# Modification of the cumulative concept of time

The past is part of the present, in the sense that part of the present is the same as the past, or is based on something of the past. For example, “I was 10 years old in the past” is the necessary condition for “I am 20 years old in the present”.

However, not all of the past is still part of the present, because some of the past is already lost. In other words, some of the past is not stored in the present.

.

You need physical macroscopic law (induction) in order to get the cumulative property of time.

Microscopically, due to the unitarity of the Schrödinger equation, any past quantum state has a one-one correspondence to a quantum state at any particular future moment. So any future quantum state already has all the information needed to deduce its past state. In this sense, there is no time microscopically.

Time is not cumulative microscopically, because the past is not part of the future.

We can also say that time is 100% cumulative microscopically, because the past is all of the future; instead of being part of any future quantum state, the past quantum state already has all the (equivalent) information of a quantum state at any particular future moment.

— Me@2013-08-10 07:45 PM

— Me@2021-04-21 04:24 PM

.

.

# Time travel, 3.2

.

If you keep deleting your blog posts one by one, your blog effectively keeps becoming its past. However, its environment is still cumulative. In other words, the environment is not becoming its past.

If the environment and the blog interchange labels, the blog’s environment is going to the past, while the blog is not.

— Me@2013-08-10 07:41 PM

— Me@2021-04-12 06:02 PM

.

.

# Conscious time, 2

If no one has any kind of date, records, memories, or evidence about the past, retro-diction MAY be the same as prediction. But in such a case, it is by definition not our “past” any more.

— Me@2013-08-08 3:11 PM

.

If no one has any kind of date, records, memories, or evidence about the past, then consciousness ceases to exist.

We, as conscious beings, cannot exist anymore.

— Me@2021-03-30 4:08 PM

.

.

# Event Realism 6.2

.

Lee’s event realism ~ past realism

should be transcended by now-realism, in which the past is part of the present.

— Me@2013-07-20 03:38 PM

— Me@2021-03-19 11:02 PM

.

.

# Logical arrow of time, 6.4.2

Logical arrow of time, 6.1.2

.

The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference between prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

.

— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really making a prediction.

— guess —

.

— Me@2013-10-25 3:33 AM

.

A difference between deduction and observation is that in observation, the probability is updated in real time.

.

each update time interval ~ infinitesimal

.

In other words, when you observe a system, you get new information about that system in real time.

Since you gain new knowledge of the system in real time, the probability assigned to that system is also updated in real time.

— Me@2020-10-13 11:27:59 AM

.

.

# Memory as past microstate information encoded in present devices

Logical arrow of time, 4.2

.

Memory is of the past.

The main point of memories or records is that without them, most of the past microstate information would be lost for a macroscopic observer forever.

For example, if a mixture has already reached an equilibrium state, we cannot deduce which previous microstate it is from, unless we have the memory of it.

This work is free and may be used by anyone for any purpose. Wikimedia Foundation has received an e-mail confirming that the copyright holder has approved publication under the terms mentioned on this page.

.

memory/record

~ some of the past microstate and macrostate information encoded in present macroscopic devices, such as paper, electronic devices, etc.

.

How come macroscopic time is cumulative?

.

Quantum states are unitary.

A quantum state in the present is evolved from one and only one quantum state at any particular time point in the past.

Also, that quantum state in the present will evolve to one and only one quantum state at any particular time point in the future.

.

Let

$\displaystyle{t_1}$ = a past time point

$\displaystyle{t_2}$ = now

$\displaystyle{t_3}$ = a future time point

Also, let state $\displaystyle{S_1}$ at time $\displaystyle{t_1}$ evolve to state $\displaystyle{S_2}$ at time $\displaystyle{t_2}$. And then state $\displaystyle{S_2}$ evolves to state $\displaystyle{S_3}$ at time $\displaystyle{t_3}$.

.

State $\displaystyle{S_2}$ has one-one correspondence to its past state $\displaystyle{S_1}$. So for the state $\displaystyle{S_2}$, it does not need memory to store any information of state $\displaystyle{S_1}$.

Instead, just by knowing that $\displaystyle{t_2}$ microstate is $\displaystyle{S_2}$, we already can deduce that it is evolved from state $\displaystyle{S_1}$ at time $\displaystyle{t_1}$.

In other words, microstate does not require memory.

— Me@2020-10-28 10:26 AM

.

.

# Logical arrow of time, 6.4

The source of the macroscopic time asymmetry, aka the second law of thermodynamics, is the difference of prediction and retrodiction.

In a prediction, the deduction direction is the same as the physical/observer time direction.

In a retrodiction, the deduction direction is opposite to the physical/observer time direction.

.

— guess —

If a retrodiction is done by a time-opposite observer, he will see the entropy increasing. For him, he is really doing a prediction.

— guess —

.

