# Does shortness from length contraction have a real physical effect?

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• syfry
syfry
TL;DR Summary
Does length contraction have a real physical effect, such that the shortenings would affect physics, but only from the perspective of someone observing the contraction?
Do the contractions affect physics in any frame?

Examples:

If length contraction reduces mass in the direction of motion, and therefore reduces the total momentum. (from observer's perspective)

If in the reference frame of a station, the moving train weighs less than it did when parked, because the train is shorter when moving. (and from the moving train's perspective the station also weighs less)

If from the perspective of a spacecraft that's approaching near the speed of light, the Earth's incompressible ocean water is compressed beyond the point that it could be compressed. (or instead merely appears that way)

If that same spacecraft were approaching a star whose degeneracy pressure is at the max, would electron capture into all of the nucleus already be happening from the person's perspective? (by the star being further compressed)

If the same spacecraft were approaching an object already compressed to near to its swartzchild radius, would the object have crossed that threshold and became a black hole from the person's perspective?

I'm aware that all might sound like a ridiculous premise, but so did the notion of length contraction to many scientists when Lorentz introduced the concept. So better to check and be sure.

Many of those results seem absurd so I'm thinking that the contraction doesn't produce 'relative physics' that happens only in the frame of the observer who's perceiving the contraction.

But I could be wrong, so here we are.

Length contraction is an effect caused by picking a different definition of simultaneity, so you see a differently shaped 3d slice through the 4d structure of the object. It's very closely akin to slicing a sausage perpendicular to its length and getting a circular slice versus slicing at an angle and getting an elliptical slice. The sausage is the same, you just selected different parts of it.

So length contraction makes no difference to anything. It's just you making different measurements.

cianfa72, vanhees71 and syfry
syfry said:
Many of those results seem absurd so I'm thinking that the contraction doesn't produce 'relative physics' that happens only in the frame of the observer who's perceiving the contraction.
If something happens, it happens no matter what frame we choose to describe the situation. So the effects of length contraction (and time dilation, and relativity of simultaneity - we generally have to consider all three to arrive at a consistent description) are present in all frames.

For an example, consider muons created by cosmic rays. These particles decay very quickly, so quickly that they shouldn’t live long enough to travel 100 kilometers or so from where they are created in the upper atmosphere to the surface of the earth. But they do (and this was one of the early observational tests of relativity).

Using the frame in which the earth is at rest we say that this is explained by time dilation: time passes less quickly for the fast-moving muon so it lives long enough to travel the entire thickness of the atmosphere before it decays.

But there’s no time dilation when we use the frame in which the muon is at rest and the earth is rushing towards it (OK, there is for the moving earth but that doesn’t affect the muon) - so how does the muon live long enough to pass through the atmosphere? When we use that frame, the thickness of the atmosphere is length contracted so the muon doesn’t have to go as far.

So either way, the muon lives long enough to reach the earth’s surface, and that is the effect of time dilation and length contraction.

vanhees71, syfry and Sagittarius A-Star
Nugatory said:
If something happens, it happens no matter what frame we choose to describe the situation. So the effects of length contraction (and time dilation, and relativity of simultaneity - we generally have to consider all three to arrive at a consistent description) are present in all frames.

For an example, consider muons created by cosmic rays. These particles decay very quickly, so quickly that they shouldn’t live long enough to travel 100 kilometers or so from where they are created in the upper atmosphere to the surface of the earth. But they do (and this was one of the early observational tests of relativity).

Using the frame in which the earth is at rest we say that this is explained by time dilation: time passes less quickly for the fast-moving muon so it lives long enough to travel the entire thickness of the atmosphere before it decays.

But there’s no time dilation when we use the frame in which the muon is at rest and the earth is rushing towards it (OK, there is for the moving earth but that doesn’t affect the muon) - so how does the muon live long enough to pass through the atmosphere? When we use that frame, the thickness of the atmosphere is length contracted so the muon doesn’t have to go as far.

So either way, the muon lives long enough to reach the earth’s surface, and that is the effect of time dilation and length contraction.
Cool, makes sense! Almost seems as though time dilation is length contraction in another frame, and vice versa. (sort of like electric and magnetic fields from different frames of reference)

syfry said:
TL;DR Summary: Does length contraction have a real physical effect, such that the shortenings would affect physics, but only from the perspective of someone observing the contraction?

