B Measuring Michelson–Morley light beams

[robphy]

Here's something that might be helpful.

https://www.geogebra.org/m/XFXzXGTq "Relativity-LightClock-MichelsonMorley-2018 (robphy)"

It's based on an old paper of mine
"Visualizing proper-time in Special Relativity" https://arxiv.org/abs/physics/0505134
and an old visualization (from http://visualrelativity.com/LIGHTCONE/LightClock/ )
that's now on youtube


With no length contraction, the Galilean-expected time-difference can, in principle, be measured by a very precise wristwatch.
But instead an optical interference experiment was used by MIchelson and Morley.
https://history.aip.org/exhibits/einstein/ae20.htm

 

[P J Strydom]

Not a 3-D ball. A spherical shell that expands over time.

Surprisingly, the invariance of light speed means that we can adopt the frame of reference where the source is at rest and observe an expanding spherical shell always centered on the source. It also means that we can adopt a frame of reference where the source is moving and observe an expanding spherical shell always centered on the place where the source was when it emitted the pulse. Both descriptions are correct!

The resolution to this seeming contradiction is the relativity of simultaneity. Each spherical shell is a snapshot at an particular instant in time. But time and, in particular, simultaneity, is judged differently from different reference frames.

Thanks, this is the first time someone said it in a way I understand.
if my terminologies are sounding funny, it is because I am not English, but well said.
What I like about your explanation is that you describe these expanding shells that is a snapshot in time.
these spheres of lifgt will obviously be as round as round can be, because the source of the light's velocity will have no effect upon it.

 

[P J Strydom]

Here's something that might be helpful.

https://www.geogebra.org/m/XFXzXGTq "Relativity-LightClock-MichelsonMorley-2018 (robphy)"
View attachment 236725View attachment 236726

It's based on an old paper of mine
"Visualizing proper-time in Special Relativity" https://arxiv.org/abs/physics/0505134
and an old visualization (from http://visualrelativity.com/LIGHTCONE/LightClock/ )
that's now on youtube


With no length contraction, the Galilean-expected time-difference can, in principle, be measured by a very precise wristwatch.
But instead an optical interference experiment was used by MIchelson and Morley.
https://history.aip.org/exhibits/einstein/ae20.htm

I will take the time an read everything over this weekend.
Much appreciated.

 

[Ibix]

I will take the time an read everything over this weekend.
Much appreciated.

Worth noting that these are the Minkowski diagrams I was recommending you learn about.

 

[Herman Trivilino]

Amaizing.! (The accuracy of excel)
This now forces me to go an work it out manually by hand.

Most of the Excel issues are probably due to the fact that the machine does its arithmetic in base 2. Try choosing values of $\frac{v}{c}$ that are powers of two.

 

[P J Strydom]

Whilst I am busy with the "Homework",
Can anyone explain in the simplest forms how Lorenz transformation lead to SR and GR?
I have difficulty understanding what the guys try to tell on You tube.
They contradict each other in many ways.

let me summarize how I understand it.
1. MM could not detect aether.
2. they thought a beam traveling in the direction of the aether will arrive later than one traveling across the aether.
3. They found the beams arrived at the same time.
4. but, Lorenz came forward with the length contraction calculation which says that anything moving against aether will undergo length contraction?
5. now, what does he say, there must be aether and everything squashes into itself as it travels against aether? (Confusion no 1)
6. then Einstein, and co came up with the Special relativity theory.
7. they say, as we travel in a direction, and we pulse a light beam forward and perpendicular to the direction of movement, the light beam that will reflect (in our time clock) from the ceiling, and the light beam that reflects from the front of our space ship, will arrive at the same time.
8. the beam that traveled to the ceiling, will travel a longer distance, but time will slow down for this beam, and it will arrive at the ceiling at the exact time the other beam reaches the nose.
9. upon these 2 beams return, the beam traveling from the ceiling will again travel further than the one from the nose, but time will again slow down for the beam from the ceiling, and both beams will arrive at the same time again.
lets stop here for now.
is this correct so far?

 

[vanhees71]

Here are my 2cts in trying to explain Special Relativity:

https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[Ibix]

let me summarize how I understand it.

1-5 is more or less correct, except it's Lorentz. Lorenz was a different mathematician and physicist active at around the same time.

Lorentz and Fitzgerald proposed length contraction for no reason other than it explained the null result of Michelson-Morley. Lorentz later proposed the Lorentz transforms to fix the problems with Maxwell's equations which had started this whole line of investigation. But he just saw them as a patch to Maxwell's maths, for use in electromagnetism only.

Einstein showed independently that the Lorentz transforms arise from the principle of relativity and the constancy of the speed of light. He realized that they applied to everything and that, therefore, Newtonian physics was an approximation that is only valid at low speeds.

