Science a GoGo's Home Page Forums General Discussion Physics Forum Relativity, Time Dilation and Space/Time

For the sake of thoroughness, I would like to preface the “meat and potatoes” of this concept with other concepts.

The first is reduction or consolidation:

There is a nightmare of a formula called the Quadratic Equation. Basically this formula sets up the inter-relationship between the 3 sides and 3 angles of any triangle. When one of the angles is “known” to be 90 degrees or there is a side length that will result in a 90 degree angle, the Quadratic Equation can be reduced (or consolidated) to the Pythagorean Theorem. It’s amazing that one filled-in variable can reduce that monstrosity to a one-liner and it sure is convenient.

It behooves math, science and man to consolidate whenever possible. We reduce things down to their basic elements, rules and equations. Of course there is nothing that prohibits anyone from using the quadratic equation to solve right triangles either but it seems insane to do so.

The next concept is over-reduction:

Let’s run a quick mind experiment.

You and I just returned from a heist and being mindful of reduction I declare that my take was 1/2 of the total loot. You say; to hell with that, I got 2 out of 4 dollars!

Your (non-reduced) definition contains more information regarding the actual nature of the heist which was a complete and utter failure. My definition is justified but highly misleading. This time, consolidation of the math has gone too far and good information has been lost. Such are the dangers of over-reduction…over-simplification. Just because something is reducible doesn’t mean that it will remain intact.

Space/ Time and Relativity:

If we look at all of the Lorentz Transformation formulas for length contraction, time factor (dilation) and mass increase it is readily apparent that all of these formulas inter-relate. Specifically, at any given speed, length contraction and time factor are reciprocal values. Lets me throw out some examples:

Object is traveling at 0.0c, new length is 1.00, time factor is 1.000
Object is traveling at .25c, new length is .968, time factor is 1.032
Object is traveling at .50c, new length is .866, time factor is 1.154
Object is traveling at .75c, new length is .661, time factor is 1.512
Object is traveling at 1.0c, new length is 0.00, time factor is infinity

Another way of looking at this is that; new length and new time is exactly equal. For instance; if you are traveling at .5c, your length is 86% of what it was at rest, and time is passing 86% slower for you then when you were at rest.

If we take the dimensional (space) contraction and lump it together with time dilation; rather than do the calculation twice we can simply do it once. Likewise, we can treat space and time as the same thing…hence space/time…an underlying fabric. This is the very essence of the immutable connection between space and time…this is the justification…same formula – same thing.

I am proposing that the connection between space and time does not occur at this point in reality. There is the possibility that an over-reduction has occurred. Just because they both “enjoy” the same formula does not make them the same thing.

Ok. If the fabric of space/time is not how they are connected then where is the connection? How can we possibly retain the obvious immutable (fixed) relationship between the two of them without space/time?

Here goes:

Hollywood movies love to manipulate and exercise time dilation. There aren’t any movies set against a background of length contraction. Time dilation gets all the glory. Time travel…grandfather paradoxes are cool and interesting….flat as a pancake, well that just doesn’t make it into the script.

Time dilation gets all of the glory while length contraction does all of the work.

I propose that the characteristic of length contraction results in time dilation and that this is where the connection between time and space should be made. Why would it be surprising that they share a common formula?

Perhaps there is something about the dynamics of length contraction that brings about a corresponding “proportion” of time dynamics.

BTW, the reciprocating relationship between length contraction and time factor isn’t the only interesting aspect of LT:

Object is traveling at .500c, new length is .866
Object is traveling at .866c, new length is .500
Object is traveling at .707c, new length is .707

In the future, I would like to discuss this tidbit also.

Would it not be that if this relationship didn't work the Time/distance calculations would not add up for someone travelling at (for example) 0.5c; so she would know she was in motion.

I should have started by complimenting you on starting a thought provoking thread. It requires some pondering, but should spark some fascinating discussion.

I’m not sure that I follow. They say that from her (the traveler’s) viewpoint, that her boobies are just fine (not flatter) and that she is unaware that time is passing slower. Even at .5c, without additional acceleration she is unaware that she is in motion…she feels like she’s floating in space. However, just like us; if she conducts some external measurements she’ll be able to verify her current speed.

That's odd. I posted a reply last night, but it doesn't show up here now. I will try again



That isn't quite right. A Quadratic Equation is any equation of the form aX^2 + bX + c = 0. This can be solved algebraically to give the Quadratic Formula. Using the Quadratic Formula you can determine the roots of the equation, that is the values of X for which the equation is true. It may be possible that it simplifies to the Pythagorean Theorem for a right triangle, I don't know.

As far as the relativity formulas being similar, that is perfectly natural. They are derived from the observation that C is that fastest that anything can travel in the universe. They match because they are different solutions to the same formula.

For your last point:


Did you happen to notice that those values match a sine (or cosine, which ever way you start) function?

