# QuestionIs lorentz contraction detectable and verifiable by our motion through the universe?

#### Greenlight

I read our local cluster is moving ~600km/s relative to the CMB. At the same time we are orbiting the galaxy at ~250Km/s

so depending on the orientation and motion, relative to the CMB we could be changing from 350km/s up to 850km/s and then back down to 350km/s every rotation about 250k years.

since i am unsure of the milky way's orientation compared to the local motion i am just going to use the avg.

a change from 850 - 350 over 125k years gives an avg. deceleration rate of 500kms/125k y or
0.00000012675 m/s/s

If we are currently going 600km/s and say we are decelerating at 0.00000012675 m/s/s
according to an online contraction calculator a distance of 1MPC with a change from 600.00000000012km/s to 600km/s gives a change in length of about ~25km/s/mpc. Do we see any kind of expansion like this in the real world observations?

#### billslugg

Lorenz contraction is a function of speed, not acceleration. Our movement relative to the CMB shows up as a slight temperature difference due to Lorentz contraction.

#### Greenlight

Lorenz contraction is a function of speed, not acceleration. Our movement relative to the CMB shows up as a slight temperature difference due to Lorentz contraction.
does acceleration cause a constant change in speed, thus a constant change in contraction?

#### billslugg

Yes, as you accelerate you go faster, as you go faster the Lorentz contraction in front of you increases.
This is what causes parallel conductors to repel each other. An electron in one conductor sees electrons coming at it in the other conductor. They are Lorentz contracted thus more electrons are seen in the other conductor, increasing the charge seen thus increasing the force seen.
The velocities are very low. A 100 Amp direct current in a #10 wire has the electrons travelling at only about 3 millimeters per second. The amount of Lorentz contraction is miniscule but the forces between charges is enormous as compared to what we are used to in our daily experience.
Conversely, when two wires carry current in the same direction all electrons see all other electrons as stationary but the electrons in one wire see positive holes moving towards them, with Lorentz contraction they see more than normal thus attract them.

#### Helio

Lorenz contraction is a function of speed, not acceleration. Our movement relative to the CMB shows up as a slight temperature difference due to Lorentz contraction.
APOD has a nice image of that today. It’s due to the speed of our galactic group relative to the CMB (Hubble Flow). I think this is a Doppler effect.

As for contraction, I’ve yet to see hard evidence of actual contraction that could not be explained by time dilation, but the theory seems to support something long traveling near c that would fit in a shorter, say, garage. Simultaneity, however, seems to complicate all this. I’m no expert, but any lucid explanation would bee nice.

Catastrophe

#### Unclear Engineer

As for contraction, I’ve yet to see hard evidence of actual contraction that could not be explained by time dilation, but the theory seems to support something long traveling near c that would fit in a shorter, say, garage. Simultaneity, however, seems to complicate all this. I’m no expert, but any lucid explanation would bee nice.
Apparent contraction due to speed is along the dimension of the relative motion, as seen by 2 observers who have a difference in their speeds that is near the speed of light.

The apparent paradox comes when we hypothetically start with the two observers at the same speed, so that they can agree on the dimension of something like a long pole and a long box that is shorter than the pole. Then, the thought experiment is for one of the observers to accelerate to some speed approaching the speed of light and run past the other observer.

The observer who remains "still" sees the pole carried by the speeding other observer to be shortened, so that it will fit into the box, while the observer who is running sees the pole stay the same length as when he was "still" but sees the box get shorter, because it is now coming at him at speed near the speed of light. So, as the "still" observer sees it, the pole has become shorter than the box, but the speeding observer sees the box becoming even shorter than it was, and much shorter than the pole.

So, it looks to the still observer that the forward end of the pole enters the box and does not exit before the rear end of the pole has entered the box, because the speeding pole seems to have become shorter than the box. But, the speeding observer sees the reverse, that the forward end of the apparently unaltered pole goes out the far end of the shortened box before the rear end of the pole enters the box.

So, how can that physically be? The answer is in the apparent differences in the timing of the events of the pole ends being at the box ends, depending on the relative motion of the observers. Those ends of physical objects are at two different locations, which are perceived as having different times that depend on the speed of the observer when the speed of light is constant. This is not the "time dilation" caused by the proximity of mass that is described by General Relativity, but rather the result of the Lorenz Transformations that describe Special Relativity - the effects of motion on measurement of distance and time.

The net conclusion of this thought experiment is that things that appear to be simultaneous in one frame of motion can appear to be non-simultaneous, in a different frame of motion that has a much different speed - unless the two things are happening at the same location. The apparent order of 2 events at 2 different locations can be the opposite for 2 different observers who are moving at different speeds, when the speed difference approaches the speed of light to those observers.

