Relativity and Cosmology

I'm having trouble getting the projectile up to 0.7C.

Should I use a spring or an elastic band?

Hi ffej, what about an outsize trebuchet?

From Wikipedia: n 1959 Roger Penrose and James Terrell published papers saying that the Length contraction cannot be observed[20][21]. Rather there would be a kind of rotation now called Penrose-Terrell rotation[22]. Abraham Ungar, using gyrogroup techniques, disputes Penrose and Terrell's position:"A case in point is Einstein's 1905 view of the Lorentz length contraction, which was contradicted in 1959 by Penrose, Terrell and others. The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein.", "Length contraction shows up in visual and in photographic observation of moving objects, as Einstein predicited in 1905."[23]. The observability, or not, of the Length contraction should be able to be experimentally tested in the LHC[24]." So, let us wait until the LHC is back up and running, and then re-address this issue...

Hi cwarner7_11, you wrote: "So, let us wait until the LHC is back up and running, and then re-address this issue..."

I don't know of any LHC test planned for that. Theoretically, I suppose one can measure the length of a beam of protons at various speeds, but it is not a very direct test, because the proper spacing between the photons could have changes between tests.

The "standard" theoretical way of observing length contraction is to have a large in-line set of inertial observers with synchronized clocks in a reference frame. They then record the time of passage of the front and rear of an object. This way they can deduce the length of the passing object in their frame. Not easy in practice...

-J

Hello Jorrie,

This is hypothetical physics. I suppose it is of use figuring out how far distant stars are but I can think of no use on earth for it. Unless, it gave some indication of how a spacecraft is affected tribologically, the comparatively slow speed, well, barely moving compared to C. It would none the less expand due to friction. Or is that to 'real' a result?

I guess when we get into the realm of Relativity and quantum physics, the 'world' and all we think of as 'real' and 'fact', are just a distant blur.

Lorentz contraction is an 'in joke' between Mathematicians...........A little highfalutin for me.

Take care......................

Hi babybear, you wrote: "This is hypothetical physics. I suppose it is of use figuring out how far distant stars are but I can think of no use on earth for it."

Linear and circular particle accelerators would not work if special relativity was not factored into the design. Isn't this an earthly use?

-J

Hello Jorrie,

Hope you are fine?......................

I am really interested in physics, and can understand pretty much all 'basic' physics, (if there is such an animal?) You are living on a different plane to myself I think. I know it helps to be able to see something as 'proof' it works or exists, and also understand how some things which are not immediate obvious, like the 'red shift' are a part of reality. This is too of the wall for me I guess. I can understand how it can happen in a 'mechanical' way, but, surely Euclid never knew of this phenomenon. The Euclidean link is that some of his Geometrical working may 'fit'? When Euclid was around 'light' had barely been touched as a scientific subject.

Other than for a very few people who are 'in' on this, such as yourself and others whom 'camp out' at Particle Accelerators, of which there are very few built anyway, I will have to 'park my pen' and let other more esteemed bipeds carry on the discussion.

I had a Maths Teacher who had very little respect for the people who were his 'bread and butter'.....the pupils. And was allowed and chose to teach a quarter of the pupils (whom he thought were never going to 'do' much anyway) the same Maths over three years. I am not talking terms, I mean years. One of the 'old tie' he had made it in the Forties, coming from a wealthy family, and, people like me were but a means to an end for him. Consequently the maths and science, he was in charge of both, were basic to say the least............So as I say, I will park my pen, and watch from a distance ................

No offect to you and others who will read and reply. I understand the principle, and can actually 'see' this rod going though and making the slit, but that is as far as it goes.

Take care....................And thank you for your reply post!

"Assume that neither projectile nor target are deflected in any way."

Anything that has even the slightest mass, even something subatomic with a positive or negative charge, is going to react to the collision, in some way. Even light bends around large celestial objects.

I suspect that this is an improbable assertion and invalidates the entire matter.

Admittedly, this is not my area of expertise or interest. The closest I ever got to being a Quantum mechanic was changing the brake pads on an Audi.

L.J.

Hi Jorrie.

This post reminds me another post of yours concerning the relativistic time dilation (i.e. if it's real or not). In this case, a (e.g.) spaceship accelerates from our reference frame getting a final stable speed near c. As long as the reference frame of the spaceship is inertial there is a time dilation relative to us [No matter if this is observable or not... remember our discussion in the last cr4 challenge... I'm not convinced yet that we have to "meet" twice the spaceship, (i.e. not an inertial / symmetric case) in order to observe any kind of dilation... ] Of course, if the spaceship decelerates and meet our inertial frame, its clock will be again synchronised with our clock.