Do the contractions affect physics in any frame?
The first postulate of SR is that the laws of physics are the same in every inertial reference frame. From that it's clear the answer is no. That also means that we have to express the laws of physics correctly. In this case, the rest length of an object is the invariant quantity. Likewise a clock measures its own proper time. Not general coordinate time. And the rest mass of an object is the invariant quantity. Relativistic mass is not very useful for expressing the laws of physics, precisely because it is frame dependent.

syfry and vanhees71
syfry said:
TL;DR Summary: Does length contraction have a real physical effect, such that the shortenings would affect physics, but only from the perspective of someone observing the contraction?

Do the contractions affect physics in any frame?
As you say, there is nothing unusual happening within the physics of an IRF, call it F1. It is always as though it is stationary. To an external IRF, call it F2, that is moving relative to F1, the length and time measurements are different and the explanation of invariant events may be different. An invariant event is one that would be observed and agreed upon in any reference frame (a collision, explosion, simultaneity at a single location, etc.)
It is certainly true that SR must be considered when the physical behavior of a fast moving object is observed. Fast moving subatomic particles will not disintegrate at the same average time as when stationary. That is important in particle colliders. There, target objects may be bombarded by very fast particles that would otherwise not exist long enough to reach the target. But, because of SR, the particles last "long enough" (measured in the "stationary" frame) to reach the target.

syfry said:
Does length contraction have a real physical effect, such that the shortenings would affect physics, but only from the perspective of someone observing the contraction?
Depends on what you mean by "real physical effect". In the frame of someone observing an accelerating rope, that is forced to keep a constant length, the rope will break, because the contracting rope-atoms cannot span that length anymore:

syfry and Sagittarius A-Star
A.T. said:
Depends on what you mean by "real physical effect". In the frame of someone observing an accelerating rope, that is forced to keep a constant length, the rope will break, because the contracting rope-atoms cannot span that length anymore:
To be clear, the rope would break in all frames, right? (even if from perspectives in which they don't see a reason for the rope to break)

syfry said:
the rope would break in all frames,
A frame is just a choice of coordinate system. "Does the rope break in all frames" is closely analogous to "does the river still exist if I turn the map around". Yes it does, and yes the rope breaks according to all frames.

FactChecker, PeterDonis and syfry
syfry said:
perspectives in which they don't see a reason for the rope to break
There are no such perspectives. Different frames might give different interpretations of why the rope breaks, but all frames will agree that it does.

syfry, Ibix and FactChecker
PeterDonis said:
There are no such perspectives. Different frames might give different interpretations of why the rope breaks, but all frames will agree that it does.
Yes, the rope breaking is universally agreed on. Because the measurements of time, distance, and simultaneity are different, the various inertial reference frames have different explanations for it breaking. The relativity of simultaneity is one thing that seems to be overlooked more often than most.

Ibix
syfry said:
To be clear, the rope would break in all frames, right?
If the rope breaks when we analyze the situation using one frame, then it will break in all frames. Furthermore, if we have a strain gauge in the rope, we will agree about it what reads, and that the rope breaks when its reading reaches the breaking strength of the rope.
(even if from perspectives in which they don't see a reason for the rope to break)
There will be no frame in which we will not see a reason for the rope to break. Some frames may describe the situation as the length of the rope remaining fixed while the endpoints move apart; others will describe it as the rope contracting while the end points remain the same distance apart; and yet others will describe a combination of the two effects.

In all cases (and this is the key to Bell's paradox) the underlying issue is the relativity of simultaneity - the different frames will disagree about where the endpoints are at the same time.

Last edited:
FactChecker
syfry said:
To be clear, the rope would break in all frames, right?
Yes.
syfry said:
(even if from perspectives in which they don't see a reason for the rope to break)
There is no such frame. A "reason to break" is a combination of boundary conditions and quantities derived from them, which in combination are inconsistent with an intact rope. For example, In the rest frame of one rope end the atoms are not contracted, but here the other rope end doesn't start its proper acceleration simultaneously, so the distance between the rope ends increases. In general, the "reason" for any frame is a mismatch between the changes in atom size and the length they have to span.

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FactChecker

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