Unfortunately special relativity completely breaks Newtonian gravity. Because there's no propagation speed in Newtonian gravity it allows instant communication. But relativity says that "instant" is nonsense - different frames don't agree on what it means.

Minkowski pointed out that the Lorentz transforms were equivalent to the statement that space and time are part of a 4d entity we call spacetime. Einstein and others eventually realized that gravity could be explained by taking the flat spacetime and letting it curve.

Note that Michelson and Morley only appears in this as an inspiration for Lorentz-Fitzgerald contraction, which in turn is inspiration for the Lorentz transforms. Einstein was interested in the latter and their ability to solve problems with electromagnetism. Although the experiment is explained by relativity, it wasn't Einstein's motivation.

Applying the full Lorentz transforms doesn't make any difference to the analysis of the Michelson-Morley experiment. As long as you remember length contraction in the frame where the interferometer is moving the analysis can be done in either frame without worrying about the transforms.

 

[Ibix]

8. the beam that traveled to the ceiling, will travel a longer distance, but time will slow down for this beam, and it will arrive at the ceiling at the exact time the other beam reaches the nose.

No. Both beams travel the same distance. You do not need time dilation to understand the Michelson-Morley experiment. And the reflection events do not happen simultaneously except in the rest frame of the interferometer.

 

[Herman Trivilino]

7. they say, as we travel in a direction, and we pulse a light beam forward and perpendicular to the direction of movement, the light beam that will reflect (in our time clock) from the ceiling, and the light beam that reflects from the front of our space ship, will arrive at the same time.

The phrase "travel in a direction", or indeed just the word "travel" implies that there is something else involved, because there must be something that you're traveling relative to. An observer at rest relative to that something will indeed see both pulses leave at the same time and arrive at the same time. But that observer will see those pulses move further distances and therefore take more time.

Note that we are comparing what's observed by two different observers. We are not comparing the travel times of two different pulses measured by one of the observers.

8. the beam that traveled to the ceiling, will travel a longer distance, but time will slow down for this beam, and it will arrive at the ceiling at the exact time the other beam reaches the nose.

To either observer both beams take the same amount of time. The observers disagree on the amount of that time.

 

[P J Strydom]

The phrase "travel in a direction", or indeed just the word "travel" implies that there is something else involved, because there must be something that you're traveling relative to. An observer at rest relative to that something will indeed see both pulses leave at the same time and arrive at the same time. But that observer will see those pulses move further distances and therefore take more time.

Note that we are comparing what's observed by two different observers. We are not comparing the travel times of two different pulses measured by one of the observers.

To either observer both beams take the same amount of time. The observers disagree on the amount of that time.

Damn, let me try to understand this part first.
First. If we...
are in a spaceship in space.
And we do not know if we are traveling, or stationary...
and we pulse a light...
Einstein says that the light will travel at c independently from it's source.
we know the light will expand in a 3D shell from it's source.
Now, if the spaceship is stationary, We on this ship will observe the light traveling to the ceiling, tail and nose, arriving at its destination at the same time.
however, if this ship is moving in some direction, let's say forward in relation to the nose of the ship for this argument,
we on this ship should observe the light arriving at the tail, before the nose.
However, this is what length contraction stipulates...
The ship will contract in length and the 3D shell of light, will then reach the nose and the tail at the same time.

But, someone observing the ship from a distance. because this is what a different time frame is in my understanding,
he will see the ship moving forward, and the 3D shell of light will move to the back of this ship we are on.

is this correct?

 

[Ibix]

however, if this ship is moving in some direction, let's say forward in relation to the nose of the ship for this argument,
we on this ship should observe the light arriving at the tail, before the nose.

How are you going to observe it? You have to wait for the light to get back to the middle of the ship to see when the reflection happened, and we already know the light will return at the same time from both ends regardless of the state of motion of the ship. If you think you can get round this by using clocks at the end of the ships, think about how you would synchronise the clocks.

You are correct that, if you regard the ship as moving, the reflections do not occur simultaneously. But there is no way to observe this - any observations you make can be consistently explained either in terms of a stationary ship (identical forward and backward travel times leading to a simultaneous return) or a moving ship (longer forward and shorter backward travel times leading to a simultaneous return).

 

[Herman Trivilino]

And we do not know if we are traveling, or stationary...

There's no difference between those two things, so of course there's no way to know.

Now, if the spaceship is stationary, We on this ship will observe the light traveling to the ceiling, tail and nose, arriving at its destination at the same time.

Then that's what happens if the ship moves in a straight line at a steady speed.

however, if this ship is moving in some direction, let's say forward in relation to the nose of the ship for this argument,
we on this ship should observe the light arriving at the tail, before the nose.

No. Why would you think that?

However, this is what length contraction stipulates...
The ship will contract in length and the 3D shell of light, will then reach the nose and the tail at the same time.

There is no contraction according an observer resting in the ship.