So, I remember your statement that this time dilation (on pure inertial systems) is, also, illusional.

The whole issue is "what is a fact or not". In Relativity there is not such a thing like "absolute truth". I mean that we have to decide that sth is real or not relative to what???... If there was sth "absolute" (like aether) then we could decide if sth else is real or just apparent (or illusional) with respect to this "absolute, privileged frame". But there is not such a frame. According to Relativity all inertial frames are equivalent. If you are on an inertial frame you live (observe or consider) your own "unique reality" (i.e. different from the reality of any other inertial observer, travelling at different speed).

Concerning your example: The slit is always 1.4 feet in length on the target's inertial frame (as the movement of the projectile is perpendicular with respect to the target). We just consider it as being 1 foot (from our inertial frame). When the target "meet" our inertial frame we, also, see the slit being 1.4 feet in length... The slit was always 1.4 feet in length... the issue is that when the target and the projectile are in movement (near c) relative to us we "see" a distorted reality on their reference frames. But, anyway, this is a reality for us. We have right when saying that there is a time dilation or a length contraction on these frames.

I think that this is the whole revolutionary concept of Relativity: The "reality" is relative and different for any inertial obesrver... There is no "absolute reality"...

Regards.

Hi George.

Yes, I remember that we could not quite reach agreement on the observability (or not) of relativistic time dilation in the case of purely inertial frames in free space and whether those relative dilations are illusionary or not.

I think the problem with SR is that it is a very incomplete theory. There is probably no thing like gravity-free space where SR completely holds, yet we often state situations as if it is the case. When taken to the limits, inconsistencies are bound to appear. In GR we know that the gravitational field creates a sort of "preferred frame" (Einstein's "new aether"), so it is much nearer to complete and most of the inconsistencies disappear.

-J

I strongly disagree. Special relativity has no more bearing on absolute truth than Euclidean perceptions. I can say that you live about 1500 miles away. Someone in Athens might say that you lived about one mile away. Both statements could true - and can be seen to be true by both people - all that is needed is to move the origin (a transformation).

The same applies to time dilation. I may say that A on this Earth took a week and that identical action B on a moving object took a month. My friend working on the moving object would be able to swap the times around. However, we could readily transform each other's observations and show that they were equivalent. So all that says is that elapsed time is not an absolute measure, any more than distance away was in the first case. It's a more complex transformation, but in no sense is it different in kind. The only problem is that it contradicts our experience-based intuition that elapsed time bears similar relationships for all observers.

"I strongly disagree. Special relativity has no more bearing on absolute truth than Euclidean perceptions."

I only mean that Newtonian perception (or approach) accepts absolute values for some issues like time, length and mass (i.e. that they are independent of the kinetic situation of an object... or the inertial frame of the observer if you like... and it's a very good approach for low speeds...) In contradiction, SR tells us that these issues have not an absolute meaning any more: they are dependent on the observer's inertial frame.

So, in a way, in the light of SR, the reality is more "relative" (than in Newtonian theory).

(Or, maybe, I didn't get your objection... ...)

All I'm saying is that there is as much justification for your statement that "there is no "absolute reality"" in Newtonian mechanics as there is in Special Relativity. Perhaps I should have taken the Newtonian version a step further. In Newtonian mechanics velocity will depend on frame of reference (Newtonian mechanics also does not require a unique frame of reference - any inertial one will do). So velocity is a property that looks different in different frames.

The same applies to time in a relativistic frame. All it means is that the measure of time needs to be transformed as we change reference frames.

In both cases I am happy to say that "there is no absolute measure" for certain parameters. But that is completely different from saying "There is no (such thing as) "absolute reality"."
For Newtonian mechanics that applies to position and velocity, but length and time have absolute measures.
In special relativity, length and time are added to the parameters where the measure changes as we change our frame of reference. However, we can still define parameters such as "rest length" "rest mass", and "age" where the measure does not change between frames.

BTW, you may (or not) find this amusing - the "rest wavelength" of light is infinite...

O.K. Not so much "disagreement" as you thought...

BTW

rest mass of the photon = 0 → non existence of photon

rest wavelength of light = ∞ → non existence of light

(Light exists only at c... ...)

This looks like a rather special case. It is equivalent to moving the needle through a stationary object at 45^O to its axis - when it becomes obvious that the contractions must be equal along the needle and perpendicular to it.