Helio

#### Greenlight

so is Lorentz contraction a completely different effect than the length contraction due to time dilation that has almost the identical formula? Do they stack? It is my understanding that time dilation causes length contraction in the radial direction where lorentz only affects in the direction of motion.

#### Helio

so is Lorentz contraction a completely different effect than the length contraction due to time dilation that has almost the identical formula?
I'm fairly sure the answer is no.

They do have the same formula, essentially, and for the same reason - c is one speed no matter who measures it. To derive the time dilation equation, only the equation of Pythagoras is needed.

Imagine you are watching a train go by you and there happens to be a person on a flatbed car on that train that is timing how long it takes to shine a flashlight from one height to a sensor on deck. The distance can be determined as simply ct, and we know the value of c. [BTW, this reliability in c now determines the length of one meter.]

Since the train is moving, you, the observer, will see the person and flatbed moving so you will observe the travel distance of the light along a diagonal as it travels toward the deck. Normally, we could explain the extra distance along the diagonal by taking the speed of the train into consideration, even for light, but since light can only have on speed then something else requires adjustment. You could argue that the distance traveled along the diagonal would be ct' (where t' is a different rate of time) so that you adjust time itself to explain the result. Alternatively, you could say that the distance (ct') was shrunk to explain things.

Do they stack?
No. To determine the travel time to, say, alpha Cen., then the time dilation can be used, or length contraction could be used, but not both. [Perhaps some contorted math could allow a portion of each be used, but this seems unlikely something real.]

So, if length contraction is "real" and time dilation is "real", why aren't both required to determine the time to reach alpha Cen.? Don't ask me. The problem is likely in trying to squeeze "real" into a box it is too big to fit. Einstein's spacetime changes how we must see the universe.

It is my understanding that time dilation causes length contraction in the radial direction where lorentz only affects in the direction of motion.
I doubt this is the case. A space traveler traveling near c will see odd effects in all directions, more so along the axis of travel, of course.

#### Unclear Engineer

so is Lorentz contraction a completely different effect than the length contraction due to time dilation that has almost the identical formula? Do they stack? It is my understanding that time dilation causes length contraction in the radial direction where lorentz only affects in the direction of motion.
I don't know how to address your question about "completely different" and "stacking" of the effects and your apparent distinction between "radial" and "direction of motion". I see that your original post is trying to envision relativistic effects for the perspective from Earth that is revolving around the center of our galaxy, so I will try to get to that. But, envisioning how things will appear in relativistic conditions is very hard.

Concerning "different" and "stacking", it is necessary to remember that the Lorentz Transformations were developed as an explanation for the observed experimental result, that the velocity of light does not appear to change when taken in any direction, at any speed. So, all of those equations in Special Relativity Theory need to be applied to appropriate observations to predict how those observations would appear to a different observer traveling at a different speed. In that sense, they "stack" so that both length measurements and time interval measurements need to be recalculated with those equations in order to adequately explain all observable changes in perceptions between two observers. Conceptualizing how to do this is not trivial for us, because we are not used to the effects at such high speed differences.

Astronomy forces us to try to envision some of these effects to make sense of our observations, because some of the speed differences that we see are sufficient to create observable effects. But, even the Lorentz Transformations are not sufficient to explain all of our observations. So, we have added the Theory of General Relativity to explain the effects of extreme gravity on apparent measurements in our observations (as well as the relationship between mass and energy). But, even that is not enough to explain the Hubble observation about the observable universe seeming to be expending away from us in all directions at the same rates, with the rates only a function of distance from us here on Earth. So, to make that consistent with the theories of Relativity, we have added assumptions that there is a lot of "dark matter" that we cannot see, to "explain" the apparent extra gravitational forces that are needed to make our galactic orbital velocities match our equations. And, we have added an assumption that there is an unknown force called "dark energy" that somehow makes space itself expand, so that two places in space can be moving apart faster than the speed of light even though no matter can be moving through space any faster than the speed of light.

It is important to remember that all of these theories about measuring lengths and time intervals and masses and energy levels are just mathematical tools that work to quantitatively describe our observations in a manner that seems to work. Why that math describes our observations is not explained by those theories.

There is a similar situation in the very tiny, "quantum world", where we find that sometimes light particles (photons) and sub-atomic particles (e.g., electrons) behavior must be described by the mathematics for particles, and other times we must use the mathematics for waves in medium. Google and read the discussions about the "double slit refraction paradox" which seems to challenge the concept of cause and effect, even suggesting time-travel to explain apparent violations. I point this out to help you realize that even successful mathematical quantitative description of some physical process does not actually help us understand why it works as described.

