Several forums dealing with Einstein's special theory of relativity have been openned by RG researchers. Most, if not all, are critical of the theory and its consequences. Among the consequences are time dilation and length contraction that nominally occur as velocities approach that of light. Are these consequences really real? We invite discussion:
For the moment let us suppose that Einstein’s special theory of relativity (STR) is an accurate representation of Nature within the theory’s inherent domain of applicability. STR fundamentally is a theory of space, time and the velocity of light c. When we speak of time and space in STR, we find them linked together by c in a four-dimensional manifold labeled “spacetime.” When we speak of clocks and meter sticks in the context of STR, we find ourselves confronted with the issues of time dilation and length contraction. These foundational aspects of STR have stirred considerable debate as well as spawning various interpretations and misunderstandings. We here revisit relativistic time dilation and length contraction with the ambitious hope of showing in a simple, straightforward way how these hallmark consequences of STR arise.
Two photons traveling towards each other should have relative velocity of twice the speed of light but still we find that light only travels at the speed of light with respect to other photon. General Relativity theorists have a hard time answering questions like this because it is difficult for them to accept that the concept of time used in Einstein’s theory is not perfect. But it is much better than Newton’s absolute time.
According to Einstein, space and time are not independent of each other but make up a continuum. This is mathematically presented as the sum of three dimensional Euclidean space squared and time multiplied with constant velocity of light squared with negative sign. This sum is zero in special relativity and is denoted by invariant s^2.
s^2 = x^2 + y^2 + z^2 – (ct)^2
This is a major improvement over absolute time in Newton’s theory. The major consequence is that as we look deeper into space, we are always looking backward in time.
In my opinion, this description of linear time in Einstein’s relativity theory is not perfect because the relativistic invariant does not directly relate with the physical reality and is somewhat imaginary. But the reality is based on non linear periods and wavelengths of fundamental particles of physics. In a theory called periodic relativity, the corresponding invariant is written as,
s^2 = L^2 – (VT)^2
where L is the wavelength of the particle wave and V is the velocity of the phase of the wave and T is the period of the wave.
Photons traveling in opposite directions see each other having twice the frequency of what an observer at rest will see. With the change in the frequency, the wavelength and period of the wave will also change. In case of light, the velocity of the phase of the wave is equal to the velocity of the particle (photon). This velocity is given by the ratio of the wavelength to its period. In case of light, this ratio is always constant and equal to the velocity of light, no matter how much frequency shift occur. Period is inversely proportional to frequency. Therefore frequency shift due to the motion of two photons travelling in opposite direction does not alter the ratio of the wavelength to its period. It is always constant. This is what I call space time dialation. General relativity theorists only talk about time dilation and comfortably ignore the space dilation (what they call length contraction). They measure length contraction on some measuring rod or such object and at that time do not talk about time dilation. In rest of the general relativity theory you must talk about space time continuum as a whole, but time dilation and length contraction are exceptions. Why?
This is a proof that time is periodic in nature. More details in following article.
https://www.researchgate.net/publication/225712819_Periodic_relativity_basic_framework_of_the_theory?ev=prf_pub
https://arxiv.org/abs/0707.4539
The effects are best understood by drawing a Minkowski Diagram of whatever scenario is under consideration. Nature doesn't include coordinates stamped onto objects for our convenience so we overlay events with a grid like that used by archaeologists and divers (see the illustration). If that grid is rotated in space, the X and Y distances between objects changes even though the objects have not moved. Length contraction and time dilation are the same in principle but applied in the X-T plane rather than X-Y. The physical nature of time and space means that the 4-dimensional equivalent of Pythagoras Theorem includes a negative sign for time if the spatial components are positive which has a significant impact in many cases. On a Minkowski Diagram, you can show the unique events but also overlay them with more than one coordinate system.
The key thing to understand is that they don't represent anything happening to the objects, only the coordinate system is being changed.
For more information, Google "Parable of the Surveyors".
Dear George,
I do believe that we are in full agreement and I apologize for not being aware of your work. What I am trying to present is an easily digestable approach to what, for some, seems to be the problematic issues of time dilation and length contraction in relativity. I was spurred on by a comment in which the commentor fretted over physically shrinking distances in and between atoms under length contraction. I intentionally did not introduce Minkowski space or Lorentz transformations by name as neither appear in Einstein's original 1905 paper.
Dear Vikram,
I think it to be an error to think of two photons "seeing each other". They do not have twice the frequency because to increase the frequency would require the addition of energy to the photon from an external source. The moving photon has energy E = hν, where h is Planck's constant and ν is the frequency of the wave packet that represents the photon. Each photon is characterized by its energy and frequency. Each photon travels with the velocity of light and they pass each other at the velocity of light. Their relative velocity is effectively zero.
It is counterproductive to think anthropormorphically at velocities approaching that of light.
Dear Dwight:
Unfortunately I disagree on almost everything you said.
Regards,
Vikram
Dear Christian,
I concur that to speak of the "really real" in general is rather meaningless. But you in your own personal reference frame are to you "really real", are you not? Therefore all that you perceive in a conscious, unimpaired state is "real" to you, that is, is something on which you can act and something that can act on you. This is your reality. By joining others and sharing their realities you mutually agree on a general "universal" reality. As a scientist it is this universal reality that you accept and explore and share with others. So "reality" becomes a consensus between you and your colleagues. There is no "absolute reality"; there is only that "reality" that is relative to you and your assessments of what is or is not real based on your observations and experiences. There is a "reality" but its essence is in the eye of the beholder and his or her concurrence with the experiences and observations of others.Thus, we might speak of the "relativity of reality".
Dear Vikram,
You disagree with all that I have said and, of course, that is completely your right. I would, however, like to know why you disgree. If I have comitted a gross error I should like to correct it. Thank you for your response!