It would be more revealing if you considered what happened if you try your test with projectile moving at (say) 0.7c and target moving at 0.35c.

I just noticed that the original posting was by Jorrie. So it's a leg-pull - and not even April 1st!

Hi Fyz: "So it's a leg-pull - and not even April 1st!"

No, not a leg-pull, rather a bit of "brain-pull"!

Yes, the identical speeds were a bit of "deception". I rather hoped someone would spot it soon, because using different speeds for the needle and target reveals a lot more of the bare relativity, as you implied.

Doing exactly the calculations that I have shown in the OP yields two different lengths of the slit for the Galileo and Einstein methods respectively. As an example, I've used the target speed as 0.6c at right angles to the needle's 0.7c and I got a Galilean slit of 1.2 feet long. The relativistic slit (once the target is brought to rest) works out to 1.08 feet. The question is, can this be right, or is there an error in the method? After all, we usually say that Lorentz contraction can only be observed (in principle) while there is relative movement.

-J

"The question is, can this be right, or is there an error in the method? After all, we usually say that Lorentz contraction can only be observed (in principle) while there is relative movement."

Yes, the principle of these calculations is fine and the answer (to the best of my knowledge) correct. (Although I think the analysis is much more transparent if you calculate the movements and the effects in the frame of reference of the target).
The problem is that what we "usually say" is too open to misinterpretation. Perhaps Marc Anthony had it right?
"The contraction that things do lives after them..."
In other words, you can only observe the actual contraction while there is relative movement, but the effect of any the contraction on interaction lives on.

If that were not to be the case, we might just as well transform our initial observations to self-referenced lengths, and then make all our calculations of what happens using Galilean methods. That would mean that we would not ever need to make any SR length modifications for particle physics, as the initial lengths are known.

I think the clock paradox already mentioned in this thread illustrates this nicely. While the clocks are moving without acceleration the observations will depend on the frame of reference. But if one of the clocks is accelerated so that it returns to its original position in the frame of reference of an unaccelerated clock, the number of ticks (for each clock) that will have occurred in the interim is independent of the frame of reference.

Hi Jorrie,

By "definition" the length contraction is only to an observer, so I agree with GK, and give him a good answer. I was about to say "what is the mystery" until your post 12. Concerning your post 12, there must be a problem with the method or you made a mistake. Assuming you have checked your work, this is perplexing. The "at rest" distance should match Newtonian calculations. Maybe you have found the limits to the theory. Maybe two relativistic speeds at 90 degrees requires more theory? Anyway, good thread as usual. Keep us posted if you solve it.

Regards,

S

You are right that the length of the slit (in the reference frame of the slit) remains unchanged when you change its velocity. But, unless the two velocities measured in our frame of reference are the same, the length of the slit is not the same as it would be in a Galilean/Newtonian world.

Part of the problem lies with the loose terminology that is so often used when describing relativistic events. In everyday language, "observer" only implies "seen" - whereas the important ramifications of SR are in its effects.

Be that as it may...
One of the problems is in the transformation. In our frame of reference the needle appears orthogonal to the target. In the target's frame of reference, that is no longer the case - the transformation is more complex than that.
So, in order to demonstrate the principle, it will be easier to start with a different problem - one that is couched in the frame of reference of the target. We can postulate a needle that is orthogonal to the target plane and that is moving both orthogonally to that plane and parallel to it, both components of the velocities being 0.7c. The rest-length of the needle is 1.4-metres - how long is the slit? All we need to know is how long it takes for the needle to pass though the slit. What happens is simply that the observed length of the needle is reduced by a factor of √(1-0.7²). The speeds are all in the frame of reference of the target, so for this simpler case the slit length is reduced (relative to Newton/Galileo) by a factor of about 0.714.

Hi Fyz, you wrote: "In our frame of reference the needle appears orthogonal to the target. In the target's frame of reference, that is no longer the case - the transformation is more complex than that."

I "fiddled around" with the transformation and eventually concluded that a needle, orthogonal to a moving target, with horizontal needle speed v_n and vertical target speed v_t in the reference frame, will make an angle (ψ) from the orthogonal in the target rest frame, where:

tan(ψ) = (γ_t -1)v_t/v_n and γ_t = 1/√[1-v_t²/c²]

This is however not a pure rotation, but rather a vertical offset of the rear end of the horizontally contracted needle in the direction of vertical movement, by a distance:

ΔS = (γ_t - 1)L'v_t/v_n where L' is the contracted length of the needle L'=γ_nL.

