Is relativistic effect of length contraction physically real ?

[granpa]

If you multiply every vector in DaleSpam's diagram with

\gamma\begin{pmatrix}1 && -v\\-v && 1\end{pmatrix}

The diagram will turn into its mirror image with black and white swapped, i.e. the white lines will look the way the black lines do now, and the black lines will look like the white lines do now except they'll be tilted the other way.

It makes no sense to say that one of these diagrams represents reality and that the other doesn't.

well your math is out of my league but let me say this. it is perfectly true, and i have said it many times, that every observer considers himself to be stationary and every observer sees exactly the same thing (that he would see if he were indeed stationary). this is perfectly symmetrical. but the equations of relativity show that they see the same thing for entirely different reasons. some see an object to be shortened because that object is length contracted and others see objects to be shortened because the observer is experiencing a loss of simultaneity. this is not symmetrical at all and fancy math manipulation doesn't change that.

 

[Fredrik]

If you think so, it must be because you're focusing on the wrong parts of the math. For example, I don't think you have fully understood the very intimate relationship between relativity of simultaneity and length contraction. Relativity of simultaneity is precisely what makes different observers disagree about what events the endpoints are when they measure the length of the same object, and that's the reason they measure different lengths. So you can actually think of the simultaneity stuff as the cause of length contraction. But it's probably better to think of the Minkowski metric, or equivalently, the Lorentz transformation, as the cause of all of these things.

 

[granpa]

loss of simultaneity can explain some length contraction but not all. that's the point.Relativity of simultaneity is precisely what makes different observers disagree about what events the endpoints are when they measure the length of the same object,

thats exactly what i explained here:
https://www.physicsforums.com/showthread.php?t=236978
has nobody ever bothered to read it?

 

[Mentz114]

granpa,
Relativity of simultaneity is a consequence of using the Minkowski metric to describe space-time. It is not a 'cause' of anything, but an effect. As Frederik says "...it's probably better to think of the Minkowski metric, or equivalently, the Lorentz transformation, as the cause of all of these things".

And as MeJennifer remarked, the only directly observable quantity is the proper time measured by clocks along world-lines, which is invariant under Lorentz transformations, so all inertial observers agree on the value.

You probably understand this, which makes your use of your own term 'loss of simulataneity' rather unnecessary. I mean, it's all because because of relative motion is it not ?

 

[Dale]

well your math is out of my league ... this is not symmetrical at all and fancy math manipulation doesn't change that

I highly recommend taking the time to learn the appropriate math. As long as you have taken two years of high-school algebra you should do fine. What you are missing is just the first pieces of linear algebra. But here is the summary as it relates to the Lorentz transform

The http://en.wikipedia.org/wiki/Lorentz_transformation" (in standard configuration i.e. 1D motion only along the x direction, axes parallel) can be written
\begin{cases}<br /> t&#039; = \gamma \left( t - \frac{v x}{c^{2}} \right) \\ <br /> x&#039; = \gamma \left( x - v t \right)<br /> \end{cases}

for c=1 this simplifies to

\begin{cases}<br /> t&#039; = \gamma \left( t - v x \right) \\ <br /> x&#039; = \gamma \left( - v t + x \right)<br /> \end{cases} eq 1

By letting (t,x) be a vector in spacetime (normally it is (ct,x) but remember we are using c=1) we can write the above expression for the Lorentz transform in matrix form as Fredrik did

\left(<br /> \begin{array}{l}<br /> t&#039; \\<br /> x&#039;<br /> \end{array}<br /> \right)=\gamma\begin{pmatrix}1 &amp;&amp; -v\\-v &amp;&amp; 1\end{pmatrix}.\left(<br /> \begin{array}{l}<br /> t \\<br /> x<br /> \end{array}<br /> \right) eq 2

