformation)*n!

 

:hihi:

[Qfwfq]

But new paradigm has no excitement and doesn’t give philosophic addition.

Especially if nobody here knows what your new paradigm is.

[xersan]

Especially if nobody here knows what your new paradigm is.

 

I would want to exhibit it here. It is very simple. But some simple realities are not comprehended because of partisanship for SR. Nearly they wrıte a blinker story. (They have sympathy for the theory by soft wording. But scientific subjects are never examined by sentiments like sympathy.) I wish that the members have consciousness for neutral vision. Probably, positive results may be obtained by our neutral vision.

 

For example I explained some simple arguments against SR (The theory takes the point S1 instead of So to calculate the velocity of light; or the source is never the first reference/coordinate system for the light, the source has just passed from the point So.) These are very simple. But they are required only neutral vision for perceiving.

 

I am working to present the explanations one step beyond according to others. For example I differed the place of the source a little ( under the thread <arguing Einstein> # 41 )and I had shown that obtainıng time contraction by the same logical procedure of SR.

 

I