Is this analogy of travel near "c" correct?

1. May 18, 2014

Logician

I have been doing a lot of regarding about relativistic physics since my earlier posts and I think I now understand the mechanism of the so called cosmic speed limit.

This is how I visualize it.

I know that the ball on a sheet analogy is not perfect but for this I think it will suffice. With that analogy the more mass the ball has the deeper the bowl is created. So as one puts more energy into acceleration the relativistic mass increases which deepens the bowl more due to the action of the gravity on the increased mass. Therefore as you try and approach "c" the well keeps deepening due to relativistic mass increase and so for every unit of energy put into acceleration the bottom of the bowl gets further away and you can never actually reach the bottom of the bowl and start up the other side. That also explains to me why time travel might be possible because with the bowl analogy as the bowl deepens the other side appears to get closer so at intensely high gravities the jump across through a wormhole becomes more possible as the apparent distance between the two sides decreases.

Is this an apt analogy for high speed travel? It also helps me understand time dilation as time is a part of the space time curvature.

Please be kind I am trying to wrap my mind around how to imagine these effects in my mind as real world ideas.

I know I do not have the full knowledge I need but I am getting it and I do appreciate the help and knowledge from the rest of you on here.

Thanks,
Logician

2. May 18, 2014

Staff Emeritus
You are mixing two completely different theories: special relativity, which is a theory of motion, and general relativity, which is a theory of gravity. This is one reason why you are confused. The second reason you are confused is that you seem to want to make your own explanations - one might even say theories - before you fully understand it. This never works. Finally, you seem to want to jump in the middle. It really is slower than to start at the beginning - it looks like you will save time, but it seldom works out that way.

3. May 18, 2014

Staff: Mentor

No. Spacetime curvature describes gravity; it is part of general relativity, not special relativity.

4. May 18, 2014

ghwellsjr

No, it's not. The Lorentz Transformation is all you need to understand how high speed travel results in Time Dilation and there is no space time curvature in Special Relativity. It's really simple. Einstein said so himself. If you are having trouble understanding Special Relativity, it's because you haven't applied the Lorentz Transformation. Just start with a spacetime diagram showing a stationary clock and the transform it to a any speed you want (short of c) and make another spacetime diagram and you'll see the Time Dilation right there before your eyes.

5. May 18, 2014

Logician

Misunderstanding

I think I am not doing a very good job of describing what I am trying to ask. I am not trying to propagate a theory but rather trying to VISUALIZE in a real world way what is happening at near "c" speeds. I think my main problem with understanding this type of thing is I am still trying to grasp what relativistic mass is in a visualization. I understand that it is either very difficult or impossible to accurately visualize what is happening at near "c" speeds for me but I want to try. I want to visualize a scenario of why there is a cosmic speed limit, or perhaps a better explanation would be that I want to try and visualize the mechanism of why this happens.

Thanks,
Logician

6. May 18, 2014

Logician

Can you put a diagram up for me please I am not quite understanding exactly what you are saying.

Thanks,
Logician

7. May 18, 2014

ghwellsjr

You can see lots of diagrams made by me. Just do a search on "diagram" with my username.

EDIT: Here's a good one I found:

Last edited: May 18, 2014
8. May 18, 2014

Logician

Ok I saw that and thank you. I think I understand the Time dilation effect now.

Here is another question the. Does relativistic mass have effects on the macro scale? What about the quantum scale. For instance does Rmass affect the orbits of electrons in their shell?

I think by asking specific individual questions I can get a grip on thi. Thank you for your help.

9. May 18, 2014

dauto

Relativistic mass isn't a very useful concept because it is just the energy under another name. Since it is just the energy, why not call it energy and be done with it? The relativistic mass concept is more trouble than it's worth. If I have it my way it would be abolished from physics books.

10. May 18, 2014

pervect

Staff Emeritus
A good way to visualize what happens at relativistic velocities is to visualize that NOTHING happens at high velocities. For instance, you right now are at a very high relativistic velocity in some frame of reference. Do you feel any different?

The important thing to know about relativity is that your velocity doesn't matter to the physics. The idea is that if you are in a sealed box, without looking outside the box to measure your velocity relative to anothr object, you can't even tell whether or not you and the box are moving at relativistic velocites or not.

I hope you've at least heard this before.

I don't think your attempt at "visulaization" is going to lead to this conclusion, and I'm rather concerned that it will lead you astray - it seems to me your current line of thining may be at odds with the above, very important, principle of relativity.

You don't need relativistic mass to understand why light speed is a limit. Thus I don't agree with your self-assesment.

Rather than go off at a tangent about the use and misuse of relativistic mass, lets stick to what you do need to understand to understand why the speed of light is "as fast as you can go". This is not relativistic dynamics, but relativistic kinematics. Kinematics is "the study of classical mechanics which describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion.".

Specifically, in this case, kinematics is the relativistic velocity addition formula.

Given that you have three object A, B, and C, and the relative velocity between A and B is v1, while the relative velocity between B and C is v2, let v_tot be the velocity between A and C, the "sum" of v1 and v2. Then:

v_tot = (v1+v2) / (1 + v1*v2/c^2)

This formula does not use, or need, any consideration of "forces" or other causes of motion, but if you have v1<c and v2<c, mathematically it tells you that the total velocity v_tot must be less than c. This might be obvious, s a short proof. Let v1 = c - e, and v2 = c - f, where e and f are positive. Thus e is a postiive number, which approaches zero as you approach the speed of light, but never goes to zero. Then we can say that

$$v_{tot} = \frac{2c - e - f}{1 + \frac{\left(c - e\right) \left(c - f\right)}{c^2}} \quad = c \frac{2 - \frac{e}{c} - \frac{f}{c}} {2 - \frac{e}{c} - \frac{f}{c} + \frac{ef}{c^2}}$$

and because the denominator is greater than the numerator, (v_tot / c) < 1.

Any attempt to explain "why" the total velocity is less than c based on forces ior other dynamic concepts s going to be misleading, because you don't even need the CONCEPT of force, or "cause of motion", to prove this fact. Thus forces cannot be a key element of the explanation of "why" given that they're not needed to demonstrate the fact, any attempt to "explain why" based on forces will be illusionary.

What you DO need to study is issues like "how the velocities add". No amount of "visualization" of forces, or other irrelevant entities such as curved space-time is going to explain this. What will work is studying the Lorentz transform. Other posters have pointed you at some resources that may aid you at this.

Once you understand the kinematic issues, related to how velocities (and other quanties) transform when you change your frame of reference, you may be ready to undertake the study of relativistic dynamics. Until you reach this point, though, you should focus on understanding the kinematic issues first.