So eq 2 is just another way to write eq 1, which is the (simplified) Lorentz transform. One advantage of writing it this way is that it let's you see the symmetry more clearly. Specifically:
\begin{pmatrix}\gamma &amp;&amp; -\gamma v\\-\gamma v &amp;&amp; \gamma\end{pmatrix}=\begin{pmatrix}\gamma &amp;&amp; \gamma v\\\gamma v &amp;&amp; \gamma\end{pmatrix}^{-1} eq 3

What eq 3 shows is that to undo the Lorentz transform you just take the Lorentz transform with the opposite velocity. In other words, after Lorentz transforming to a frame moving to the right at v, if you want to go back, you simply Lorentz tranform to the left at v. This implies that all effects of the Lorentz transform (length contraction, time dilation, relativity of simultaneity) are completely symmetrical between the two frames. The other frame is always both length-contracted and "unsimultaneous".

 

[Mentz114]

granpa,

I read your post that you linked to above. If you are showing that LC, TD and LOS are all necessary ( and sufficient ?) to get SR, you are right. It's just much neater to roll all the effects into one neat package.

You might find this amusing if you want to play with space-time diagrams.

http://www.blatword.co.uk/space-time/minkowski_help.html

 

[Dale]

Hi Mentz,

Cool little app! I quickly recreated the spacetime diagram from the "https://www.physicsforums.com/showthread.php?t=236885"" thread.

 

[granpa]

granpa,

I read your post that you linked to above. If you are showing that LC, TD and LOS are all necessary ( and sufficient ?) to get SR, you are right. It's just much neater to roll all the effects into one neat package.

You might find this amusing if you want to play with space-time diagrams.

http://www.blatword.co.uk/space-time/minkowski_help.html

i was saying that and i was also saying that there is nothing magical about the fact that object a, which is moving and is length contracted, perceives object b, which is stationary, to be shorter than itself. it follows very simply from loss of simultaneity.

 

[paw]

granpa,

I read your post that you linked to above. If you are showing that LC, TD and LOS are all necessary ( and sufficient ?) to get SR, you are right. It's just much neater to roll all the effects into one neat package.

You might find this amusing if you want to play with space-time diagrams.

http://www.blatword.co.uk/space-time/minkowski_help.html

I don't suppose you have a version that'll run under Win98SE do you?

 

[Mentz114]

paw,
PM me with the details of the problem. I may be able to help.

M

 

[paw]

paw,
PM me with the details of the problem. I may be able to help.

M

Done

 

[kahoomann]

I really like Schutz because I think the SR section in his "A first course on general relativity" is awesome, but this is just wrong. One way to see that is to consider the acceleration of a single classical point particle. It's energy will increase by \gamma mc^2-mc^2, and it's definitely not because atoms are being squeezed together. See e.g. the recent thread about derivations of E=mc².

Consider what happens when we accelerate a box filled with gas.
Will its energy increase by the same amount as a solid body, i.e. \gamma mc^2-mc^2? In other words, will the pressure of the gas play a roll in its energy increase?

 

[john 8]

Here is the question:

Is relativistic effect of length contraction physically "real"?

You said:

It's very real, but not in that sense. This should be obvious if you consider that it doesn't matter if it's the object or you who changed velocity.

What do you mean by not in that sense? If you think length contraction is not a physical occurrence then what do you mean?

 

[john 8]

It is physically real, this can be seen by the fact that particle accelerators require relativistic corrections to the "bunch length" in order to determine the interactions of the particles..

So you think that length contraction is a real occurrence. OK, let's look at this idea. We all agree that when we talk of length contraction we are talking about a physical object contracting in length. So in order to change the length of an object we need to apply an equal force to both ends of the object in order to change its length.

So where does this force come from? And in what way does this force contact the object in order to push on it?

Next, As in the examples given by Einstein in his explanation of length contraction he used the idea of rods contracting.

So let's use his examples, now let's suppose that we have four rods all moving in the same frame of reference. One rod is made of wood, one rod is made of iron, one rod is made of paper, and one rod is made of glass.