This seems to remove the discrepancy that I mentioned in #25. In the low speed limit, (γ_t -1) -> 0 and the Galilean result (no rotation or offset) falls out. I think the vertical offset is due to simultaneity differences between the original reference frame and the target frame (as measured by the synchronized clocks and rulers of the target frame).

-J

Agreed in principle - I'd assumed the contraction - so it couldn't be pure rotation. But I seem to remember that I've fallen over myself elsewhere in this thread - I'll try to recover when I have enough of a break to think about it more clearly (that could be a while).

Hi S, you wrote: "Maybe two relativistic speeds at 90 degrees requires more theory?"

It would seem so, yes. Recall that I calculated the proper length of the slit in post 12 as 1.08 ft, once the target has been brought to rest in the reference frame (and Fyz seemed to confirm this result). However, if I do a calculation for the scenario that Fyz proposed, i.e., the target as reference frame and the needle having parallel and orthogonal speed components (0.6c and 0.7c to fit my previous example), I get a proper length for the slit as 0.86 ft.

The two results (1.08' and 0.86') cannot differ, so one of the two methods, or both, must be erroneous. The suspicion is on the latter method, because as Fyz pointed out: "One of the problems is in the transformation. In our frame of reference the needle appears orthogonal to the target. In the target's frame of reference, that is no longer the case - the transformation is more complex than that."

I hope Fyz and myself can work out what the orientation of the needle is relative to the target!

-J

If two needles are placed side by side on an inertial reference frame and if one needle starts moving to the right at 0.7c and other to the left at 0.7c then what will be the length of the slit made on the reference frame after one second. I know it is not possible to have 1.4c .Sorry, My Knowledge on SR is limited. I can only ask questions.

Hi k.v.gopalakrishnan, I don't quite understand your question, but there is no problem with having two objects moving in opposite directions, both at 0.7c (or any speed less than c). Their relative speed is given by: v = (v1 + v2)/(1 + v1 v2), which gives 0.94c in this case. As you can check, relative speeds will never exceed c.

-J

Hi Jorrie, My question is, suppose I stand in front of a sheet of film which extends to infinity on both left and right side and I set two needles to cut a slit on the film ,one start moving at velocity c away from me in the left direction and similarly the other needle moving at c in the right hand side.After one second if I look at the film to my left , the needle would have created a slit length equivalent to one c and similarly in the right side the length would be one c and therefore after one second a slit length of 2c is created. Is it possible , if not why?

Hi k.v., yes, from your perspective, stationary relative to the film (the reference frame) it is possible, provided the "needles" are not physical objects. Even physical objects, traveling at more than half the speed of light in opposite directions, can have a velocity difference in excess of c in the reference frame. After all, you will measure a slit that grows in length at a rate (dL/dt) greater than c!

What is not possible is for two observers, flying with the physical objects, to measure each others recession speed as exceeding c. Even if each is at 0.999c relative to the film, they will measure each others recession speed as just less than c. This is because the reference frame distances are Lorentz contracted from their perspectives. They will each measure a much shorter slit than what you in the reference frames measure.

-J

Thank you Sir, for the explanation. The restriction of c applies only to physical objects and not to our imagination- Our mind can definetly travel faster than light.

Hi k.v.,

I must object slightly to Jorrie's answer because c is not a length, but a velocity. The formula d=vt should still hold, so each needle would cut a length of approximately 300,000 km every second. After 1 second you would have a total length of 600,000 km.

Regards,

S

Hi S, you wrote: "The formula d=vt should still hold, so each needle would cut a length of approximately 300,000 km every second. After 1 second you would have a total length of 600,000 km."

I also have a "slight objection"! The 600,000 km would be coordinate dependent - in k.v.'s case, only true in the film frame, not in the needle frames.

J

"in k.v.'s case, only true in the film frame, not in the needle frames."

That was the frame of reference in k.v.'s post 31. If he took a tape measure and measured the length, it would be 600,000 km.

The example I recall is muons created in the upper atmosphere. They would normally only live about 2 microseconds, but travelling at close to light speed, from our perspective, their time is slowed down, so they reach the earth's surface. From their perspective, they live 2 microseconds but the earth's atmosphere is Lorenz contracted.

Agreed - great example. Unfortunately, some people who happily accept the effect of time contraction get spooked by the "observer/see" verbiage that surrounds size issues...