— Me@2013-10-25 3:33 AM

.

The existence of the so-called “the paradox of the arrow of time” is fundamentally due to the fact that some people insist that physics is about an observer-independent objective truth of reality.

However, it is not the case. Physics is not about “objective” reality.  Instead, physics is always about what an observer would observe.

— Lubos Motl

— paraphrased

— Me@2019-01-19 10:25:15 PM

.

.

# How far away is tomorrow?

.

The cumulative part of spacetime is time.

It is the cumulative nature of time [for an macroscopic scale] that makes the time a minus in the spacetime interval formula?

$\displaystyle{\Delta s^{2} = - (c \Delta t)^{2} + (\Delta x)^{2} + (\Delta y)^{2} + (\Delta z)^{2}}$

— Me@2011.09.21

.

Space cannot be cumulative, for two things at two different places at the same time cannot be labelled as “the same thing”.

— Me@2013-06-12 11:41 am

.

There is probably no directly relationship between the minus sign and the cumulative nature of time.

Instead, the minus sign is related to fact that the larger the time distance between two events, the causally-closer they are.

— Me@2018-10-13 12:46 am

.

— Distance and Special Relativity: How far away is tomorrow?

— minutephysics

.

.

# Tree rings, 2

Time-traveling to the past is like “making an outside ring more inside”, which is logically impossible.

— Me@2011.09.18

Me@2010

.

.

# Euler Formula

Exponential, 2

$a^x$

general exponential increase ~ the effects are cumulative

$e^x$

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM

exponent growth

$e^x = \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n$

~ compound interest effects with infinitesimal time intervals

multiply -1

~ rotate to the opposite direction

(rotate the position vector of a number on the real number line to the opposite direction)

~ rotate 180 degrees

multiply i

~ rotate to the perpendicular direction

~ rotate 90 degrees

For example, the complex number (3, 0) times i equals (0, 3):

$3 \times i = 3 i$
$(3, 0) (0, 1) = (0, 3)$

multiplying i

~ change the direction to the one perpendicular to the current moving direction

(current moving direction ~ the direction of a number’s position vector)

exponential growth with an imaginary amount

$e^{i \theta} = \lim_{n \to \infty} \left( 1 + \frac{i \theta}{n} \right)^n$

~ change the direction to the one perpendicular to the current moving direction continuously

~ rotate $\theta$ radians

— Me@2016-06-05 04:04:13 PM

# Exponential

a^x

general exponential increase ~ the effects are cumulative

e^x

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM

# 回到過去 3

Cumulative concept of time 20

（Me：那樣，如果我只是「回到過去」，但不「經歷過去」，我豈不是不會「失去青春」？）

— Me@2014-04-24 01:56:35 AM

# The fifth floor

The fifth floor cannot exist without the first 4 floors.

— Me@2012.10.24

That’s why time travel is logically impossible.

— Me@2014.04.17

If you remove the first 4 floors, the original fifth floor is not the “fifth” floor anymore. Instead, it would become the first floor.

— Me@2014.04.16

# Block spacetime, 8

Cumulative concept of time 18 | 原因 7

In block spacetime, whether time is cumulative or not is not an important label.

— Me@2012.10.19

# The Beginning of Time, 3.2

Cumulative concept of time 1.3.2

The past is part of the future.

The first cause is the smallest part.

cause ~ component

The first cause is not a boundary, because there is no “before”.

The first cause is a physical limit, not a physical boundary.

The first cause is a logical boundary, not a physical one.

— Me@2012.10.17

— Me@2014.02.03

# Consciousness 4

Event Realism 3.2 | 事件實在論 3.2 | Cumulative concept of time, 17.2

being conscious

~ having one’s own past information

~ having memory

~ having self-interaction

~ entanglement between past states and the present state

~ some of the past states keep existing through memories and records

~ past-self-and-present-self entanglement

— Me@2013-11-01 7:02 AM

# Information 2

Event Realism 3 | 事件實在論 3 | Cumulative concept of time, 17 | Recursion 8.3 | I am a Strange Loop, 3.3

memory ~ information of the past

Part of the past still exists, in the sense that some states and events of the past are entangled with those of the present.

— Me@2013-10-09 6:50 PM

# Bank account

For a bank account, the past balances are irrelevant and useless.

What is really relevant is the present balance.

And it has encrypted all the past money that can still be used now.

— Me@2011.04.25

— Me@2013.09.03

# The Beginning of Time, 3

Cumulative concept of time 1.3

The past is part of the future.

the earliest time

= the most remote past

= the smallest possible time circle

= a point where radius equals zero (r = 0)

= the centre of the time circle

The time t is like the radius r. It makes no sense to ask, “What happened before the beginning of the universe?”

Just as it is not meaningful to ask, “What if r < 0 ?"

— Me@2013-08-04