Now according to this whole theory of length contraction, all rods will appear to contract the same amount when viewed from a different frame of reference.

If length contraction is a real physical occurrence then that means a real physical force was applied to these four rods in order the cause them to contract.

So now we have four rods that are made of different materials, and each of these different materials will require different amounts of force to contract them.

Now we are faced with the fact that some how this force knows what amount of pressure needs to be applied to what object in order to make all the objects contract the same. Sounds like some kind of supernatural force to me.

Alright, so now on to the last unexplained phenomenon of this whole length contraction theory. If you believe that real physical objects truly contract, then once these objects have contracted, how do they regain their original length. A force was required to contract the object, so a force is required to bring it back to its original length.

Why is there no mention of any force in all the descriptions and math involved with length contraction? Can anyone provide a mathematical equation of length contraction that includes the use of some type of force?

I know that you will not find such an equation, so I say to all of you that believe that length contraction describes an actual physical occurrence, maybe it is a supernatural phenomenon.

Lorentz contraction is strain-free, as can be measured by a strain gauge, so it does not require additional energy. Don't forget that the fields around an atom also length contract.

As of today we know that Newton's laws of motion stand as undisputable facts, and these facts are the basis of physics. So with that in mind and what you just said let's try to connect the two.

You, DaleSpam say that length contraction is physically real and does not require additional energy to achieve this action. You seem to think that it is possible to get something for nothing.

Newton's first law of motion:

"A body continues to maintain its state of rest or of uniform motion unless acted upon by an external unbalanced force." This law is known as the law of inertia.


To physically move or change a physical thing it will require a force. If you take the field around an atom you have to have some type of force applied to it to change it, it does not happen on its own. You have to force something to change its natural state.

This field around the atom is in a state of equilibrium and will remain so until acted upon by an exterior force or energy. So the fact that there is a force that is moving the surface of this field around the atom in toward the center or however you want to think about it, the fact is that this field is being moved. So there is an action of motion in one direction so guess what, there is going to be an equal and opposite action against this force by the field.

Newton's third law of motion:

"To every action there is an equal and opposite reaction."

So what ever this force is, it has to be a real physical force. This brings me back to asking, where does this force come from, and why is there no mention of force in any discussion or in any equation that deals with this "real" phenomenon?

 

[john 8]

yes and no.

a moving object and a stationary object can't both be shorter than the other. 1 really shrinks. the other only APPEARS to shrink when viewed by the first.

https://www.physicsforums.com/showthread.php?t=236978

Please become more familiar with S.R. There is no such thing as stationary in S.R.

Everything is relative, the motion of one frame of refernce is relative to another frame of reference.

 

[john 8]

Bernard Schutz, in his book, indicates that Lorentz contraction does require an extra input of energy to squeeze the atoms of the body closer together. Is there anyone who agrees with him?

see this link
http://books.google.com/books?id=jR...a+solid+body"&sig=T8L2gCi4h6HUs1QKBq60HBbU-yM

How would something that is in a state of equilibrium of forces just decide or do something different if no force is involved? All objects are in a state of equilibrium, all the internal vibrating and motion of the atoms or what ever you want to believe matter is made of, is in a state of equilibrium of force. In order to change this state there has to be some type of unbalance to this equilibrium. No physical object decides to do something other than what it is doing. Physical objects only do something different when FORCED to do so, otherwise they will continue to remain as an object in a stable state of equilibrium.

 

[Vanadium 50]

So you think that length contraction is a real occurrence. OK, let's look at this idea. We all agree that when we talk of length contraction we are talking about a physical object contracting in length. So in order to change the length of an object we need to apply an equal force to both ends of the object in order to change its length.

Not true.

I know that you will not find such an equation, so I say to all of you that believe that length contraction describes an actual physical occurrence, maybe it is a supernatural phenomenon.

