My problem with relativity theory. Please help!?

Question

In another answer, Mistress Bekki has provided an answer to another person's question about the equivalence of gravity to acceleration, which contains this (I quote):

"""So, instead of considering gravity, lets imagine that you and your friend are in a rocket accelerating through space with acceleration g. You are in the front end and your friend is in the back end. You feel gravity just like on earth. You are at the top; she is at the bottom. You are sending light signals to your friend at regular intervals. During the time it takes for your signals to get to your friend, your friend continues to accelerate towards you. Consequently, your friend gets your signals at a faster rate than you send them. Conversely, if your friend at the back sends you signals, you accelerate away from her, so you get the signals at a slower rate.

So the bottom line is that she thinks your clock is running fast because your signals get to her quicker. You think that her clock is running slow for the opposite reason. And it turns out to work exactly the same in a building instead of a rocket ship. Because being in gravity is exactly the same as being in an accelerating rocket ship. The clocks on the top floor run faster than the clocks on the bottom.

If you do work out the math, you'll find that the time is dilated by a fraction (g h / c^2). For earth's gravity (g) and a building of realistic height (h), that fraction is very tiny because the speed of light (c) is relatively large. But the effect has been measured on larger scales."""

My question is this.

I understand that RELATIVELY TO EACH OTHER, me and my friend on the accelerating rocket ship PERCEIVE each other's clocks to be going either faster or slower, due to acceleration's affect on the speed of the signals. But this is ALL APPEARANCES, and in ABSOLUTE terms, my clock doesn't run any faster/slower than my friend's. It's impossible. Appearances/perceived speed with which the clocks tick DOESN'T equal to their ACTUAL ticking rate.

This is the concept that I cannot comprehend with the relativity theory. It's that appearances must = reality. No, it doesn't.

Because, if the rocket ship on which me and my friend are stops accelerating or just comes to a complete stop, then we will check each other's clocks and see that the slowness/fastness which we PERCEIVED each other's clocks to be moving with, when we were accelerating, was JUST AN APPEARANCE.

AM I WRONG? PLEASE TELL ME. I'm 21, and have read everything I can about the relativity theory, and even though I didn't dabble in the math of it, the theoretical examples given about aging, slower passage of time, etc, don't make sense to me.

A clock, no matter where it is or how fast it is traveling or accelerating, STILL TICKS at its own rate, NO MATTER HOW IT MAY APPEAR TO OUTSIDE OBSERVERS at rest.

So even though it MAY APPEAR to be ticking SLOWER WHEN it is ACCELERATING away from an observer (according to the observer's clock), when it comes back to the observer and stops, the time on the at-rest observer's clock and the traveling clock will be the same.

Am I right? Please explain.

The ONLY way I see acceleration having an affect on the ticking rate of a clock is PURELY due to mechanical/physical forces, such as air pushing on the clock's hands and slowing them down, etc.

QUESTION # 2:
If the gravity = constant acceleration, then given enough space, theoretically, can an object accelerate to the speed of light?

Thank you!

Answer 1

There's no such thing as "ABSOLUTE TERMS." There is only what is observed.



In any case, you are incorrect. When the accelerated clocks are brought back together, the upper clock does indeed show more elapsed time than the lower clock. The upper observer indeed is older than the lower observer when they meet up. It is more than just appearances. This experiment has been done repeatedly. Every time you turn on a GPS receiver, this experiment is done.



No, a body cannot, theoretically, accelerate to c because the universe exhibits Lorentz symmetry. The same amount of proper acceleration (measured by an accelerometer) yields less change in speed as c is approached.

Answer 2

"I understand that RELATIVELY TO EACH OTHER, me and my friend on the accelerating rocket ship PERCEIVE each other's clocks to be going either faster or slower, due to acceleration's affect on the speed of the signals. But this is ALL APPEARANCES, and in ABSOLUTE terms, my clock doesn't run any faster/slower than my friend's. It's impossible. Appearances/perceived speed with which the clocks tick DOESN'T equal to their ACTUAL ticking rate."



Your mind is closed. You have this "impossible" barrier to your learning further.



Is it not POSSIBLE that two people can take different paths through space, between the same start and end points, and end up with different distances traveled and different elapsed times? Or is it impossible that that could be the case?



We don't have access to Reality except via measurement. We don't have access to Absolute except via agreed on standards. Our only common sense is via the "laws of physics". It is the nature of the world around you. Is it not POSSIBLE that if you don't take the journey that mathematics makes possible, that you will always say blind to it?



If you never go faster than 1000 miles an hour, stay on the surface of this planet, and never measure time more precisely than you can with a stopwatch, you never need this stuff.



And you know the answer to your question #2, is NO. And since you cripple yourself both by your provincial attitude towards learning something new, and by not even attempting the relatively simple math, any attempt to explain it to you will be a waste of words.



http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

... 12 years at 1g acceleration, and still not reaching c. And of course, we have no idea how to accelerate that much for more than a few minutes.

Answer 3

Your remarks are very thoughtful. I remember, during my lower-division physics days, having very similar objections (and frankly, skeptical students who raise objections end up finally with the deepest understanding of the subject matter, so I encourage you to keep it up!)



First of all, I will state (without proof!) that the effect of time passing at different rates for different observers, is NOT simply a matter of perception. Our current understanding of space and time is that the two are connected and structured in a particular way that is governed by the universal constant "c"; and one of of the consequences of that structure is that the amount of elapsed time between two particular events "A" and "B", does NOT have a unique, absolute value, but varies according to the reference frame of the observer. The idea that a physical quantity's value may vary in different reference frames is not a new idea; for example, it's obvious that an object's velocity (and hence its momentum and kinetic energy) depend on the relative velocity of who's doing the measuring. Einstein's relativity adds "elapsed time" to the list of quantities that must be considered relative. Thus relativity states flatly that time REALLY DOES flow at variable rates according to who's doing the timing, and it's not just a matter of appearance, nor of some mechanical difference between the clocks.



This is ultimately a consequence of the constancy of "c". It's observed that all measurements of light in a vacuum show it to be traveling at the same speed "c" regardless of how fast, or in which direction, the observer is traveling relative to the light source. Thus all OTHER speeds are relative, but "c" is not. One way to explain this is to assume that time flows at variable rates for the different observers; but this is kind of a shocking conclusion, and frankly, early researchers DID try to explain the experimental results in other ways, by postulating that the measuring instruments themselves were somehow mechanically altered by their motion through the "luminiferous ether". But that line of reasoning turned out to be a dead end; its proponents had to jump through ever more hoops to make the all numbers come out right; and in the end everybody agreed that Einstein's explanation -- that time flow actually varied -- was the simplest explanation that fit all the experimental facts.



ALL the experiments since then have come down on the side of Einstein. In Einstein's day the clock's weren't accurate enough to actually compare the effects of time dilation, but today they are, and indeed they DO run at different rates in exactly the predicted amounts. They know this by comparing the two clocks to each other after the experiment's over, and they find that their readings are different. This has been verified both for time dilation due to speed, and time dilation due to gravity fields.



GPS satellites provide an excellent ongoing verification. Relativity predicts that the satellites' clocks should be subject to both gravitational time dilation (because they're higher up than we are) and to velocity-based time dilation (because they're moving fast in their orbits). Since the working of GPS system depends critically on extremely precise timing, engineers find that they need to tune the clock's rate in the satellite in order to compensate for the effects of time dilation. If they do NOT make this adjustment, the clocks run at the "wrong" speed, resulting in GPS position calculations that are off by many miles.