Create a spacetime graph with space on the X axis and time on the Y axis. Now in your frame of reference an object on the graph will be spacelike, that is it will have a projection on the space axis that is the same length as the object. On the time axis it will have a zero projection. Assume somebody in another frame of reference moving with respect to yours. In effect their frame of reference will be rotated from yours. If you place the graph of their reference frame on yours with the origins coinciding their graph space and time axes will be rotated from yours. In their view your object will project a smaller distance on their space axis and a larger distance on their time axis. Therefore you will appear to be partly spacelike and partly timelike. And this change will be related to the tilt of their graph from yours, and this tilt of course is related to the speed at which they are traveling.

I hope that is clear, but I can fully expect it to look like a lot of gobbledegook when you read it.


Bill Gill

“That isn't quite right. A Quadratic Equation is any equation of the form aX^2 + bX + c = 0. This can be solved algebraically to give the Quadratic Formula. Using the Quadratic Formula you can determine the roots of the equation, that is the values of X for which the equation is true. It may be possible that it simplifies to the Pythagorean Theorem for a right triangle, I don't know.”

I agree. The quadratic is a subset of the polynomial. The Pythagorean Theorem is a subset of the quadratic. However, in practice, the quadratic is a rearrangement of the terms of the polynomial that places the x variable on the left-side while the Pythagorean is a reduction of the formula when one of the terms are given. My goal was to demonstrate simplification not rearrangement.

“Did you happen to notice that those values match a sine (or cosine, which ever way you start) function?”

Why yes, I did. As a matter of fact, I found the last set to be most interesting and that’s the one that I honed in on. Right away I recognized this value as the sine/cosine of 45 degrees. The sine of 45 degrees is equal the square root of 2 divided by 2. As a retired electronics guy, I knew that you would probably be the first to latch onto this. At first it’s helpful in understanding AC power…, then RMS, then integration, then sampling. It runs the full gamut from analog to digital.

In a linear universe, .5 is halfway between 0 and 1. In an exponential universe the mid-point between 0 and 1 is .7071 (BTW, this isn’t for your benefit…this is for the benefit of anyone who may be reading that isn’t quite clear on the concept.)

So, what am I really getting at?

Let’s pretend that speed is money. (Actually this isn’t too far from the truth.) Next, let’s pretend that there is a benefit derived from saving time…time is money.

So we’re going to arbitrate speed vs. time in the relativistic universe or speed in c vs. time dilation/ length contraction.

Not surprisingly, the biggest bang for the buck is the mid-way point - .7071c. (I wish that all cost/ benefit analysis were this simple.)

Man may dream of traveling near the speed of light (aka the Concord) but people will be traveling at .707c (aka the 747).

“As far as the relativity formulas being similar, that is perfectly natural. They are derived from the observation that C is that fastest that anything can travel in the universe. They match because they are different solutions to the same formula.”

Agreed. As a matter of fact, there’s nothing magical about the math and there’s nothing magical about relativity (although that could be a hard sell to some). In my OP my goal is to leave relativity alone and intact, as-is. It is space/time that I want to alter. This is a blasphemous thing to try to do and to me, relativity is the litmus test for any alternate ideas.

My goal isn’t to actually replace space/time as an idea…but rather to add alternative ideas to the viability mix. To me, the space/time fabric is a theory that’s being treated like a fact. I would like to loosen that up a bit.

The problem with trying to get loose from the spacetime business is that it works. Einstein incorporated it into his General Theory of Relativity, because with it he could make GR work. Since GR has been extensively tested without finding any problems with it, at least at the scale at which it doesn't conflict with Quantum Theory, any changes are unlikely. If you can come up with an alternate theory that works as good maybe you can sell somebody on your idea. If that it is also simpler, or fixes the conflict with Quantum Theory.

Bill Gill

"The problem with trying to get loose from the spacetime business is that it works. Einstein incorporated it into his General Theory of Relativity, because with it he could make GR work. Since GR has been extensively tested without finding any problems with it, at least at the scale at which it doesn't conflict with Quantum Theory, any changes are unlikely. If you can come up with an alternate theory that works as good maybe you can sell somebody on your idea. If that it is also simpler, or fixes the conflict with Quantum Theory."

Bullseye. I whole-heartedly agree. Any alternate ideas should be more compatible with Quantum Mechanics and must be compatible with Relativity.

Such a theory would have to be compatible with QM and relativity in that it would have to produce the same results to a certain degree; but it could reach these results by a completely different route, so the world is your oyster, as far as imaginative thought is concerned.

Notwithstanding any lack of deleterious effects on the traveller's figure; the fact that she does not measure and slowing of time would cause her calculations to disagree with those of "mission control" if it were not for the fact that, in her F of R, the distance to destination would be appropriately contracted.

Does this run into the perennial problem that goes something like this:

SR says that nothing with mass can travel at "c".
The only thing that can travel at "c" is a photon.
Because a photon has no rest mass, it is not possible to define a F of R for a photon.
In view of these considerations, the infinite time factor that would be relevant to the F of R of a photon has no meaning?