Also not true.Consider the case where we are squeezing (or pulling) both ends of a rod, and we ask the question "how much force is necessary to make the rod the length predicted by SR." I hope you agree that this is a well defined question.

The answer turns out to be zero. For all materials. No spirits or goblins need to be invoked.

 

[john 8]

If you accelerate a real object by pushing it at one end, you will compress it a bit,.

If you apply force to only one end of an object, you will only move that object. In order to compress an object you will have to apply a force to both ends of the object. In order to compress an object you have to move one end or edge in toward the other, that other end or edge needs to be held in place so as not to have the whole object move. So where is the science behind what you are stating.

If you accelerate a real object by pushing it at one end, you will compress it a bit, but if you don't break it, every microscopic piece of it will restore itself to its original rest length in co-moving inertial frames.,.

In the real world if you compress a piece of iron it will not restore itself to its original length. So where are you getting the idea that compressed objects will just restore themselves to original length.

A Lorentz contraction is real in the sense that objects really do get shorter or longer when your velocity relative to the object changes (regardless of whether it was you or the object that accelerated). It's not just that that they appear to get shorter or longer. The reason why lengths change is that your velocity is what determines which 3-dimensional "slice" of space-time you will consider space. (There's nothing more important than this in all of SR, so you should try really hard to understand it if you're at all interested). Two observers who measure the length of the same object will disagree because they are measuring the lengths of different paths in space-time..,.

So let me ask you something, if this length contraction is a real physical occurrence than it will occur whether there is an observer or not, right?

We do not need an observer present to have any of Newton’s laws of motion to work.

A radio wave can exist and function the same whether there is an observer or not.


If you have someone who observes an object contracting as it is moving past him then is he observing a real physical phenomenon that is happening to that object. If so then that same object moving at the same speed will contract to the same length whether there is someone there to observe it or not, right?

So if this whole length contraction thing is a real physical phenomenon it will occur whether there is someone there to see it occur.

So as I sit here in front of my computer I do not see the planets moving relative to me, I do not see the cars that are moving relative to me and the people in those cars do not see me. In fact there are millions of things that I do not see that are moving relative to me, and there are millions of people moving relative to me that do not see me.

Now if you assume that this length contraction idea is a real physical occurrence than my length would depend on the frame of reference of some other moving object, now with all of these millions of objects all moving relative to each other and me, I would have to be millions of different lengths all at the same time right now, all of this physical change in my length, the length of my table, chairs, cats, dishes, plumbing, bricks, and all the objects in my environment would cause quite a bit of heat, yet all is good here.

If this length contraction is solely dependent upon an observer to be present for any contracting to occur, than you will have to show me how an object knows that there is an observer in order for it to decide to contract. You see if an object can move past a blind man will it contract? There is someone there, but that someone just was not able to perceive light reflecting off of object so this blind man did not observe the object.

If the object still contracts then that means that everything in this universe is expanding and contracting at a mad rate in order to satisfy the physical laws the require all object moving in different frames of reference to contract, and since this universe is full of so many different frames of reference that means that all objects are at the effect of this phenomenon.

Now if the object does not contract in the presence of the blind man than that means that the object knew the man was blind and so could not see, and so the object did not contract. This would also bring up the question that if objects only contract when observed than what is the physical phenomenon (the science) behind the fact that light that is reflected off of an object and enters an eye that is able to perceive the wavelengths of this electromagnetic wave can actually cause an object that is moving to contract.

So I would like you to clarify this for me. Does length contraction depend solely on an object being observed to contract, or is length contraction something that occurs without any observer being present?

 

[john 8]

Originally Posted by john 8
So you think that length contraction is a real occurrence. OK, let's look at this idea. We all agree that when we talk of length contraction we are talking about a physical object contracting in length. So in order to change the length of an object we need to apply an equal force to both ends of the object in order to change its length.

Not true..

Explain what is not true.