So, to your question about observational differences between conditions when the Earth is on one side of the galaxy vs the other side, and radial vs linear directions, all I can suggest is this: First, the situation regarding differences in apparent measurements as a function of which side of the orbit we are on in the galaxy is basically the same situation that was done with the Earth's position in its revolutions around the sun, which led to the Lorentz transformations and the Theory of Special Relativity. We don't expect to see any differences due to speed, except frequency shifts in light sources, e.g., red shifts. But, when you add in the other theories and their mathematical descriptions, and then postulate some physical phenomenon occurring at great distance and great speed differential, and then ask what it should look like, it gets extremely difficult to actually apply the mathematics of all of those theories and assumptions to answer such a question.

There are a lot of people employed to try to apply the math to observations, in the hope of actually getting a better understanding of the physics underlying our observations of our universe. But, it is very difficult work, requiring a lot of familiarity with the theories, math and conceptual visualization, then extensive, difficult computations to test whether what those theories predict we would see is what we are seeing.

I am not one of those people doing that type of work, and i don't get the impression that there are any others on this forum who do that type of work. So, I don't expect the folks here to just supply the answers to all of the questions that we come up with as we try to ponder "How can all of this be?"

Helio

#### Helio

The net conclusion of this thought experiment is that things that appear to be simultaneous in one frame of motion can appear to be non-simultaneous, in a different frame of motion that has a much different speed - unless the two things are happening at the same location. The apparent order of 2 events at 2 different locations can be the opposite for 2 different observers who are moving at different speeds, when the speed difference approaches the speed of light to those observers.
Yes, simultaneity is very tricky, and I have yet to delve into it enough to be helpful to others.

We struggle with things that aren't experienced. Simultaneity issues aren't experienced in normal life, though it's easy to understand why one person will claim over a more distant other for a different delay time between seeing lightning and hearing thunder.

#### Unclear Engineer

Some things that we observe are just seemingly impossible. A good example is the slit diffraction experiment with "individual" photons. They still make an interference pattern when we only send one through either slit during single short intervals of time, so that makes them seem to be waves. But, when we apply a detector to determine which slit each photon goes through, then we do not see a wave diffraction pattern, but rather a pair of separated particle impact locations. Even more disturbing is the apparent change in the pattern from separate particle impact locations to a wave diffraction pattern when the "detector" is turned on after the photons have passed through the slits - which seems to challenge the cause-effect relationship or even suggest travel backwards in time, somehow.

So, light and simultaneity is not just a cosmological problem, it is also a quantum physics problem. Even though we can describe it, we really don't understand how it works at the level that we think we understand things that are describable with Newtonian physics.

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Helio

#### Greenlight

if time dilation is the cause for the Lorentz length contraction how is it only in the direction of motion? Time runs differently depending on which direction you are facing?

gravitation time dilation is in the radial direction.

if mass increases when approaching c this will cause a radial contraction.

would these two contractions in the direction of motion and in a radial direction add?

#### Unclear Engineer

Time dilation due to proximity to gravitational mass does change the apparent passage of time when looking at positions that are different in the "radial direction", but that does not require any motion in the radial direction or any other direction. Two clocks placed at two different altitudes (radial positions) run at different speeds while they are in those positions, and the discrepancy can still be seen when they are brought together for comparison. See https://en.wikipedia.org/wiki/Gravitational_time_dilation .

The time dilation due to speed differences between two frames of reference seems to be independent of the dilation due to altitude differences between those frame of reference. So, yes, we would have to add the effects for something like a star orbiting close to a black hole event horizon. And, then there is "frame dragging", where the spin of the black hole makes space seem to contort into a spiral as it is dragged around the black hole. So, three different effects to untangle if you want to use them to accurately explain observations near a black hole.

Calculating the combined effects accurately is beyond my personal capabilities - I never tried to learn how to do that. And, I am not always convinced that others have done it correctly, either, because it is not only hard to do the calculations, it is hard even to conceptualize how to set up the equations properly. And, even when we seem to have agreement that it has been done correctly, it still doesn't seem to explain everything we are observing. That is why many are postulating "dark matter" to add gravitational force, although we cannot (yet) find anything massive enough to exert that much gravitational force.

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#### Helio

So, light and simultaneity is not just a cosmological problem, it is also a quantum physics problem. Even though we can describe it, we really don't understand how it works at the level that we think we understand things that are describable with Newtonian physics.
Yes, it's pretty crazy. The fact that a photon's reference frame expends zero amount of time in travel, may have something to do with it. It can't "do" much if it has no time to do it.