Sincerely,
Dwight
Dear Dwight:
I want to bring to your attention the following question asked on Quora and response by Prof. Viktor T. Toth. You will realize that your comments are in direct conflict with Prof. Toth’s comments.
When a light bulb is turned on, it emits photons at the speed of light in all directions. This means that photons traveling in opposite directions are going twice the speed of light relative to each other. How is this possible?
Viktor T. Toth, IT pro, part-time physicist
You are misapplying a simple rule.
The simple rule (derived from the invariance of the speed of light under inertial transformations) is that nothing travels faster than light in your frame of reference.
It does not say that the difference between two velocity vectors in your frame of reference cannot be greater than the speed of light. In fact, it can be as much as twice the speed of light.
Now photons do not have a reference frame, so it is pointless to ask what things happen from the perspective of a photon, but let me give you another example, with two rockets traveling in opposite directions at 99% of the speed of light. From your perspective, the difference between their velocities will be almost twice the speed of light. However, from either rocket, the other rocket will appear to move at only 99.995% of the speed of light, not faster. So no object is moving faster than the speed of light in any object’s reference frame, even though the difference between two velocities can easily exceed the speed of light.
Dear Dwight,
DH: I do believe that we are in full agreement and I apologize for not being aware of your work.
Don't worry, I'm just an amateur so I wouldn't expect you to have heard of me.
DH: What I am trying to present is an easily digestable approach to what, for some, seems to be the problematic issues of time dilation and length contraction in relativity. I was spurred on by a comment in which the commentor fretted over physically shrinking distances in and between atoms under length contraction.
Yes, I've seen that with hundreds of newbies getting the wrong end of the stick for many years because of that problem. Once they start thinking that way, it's hard to get them to step back and look at it from a different angle.
DH: I intentionally did not introduce Minkowski space or Lorentz transformations by name as neither appear in Einstein's original 1905 paper.
That I feel though is the root of the problem. Einstein's paper pre-empted Minowski's but derived the Lorentz transforms from Maxwell's equations in a somewhat empirical manner. Minkowski's approach shows how the effects arise from the geometry without needing any "physical" effects, hence a clock ticks at a rate that is unaffected by motion in the sense that it always generates the same number of ticks per unit of proper time. Time dilation comes from the geometric projection of those uniformly spaced ticks onto an arbitrarily defined coordinate time axis. Similarly length contraction isn't the sort of shrinkage you get by cooling a steel rod, rather it is like seeing the length of the shadow it casts on a wall change as it is rotated from parallel to normal to the wall.
If you want to relate back to the original papers, my experience is that you need to use Minkowski's 1908 paper which was the real start of the geometric understanding that ultimately forms the basis of GR, using Einstein's 1905 paper can only demonstrate that the observational evidence supported the fact of the effects, not an explanation.
YMMV of course but that's what I've learned over ~20 years of helping amateurs change their way of thinking about SR.
Time dilation refers to the slowing of time for objects (or living beings) moving at very fast velocities relative to those moving a slower velocities, according to the equation change in time = 1/((1-v^2/c^2)^-2). What happens is that the closer the velocity gets to c (the speed of light) the larger the change or ratio becomes. According to this equation, if the the speed of light was very nearly achieved, the ratio would become close to infinite and time would nearly stand still, relative to objects at rest. The shortening of objects working in an identical manner.
I am a graduate student in English literature, not a physical science, mathematics or engineering student, and I hope I have not mangled to math. An interesting, even important, sidelight to this issue is its use in science fiction literature. With regard to travel at relativistic speeds, there is no room to play around with the concept. With other postualted modes of travel, such as travel through hyperspace, wormholes, stargates, teleportation, interdimensional portals or in the case of time travel the basic relativistic concept of time dilation can be manipulated in various ways according to literary convention, the whims and needs to the author and what may be known about the actual or postulated physics of these phenomena. Some are thought to be actual possibilities, others pure fiction, but in every case the literary treatment of them is influenced by the theories of Special and also General relativity.
Dear Vikram,
I believe, on the contrary, that Prof.Toth and I are in complete agreement. My original answer, I agree, was not well-written and failed to clearly state my case. To speak of two photons approaching each other requires an observer outside the "reference frames" of the two photons. Neither photon can "see" the other until they pass each other when each photon will "see" the other passing by at the velocity of light c. The external observer also will see each photon passing by the other with velocities +c and -c. Naively (or flippantly, if you will) at the instant of passing each other we have of the velocities of the two photons +c -c = 0.
Let us consider two cars moving in opposite directions on a freeway. Each car can see an oncoming car and judge that they are approaching each other at their combined velocities (low-velocity Galilean relativity). An external observer will watch them approach each other at their respective individual velocities and can observe that, holding one car fixed, the second car is approaching the first at the two cars' combined velocity. What happens at the moment the two cars move past each other? Each car will say of the other car "I am meeting a car that is going xx mph." There is no combined velocity because there is no moving object that has that velocity relative to any reference frame; hence, it is meaningless to speak of such a velocity. We can speak of a combined velocity of approach and a combined velocity of recession but at the moment that the cars pass each they do so at their own individual velocites which if equal but of opposite sign (direction) sum to 0. Prof. Toth above speaks of the combined velocity of recession of two photons traveling in opposte diretions.
What if the two cars collide head-on? At the instant before the collision each car is traveling at its individual velocity and at the moment of collision all hell breaks loose and the concept of two seperatly moving cars is relegated to the complex dynamics of the collision, but to speak of there being a "combined velocity of collision" as the sum of the two individual pre-collision velocities is rather meaningles except, possibly, by analogy (e.g., the cars collided with the impact of a two-ton hitting a wall at 60 mph).