Originally Posted by john 8
I know that you will not find such an equation, so I say to all of you that believe that length contraction describes an actual physical occurrence, maybe it is a supernatural phenomenon.

Also not true...

OK. Show me why this is not true. Provide evidence please.

Consider the case where we are squeezing (or pulling) both ends of a rod, and we ask the question "how much force is necessary to make the rod the length predicted by SR." I hope you agree that this is a well defined question.

The answer turns out to be zero. For all materials. No spirits or goblins need to be invoked.

Force needs to be applied to all physical objects to cause them to contract.

"A body continues to maintain its state of rest or of uniform motion unless acted upon by an external unbalanced force." This law is known as the law of inertia.


If zero force is applied to an object that is in equalibrium, than that object will not be changed.

Squeezing or pulling is an action. Action is the result of force. If there is action there is force. To say that no force is required to cause an action or change in a physical object is to get something for nothing. Explain to me in your own words your understanding of how an object can be compressed without the use of force.

 

[Fredrik]

Here is the question:

Is relativistic effect of length contraction physically "real"?

No, that's not the question. This was the question:

Is Lorentz contraction a real contraction? For example, if one tries to accelerate a solid body, does its contraction require an extra input of energy to squeeze the atoms of the body closer together? Will this extra energy go into the total mass of the moving body?

Note that he defined what he meant by a "real" contraction. He defined a contraction to be "real" if you have to supply an extra input of energy to make the object shorter, i.e. if you have to supply more energy than you need to accelerate the atoms individually.

You said:

It's very real, but not in that sense. This should be obvious if you consider that it doesn't matter if it's the object or you who changed velocity.

What do you mean by not in that sense? If you think length contraction is not a physical occurrence then what do you mean?

It's real, but not in the sense that it satisfies his definition of "real".

You don't have to supply any more energy than what's needed to accelerate the atoms individually. You don't have to perform any work to "squeeze" the object. However, that's not a good reason to say that the contraction isn't "real".

 

[Fredrik]

"A body continues to maintain its state of rest or of uniform motion unless acted upon by an external unbalanced force." This law is known as the law of inertia.

This only says that you have to apply a force to change an object's velocity. It's true in SR too.

Explain to me in your own words your understanding of how an object can be compressed without the use of force.

You push the rear endpoint of a solid rod. The interactions between two adjacent atoms strive to keep the distance between them constant in a co-moving inertial frame. If you do the math you'll find that this makes the object shorter in the original rest frame. The forces that make the rod contract when you push it are the same forces that keep its length constant when it's at rest. No additional forces are needed.

 

[JustinLevy]

This only says that you have to apply a force to change an object's velocity. It's true in SR too.

But please note that if the force was the same on all atoms in a rod, the rod would NOT relativistically contract as it sped up. Consider for instance Bell's spaceship example. With no force from the elastic band, the spaceships will stay the same distance appart in the original inertial frame (ie. the proper length will get longer). For the length to contract between the spaceships, the elastic band must be applying a force.

Said another way it is important to realize these two situations are different:
- comparing a length measurement in one inertial frame to a length measurement in another inertial frame
- comparing several lengths measurements in the same frame, at different times, of an accelerating object

Using appropriate approximations, we can show the two should have a similar function. The two are the same only if the accelerating object has come to equilibrium (constant proper-length) to the force applied. In some cases this is not even physically possible (Rindler's horizon).

For an accelerating rod to follow the relativistic length contraction formula exactly, the proper acceleration is different on the two ends of the rod. This is a physical difference. You can indeed measure it even from the "rest frame" of the rod.

So please, if you want to debate the "realness" / "physicalness" of contraction, please be very specific about what situation you are discussing.

The forces that make the rod contract when you push it are the same forces that keep its length constant when it's at rest. No additional forces are needed.

This is incorrect, as noted above.

 

[matheinste]

Hello john 8.