To some extent I am playing devil's advocate here, because if this line of reasoning is right I have a lot of re-thinking to do.

I offer up the following mind experiment:

Let’s say that our traveler is departing Earth and the destination is Alpha Centauri (4.3 LY distant). Through the marvels of modern science she somehow conducts the entire trip at a speed of .75c. Her length contraction will be .66 and her time dilation factor is 1.5 (her clock will run .66 as fast as ours). We have 2 omnipotent telescopes. One is located on Earth and is exactly lined up with the traveler and Alpha Centauri (viewing her from behind). The other telescope is at a stationary midpoint and lined up 90 degrees from the other one (viewing her from the side). Of course, she will only be lined up for a brief instant from the side view. When I take my snapshot (brief video) from the side view; it verifies that she is .66 as thick but more importantly, all of her motions look slower. You can tell that she seems to be slothy and purposeful.

Now the telescope back on Earth sees something different. From their perspective, she is dimensionally just as wide as when she was on Earth but more importantly, all of her lateral motions are quite normal…there’s nothing slow about her.

Now, from the viewpoint of the Earth, traveling at .75c it takes her 5.73 years to transverse the 4.3 LY to the destination. From her viewpoint it took 3.78 years. (5.73 x .66). All of this was done without distance contraction.

Now, let’s do this with distance contraction. She departs from Earth at .75c and her new length as viewed from the side is .66 of what it was on Earth. She measures the distance that she has to travel as 2.83 LY (4.3 x .66). At .75c it takes 3.78 years to do the trip.

Either method works out to be exactly the same. In the first scenario she measures her speed to be faster than she “knows” it ought to be. In the second scenario, she measures the distance to be shorter than she “knows” it ought to be.

“Pick your poison.”

Without a doubt, a flat person would see distances in the direction of travel differently.

That is 4.3 LY in 3.78 years. Without length contraction that would be about 1.14c, wouldn't it?

Right. Without distance contraction that is the equivalent of 1.14c. But, this is unavoidable. Regardless of her observation that the distance was 2.8 LY; “people” on Alpha Centauri could verify that her clock says 3.78 years and that the true distance was 4.3 LY. It’s also true that she never exceeded .75c.

BTW, I don’t know if you noticed but the mind experiment was an unconventional treatment of inertial reference frames. Reference frames are considered 3 dimensional. By viewing reference frames as 2 dimensional we are able to view the same event (3D reference frame) simultaneously and remain “compatible” with relativity. Well, not quite. The difference is the rear view. The 2D reference frame allowed her lateral movements to be normal while a 3D reference frame forces her movements to be slow even though there is no visible length contraction in that direction. It does seem to work well though…that is until you replace the traveler with a pendulum swinging at a 45 degree angle. Still, I think that it’s a good mind experiment. (It’s interesting to see how time “works” in this scenario).

"SR says that nothing with mass can travel at "c".
The only thing that can travel at "c" is a photon.
Because a photon has no rest mass, it is not possible to define a F of R for a photon.
In view of these considerations, the infinite time factor that would be relevant to the F of R of a photon has no meaning?"

There are some who say that; at rest the photon has a duration that is infinitely small (1 Planck time limit?). At c its duration is infinitely long (1 universe time limit?)

I don't know. I haven't spent much time on EMW. I sure hope that I can get around to it (1 life time limit?)

Am I reading this incorrectly, or does it equate infinitely small with Planck time, and infinitely long with the life span of a universe?

That would have to be a new take on infinity.

"Am I reading this incorrectly, or does it equate infinitely small with Planck time, and infinitely long with the life span of a universe?"

In a way...except instead of equate it would be more like qualify/quantify.

I'll have to return to this because duty calls but I do want to give this a thorough treatment because I think that it relates to the incompatibility between mathematical and physical infinities that you've mentioned quite a bit.

Correct me if I'm wrong, but the planck time is the time taken for a photon to travel the planck length*. So planck units are excedingly small, but not infinitely small - merely the smallest units that could (theoretically) ever be measured. Moreover, am I not right in thinking that a theory of quantum gravity would require that certain processes occur in intervals less than the Planck time? This just springs to mind, and I haven't done my homework, so forgive if I'm off track.

*1.616252(81)×10−35 meters.

Rede,
You have a good point. The Planck units are indeed very small, but confusing them with being infinitely small can lead to some significant confusion. They are not infinitely small because they do have numeric values. I am afraid that this discussion may be based on a poor understanding of what infinity means. I'm not going to try to define infinity. It requires a much deeper study, and discussion with other people who have also made a deep study, than I have ever made or intend to make. Just letting ones mind run loose without investigating the literature on the subject doesn't help anybody to understand it very well. And of course understanding the literature probably means going back to the beginning math of infinity. Physical infinities may be different from mathematical infinities, but an understanding of physical infinities will require and understanding of mathematical infinities.

Bill Gill

Bill,
I think I agree completely with your last post. However, I have to question your plurality of physical infinities. I think there can only be one.
Nit-pickers of the world, unite!