Explaining the reality of relativistic contraction is difficult because of the difficulty of defining the meaning of real. I cannot attempt to explain this 'reality' other than saying it is not purely an effect of optical perspective. However it is quite clear from the very basic axioms of relativity that, 'real' or not, for relativistic length contraction no force is required. You must understand that the nature of this contraction is far more fundamental than a mere physical compression or shrinkage.

Matheinste.

 

[Fredrik]

But please note that if the force was the same on all atoms in a rod, the rod would NOT relativistically contract as it sped up.

I agree, and I have probably explained that in more posts than anyone else here. (Except that I usually talk about the acceleration instead of the force). I don't see why you're quoting an unrelated sentence of mine before you explain this.

So please, if you want to debate the "realness" / "physicalness" of contraction, please be very specific about what situation you are discussing.

I really don't see why you are saying this to me. I'm definitely not the one who brought up the "realness", and I have been more specific than anyone else here.

This is incorrect, as noted above.

No it's not. I think you misunderstood me, but perhaps I didn't express myself clearly enough. Inside each infinitesimal segment of the rod, the internal forces in the inertial frame that's co-moving with that segment, are always the same (except for a sound wave that's propagating through the segment, but if the force applied to the endpoint of the rod is small enough, the sound wave can be ignored).

If we consider a short segment instead of an infinitesimal one, the endpoints of the segment are accelerating differently (in the inertial frame that's co-moving with one of the endpoints), but that difference disappears in the limit where the length of the segment goes to zero.

When an accelerating solid gets Lorentz contracted, the internal forces are striving to keep the length of each infinitesimal segment of the rod equal to its rest length in the co-moving inertial frame where the segment is still at rest. That's what makes the different parts of the rod experience the specific proper accelerations that makes the rod get shorter in the in the original rest frame.

The work you have to perform to accelerate the rod is equal to the work you have to perform to accelerate the atoms individually plus the energy loss due to heating of the rod, but that's it. You don't have to do any additional work to squeeze the rod to a shorter length.

 

[Dale]

So in order to change the length of an object we need to apply an equal force to both ends of the object in order to change its length.

According to what theory? Perhaps you are referring to http://en.wikipedia.org/wiki/Hooke's_law#Elastic_materials": \sigma = E \varepsilon.

If so, I already mentioned that relativistic length contraction is strain free. Therefore, since \varepsilon = 0 we have f = \sigma A = 0 for all materials.

 

[john 8]

Originally Posted by john 8
"A body continues to maintain its state of rest or of uniform motion unless acted upon by an external unbalanced force." This law is known as the law of inertia.

This only says that you have to apply a force to change an object's velocity. It's true in SR too.

If you have an object that has a certain shape, size, location or velocity when it is experiencing an equilibrium of forces than that object will maintain that shape, size, location and velocity Indefinitely. In order to change or disrupt this equilibrium of forces you need to add additional force.

Someone gave the example of the field of an atom contracting in length contraction, and stated that no additional energy was needed to do this.

So take the example of a ball and let's use it as a model for the atom. Any point on the surface of the ball will maintain its location in relation to the rest of the atom as long as there is an equilibrium of forces, those forces being inside and outside the ball. Now in order to change the shape or location of any point on the ball you need to add an additional force to unbalance this equilibrium. It is just the way the physical universe works.

So Newton's first law of motion is relevant here and applies to any change in any state of equilibrium of force.


Originally Posted by john 8
Explain to me in your own words your understanding of how an object can be compressed without the use of force.

You push the rear endpoint of a solid rod. The interactions between two adjacent atoms strive to keep the distance between them constant in a co-moving inertial frame. If you do the math you'll find that this makes the object shorter in the original rest frame. The forces that make the rod contract when you push it are the same forces that keep its length constant when it's at rest. No additional forces are needed.

I asked for you to describe how an object could be compressed without the use of force, and you explained how force is used to compress an object. Yes additional force will be needed to compress an object.



If you push on one end of a rod, you are applying force to one end of the rod. If very little force is applied in relation to the mass of the rod, the rod will not move. If you are applying force in one direction to an object that object is going to push back. If both forces are in equilibrium than that rod will not move. When you apply enough force to cause an unbalance in this equilibrium then the rod will move.

If you want to compress a can in your hands you have to apply force to one end of the can and have a force (or hand) on the other end of the can to push back. If you do not have this force at both ends of the can then the can will just move and not compress.

 

[phyti]

Special Relativity is a set of equations that transforms coordinates, not physical objects!
The issue is length of object (in its frame) vs measured length from another frame.

As mentioned by john 8, the object is moving inertially in a state of equilibium, with no forces acting on it. The only way an object changes form is by non uniform forces.

Consider a rod in its rest frame, and A and B moving past it at different speeds. Each will measure it differently, a result of their relative speed. No forces act on the rod, and if 'real' length contraction, it would have to assume two different lengths simultaneously!

The fact that the 'measured length' changes with the motion of the observer should tell you it's perception (observer dependent).

 

[feynmann]

Special Relativity is a set of equations that transforms coordinates, not physical objects!
The issue is length of object (in its frame) vs measured length from another frame.

The fact that the 'measured length' changes with the motion of the observer should tell you it's perception (observer dependent).

Can you tell me if "time dilation" is just perception or it's physically real?

 

[Makep]

Is Lorentz contraction a real contraction? For example, if one tries to accelerate a solid body, does its contraction require an extra input of energy to squeeze the atoms of the body closer together? Will this extra energy go into the total mass of the moving body?

What we perceive as distance / length depends on our movement in space relative to other objects. In relativity we are interested in the linear translation of bodies and hence points, with respect to other points, as they move in space.
Movement is the ability of bodies to contract space. A body that is accelerating is actively contracting space / length at a rate that is directly proportinal to its acceleration. When such a body assumes a constant velocity after accelerating, it has already contracted space by a factor that is directly proportional to its initial acceleration. Its perception of spatial dimensions will be governed by the factor with which space has contracted. To itself it will perceive as 'not changed' but every spatial dimension will become smaller by a proportinality constant directly related to its initial acceleration.
Thus, Lorentz contraction does not squeeze the atoms together, rather squeezes the spaces within which they exist (contracts their space) and causes the mass to shrink in a manner proportional to its acceleration thus, maintaining their 'absolute' space but contracting their 'apparent / relative' space.
The energy needed for such a movement would not go into the total mass of the body. It would go into the total weight of the body. Thus, a body would not increase in size, it would increase in weight - mass not being a factor of concern here but its original acceleration being the factor playing on a constant mass.

 

[Fredrik]

I asked for you to describe how an object could be compressed without the use of force, and you explained how force is used to compress an object. Yes additional force will be needed to compress an object.

No. You need to apply an external force to one end of the rod to accelerate the individual atoms, but you don't don't have to push "extra hard" or "from both sides" to compress it. The internal forces will make sure that it contracts by a factor of \gamma when it's accelerated. They do this by keeping each infinitesimal segment of the rod a constant length in the inertial frame that's co-moving with that segment, which is exactly what they're doing when the rod isn't accelerating.

If you push on one end of a rod, you are applying force to one end of the rod. If very little force is applied in relation to the mass of the rod, the rod will not move.

This is only true if there's friction. The discussion is about length contraction, so it's appropriate to consider a scenario where friction can be ignored.

If you want to compress a can in your hands you have to apply force to one end of the can and have a force (or hand) on the other end of the can to push back. If you do not have this force at both ends of the can then the can will just move and not compress.

This is only true as long as the speed of the can is very small. If you increase its speed by pushing only one end of it (gently for a long time), it will get shorter by a factor of \gamma.

Do you really think it's a great idea to go to a physics forum and aggressively claim that special relativity is false without learning what the theory says first?